| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (4073 entries) |
| Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (195 entries) |
| Binder Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (3260 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Variable Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (2 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (79 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (241 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (35 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (22 entries) |
| Projection Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Instance Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (66 entries) |
| Section Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (6 entries) |
| Abbreviation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (1 entry) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (130 entries) |
| Record Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (10 entries) |
Global Index
A
acc_pt_bds_seq_ub [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]all_not_ex_func [lemma, in Waterproof.Libs.Negation]
all_func [lemma, in Waterproof.Libs.Negation]
alternative_char_unique_exists [lemma, in Waterproof.Libs.Logic.Quantification]
alt_char_continuity [lemma, in Waterproof.Libs.Analysis.ContinuityDomainR]
alt_char_inf [lemma, in Waterproof.Libs.Analysis.SupAndInf]
alt_char_sup [lemma, in Waterproof.Libs.Analysis.SupAndInf]
alt_char_continuity [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Analysis [library]
and_not_impl_func [lemma, in Waterproof.Libs.Negation]
and_not_or_func [lemma, in Waterproof.Libs.Negation]
and_func [lemma, in Waterproof.Libs.Negation]
any_low_bd_le_inf [lemma, in Waterproof.Libs.Analysis.SupAndInf]
any_upp_bd_ge_sup [lemma, in Waterproof.Libs.Analysis.SupAndInf]
archimedN [lemma, in Waterproof.Libs.Reals.ArchimedN]
ArchimedN [library]
archimedN_exists [lemma, in Waterproof.Libs.Reals.ArchimedN]
Assertions [library]
Assume [library]
as_subset [definition, in Waterproof.Notations.Sets]
Automation [library]
aux1 [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
a_seq [definition, in Waterproof.Libs.Analysis.Sequences]
a0:18 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a0:35 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a0:37 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a0:50 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a0:531 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a0:538 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:1 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:1 [binder, in Waterproof.Libs.Negation]
a:1 [binder, in Waterproof.Libs.Analysis.Subsequences]
a:1 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
A:1 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:1 [binder, in Waterproof.Tactics.Either]
A:1 [binder, in Waterproof.Util.Goals]
a:1 [binder, in Waterproof.Notations.Reals]
A:1 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:1 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
a:1 [binder, in Waterproof.Libs.Analysis.Series]
A:1 [binder, in Waterproof.Libs.Reals.Intervals]
A:10 [binder, in Waterproof.Libs.Sets.Operations]
a:10 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
a:10 [binder, in Waterproof.Notations.Sets]
A:10 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:10 [binder, in Waterproof.Libs.Reals.Intervals]
A:101 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:102 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:103 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:107 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:108 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:108 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:109 [binder, in Waterproof.Libs.Analysis.Sequences]
A:11 [binder, in Waterproof.Tactics.Either]
a:11 [binder, in Waterproof.Notations.Sets]
a:11 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:111 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:112 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:114 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:115 [binder, in Waterproof.Libs.Analysis.Sequences]
a:117 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:117 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:118 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:119 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:119 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:12 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:120 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:120 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:121 [binder, in Waterproof.Libs.Analysis.Sequences]
a:124 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:129 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:129 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:13 [binder, in Waterproof.Libs.Negation]
a:13 [binder, in Waterproof.Libs.Reals]
A:130 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:14 [binder, in Waterproof.Libs.Sets.Operations]
A:14 [binder, in Waterproof.Tactics.Either]
A:14 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
a:14 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
A:140 [binder, in Waterproof.Chains.Inequalities]
a:143 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:143 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:144 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:146 [binder, in Waterproof.Chains.Inequalities]
A:15 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:15 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
a:15 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:152 [binder, in Waterproof.Chains.Inequalities]
A:155 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:156 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:158 [binder, in Waterproof.Chains.Inequalities]
A:16 [binder, in Waterproof.Chains.Inequalities]
a:16 [binder, in Waterproof.Libs.Analysis.Series]
a:16 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
a:163 [binder, in Waterproof.Libs.Analysis.Subsequences]
a:168 [binder, in Waterproof.Libs.Analysis.Sequences]
A:17 [binder, in Waterproof.Tactics.Either]
a:17 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
a:17 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:175 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:176 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:18 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:18 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:18 [binder, in Waterproof.Libs.Analysis.Series]
a:18 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:189 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:19 [binder, in Waterproof.Libs.Negation]
a:19 [binder, in Waterproof.Libs.Reals.Rational]
A:19 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:190 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:2 [binder, in Waterproof.Libs.Sets.Operations]
a:2 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
a:20 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
A:20 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:20 [binder, in Waterproof.Tactics.Either]
a:20 [binder, in Waterproof.Libs.Analysis.Series]
A:203 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:204 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:208 [binder, in Waterproof.Libs.Analysis.Sequences]
a:21 [binder, in Waterproof.Libs.Reals]
A:21 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
a:21 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
A:213 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:214 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:22 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:22 [binder, in Waterproof.Libs.Analysis.Series]
A:22 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:227 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:228 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:23 [binder, in Waterproof.Tactics.Either]
a:23 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
a:23 [binder, in Waterproof.Libs.Reals]
a:233 [binder, in Waterproof.Libs.Analysis.Sequences]
a:235 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:236 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:237 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:238 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:239 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:24 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
a:240 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:243 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:244 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:245 [binder, in Waterproof.Libs.Analysis.Sequences]
A:25 [binder, in Waterproof.Libs.Negation]
a:25 [binder, in Waterproof.Libs.Reals.Rational]
a:25 [binder, in Waterproof.Libs.Analysis.Series]
a:253 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:254 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:255 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:256 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:257 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:258 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:261 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:262 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:269 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:27 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:270 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:271 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:272 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:279 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:28 [binder, in Waterproof.Chains.Inequalities]
a:280 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:281 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:282 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:283 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:284 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:285 [binder, in Waterproof.Libs.Analysis.Sequences]
A:285 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:286 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:29 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:29 [binder, in Waterproof.Libs.Negation]
A:29 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:295 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:296 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:297 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:298 [binder, in Waterproof.Libs.Analysis.Sequences]
a:298 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:3 [binder, in Waterproof.Libs.Analysis.Sequences]
a:3 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:3 [binder, in Waterproof.Tactics.Either]
a:305 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:306 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:307 [binder, in Waterproof.Libs.Analysis.Sequences]
a:307 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:308 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:309 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:31 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:31 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
a:31 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:310 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:311 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:312 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:32 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:32 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:321 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:322 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:323 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:324 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:33 [binder, in Waterproof.Libs.Negation]
a:33 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:33 [binder, in Waterproof.Libs.Reals.Rational]
A:33 [binder, in Waterproof.Util.Goals]
a:33 [binder, in Waterproof.Libs.Reals]
a:331 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:332 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:333 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:334 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:335 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:336 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:34 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:345 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:346 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:347 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:348 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:35 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
a:35 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:35 [binder, in Waterproof.Libs.Reals]
a:355 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:356 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:357 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:358 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:359 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:36 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
A:360 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:369 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:37 [binder, in Waterproof.Libs.Negation]
a:37 [binder, in Waterproof.Libs.Reals.Rational]
A:37 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:370 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:371 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:372 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:373 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:374 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:376 [binder, in Waterproof.Libs.Analysis.Sequences]
A:38 [binder, in Waterproof.Util.Goals]
a:383 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:384 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:385 [binder, in Waterproof.Libs.Analysis.Sequences]
a:385 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:386 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:387 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:393 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:394 [binder, in Waterproof.Libs.Analysis.Sequences]
a:394 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:395 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:396 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:397 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:4 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:4 [binder, in Waterproof.Notations.Sets]
a:4 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
a:4 [binder, in Waterproof.Libs.Reals.Intervals]
a:403 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:404 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:405 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:406 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:407 [binder, in Waterproof.Libs.Analysis.Sequences]
A:407 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:41 [binder, in Waterproof.Libs.Negation]
a:41 [binder, in Waterproof.Libs.Reals.Rational]
A:41 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:411 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:412 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:423 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:424 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:427 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:428 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:43 [binder, in Waterproof.Util.Goals]
a:431 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:432 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:44 [binder, in Waterproof.Libs.Negation]
a:445 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:446 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:447 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:448 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:449 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:45 [binder, in Waterproof.Libs.Analysis.Sequences]
a:45 [binder, in Waterproof.Libs.Reals.Rational]
a:453 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:454 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:46 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
a:46 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:465 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:466 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:469 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:47 [binder, in Waterproof.Libs.Negation]
A:47 [binder, in Waterproof.Util.Goals]
A:47 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:470 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:473 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:474 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:477 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:478 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:48 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:49 [binder, in Waterproof.Libs.Reals.Rational]
A:491 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:492 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:497 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:498 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:499 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:5 [binder, in Waterproof.Libs.Negation]
a:5 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:5 [binder, in Waterproof.Waterprove]
a:5 [binder, in Waterproof.Libs.Reals.RealInequalities]
A:5 [binder, in Waterproof.Util.Goals]
a:5 [binder, in Waterproof.Libs.Analysis.Series]
A:5 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
A:50 [binder, in Waterproof.Libs.Negation]
a:500 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:501 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:502 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:503 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:504 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:505 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:506 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:507 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:508 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:509 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:512 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:515 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:516 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:53 [binder, in Waterproof.Libs.Negation]
a:543 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:544 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:55 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:55 [binder, in Waterproof.Libs.Analysis.Subsequences]
a:55 [binder, in Waterproof.Libs.Analysis.Sequences]
a:55 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:551 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:59 [binder, in Waterproof.Libs.Negation]
A:6 [binder, in Waterproof.Libs.Sets.Operations]
a:6 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:6 [binder, in Waterproof.Notations.Sets]
a:6 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
a:6 [binder, in Waterproof.Libs.Reals.Intervals]
A:61 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:62 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:63 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:64 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:65 [binder, in Waterproof.Libs.Negation]
A:66 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:68 [binder, in Waterproof.Libs.Analysis.Subsequences]
a:68 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:69 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:69 [binder, in Waterproof.Notations.Sets]
A:7 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:7 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:70 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:71 [binder, in Waterproof.Libs.Negation]
a:71 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:72 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:72 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
A:77 [binder, in Waterproof.Libs.Negation]
A:77 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:79 [binder, in Waterproof.Libs.Negation]
A:8 [binder, in Waterproof.Tactics.Either]
a:8 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:8 [binder, in Waterproof.Libs.Reals.Intervals]
A:83 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:85 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:86 [binder, in Waterproof.Libs.Analysis.Sequences]
A:86 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:86 [binder, in Waterproof.Libs.Functions]
a:87 [binder, in Waterproof.Libs.Functions]
a:88 [binder, in Waterproof.Libs.Functions]
a:89 [binder, in Waterproof.Libs.Functions]
a:9 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:9 [binder, in Waterproof.Libs.Negation]
a:91 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:93 [binder, in Waterproof.Libs.Analysis.SupAndInf]
A:94 [binder, in Waterproof.Libs.Analysis.SupAndInf]
a:97 [binder, in Waterproof.Libs.Functions]
B
base_gc_R_Z [instance, in Waterproof.Chains.Inequalities]base_gc_Z_R [instance, in Waterproof.Chains.Inequalities]
base_lc_R_Z [instance, in Waterproof.Chains.Inequalities]
base_lc_Z_R [instance, in Waterproof.Chains.Inequalities]
base_ec_R_Z [instance, in Waterproof.Chains.Inequalities]
base_ec_Z_R [instance, in Waterproof.Chains.Inequalities]
base_gc_R_nat [instance, in Waterproof.Chains.Inequalities]
base_gc_nat_R [instance, in Waterproof.Chains.Inequalities]
base_lc_R_nat [instance, in Waterproof.Chains.Inequalities]
base_lc_nat_R [instance, in Waterproof.Chains.Inequalities]
base_ec_R_nat [instance, in Waterproof.Chains.Inequalities]
base_ec_nat_R [instance, in Waterproof.Chains.Inequalities]
base_gc_inst [instance, in Waterproof.Chains.Inequalities]
base_lc_inst [instance, in Waterproof.Chains.Inequalities]
base_ec_inst [instance, in Waterproof.Chains.Inequalities]
base_gc [constructor, in Waterproof.Chains.Inequalities]
base_lc [constructor, in Waterproof.Chains.Inequalities]
base_ec [constructor, in Waterproof.Chains.Inequalities]
bdd_below_to_bdd_above_set_opp [lemma, in Waterproof.Libs.Analysis.SupAndInf]
bdd_above_bound_iff [lemma, in Waterproof.Libs.Analysis.SupAndInf]
Because [library]
bijective [definition, in Waterproof.Libs.Functions]
bijective_iff [lemma, in Waterproof.Libs.Functions]
bijective_is_surjective [lemma, in Waterproof.Libs.Functions]
bijective_is_injective [lemma, in Waterproof.Libs.Functions]
Binders [library]
Bolzano_Weierstrass [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
Bolzano_Weierstrass_gen [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
BothDirections [library]
BothStatements [library]
bounded [definition, in Waterproof.Libs.Analysis.SequencesMetric]
bounded_by_lower_bound_propform [lemma, in Waterproof.Libs.Analysis.SupAndInf]
bounded_by_upper_bound_propform [lemma, in Waterproof.Libs.Analysis.SupAndInf]
build_seq [definition, in Waterproof.Libs.Analysis.Subsequences]
built_seq_is_index_seq [lemma, in Waterproof.Libs.Analysis.Subsequences]
ByContradiction [module, in Waterproof.Util.Goals]
ByContradiction.unwrap [definition, in Waterproof.Util.Goals]
ByContradiction.wrap [constructor, in Waterproof.Util.Goals]
ByContradiction.Wrapper [inductive, in Waterproof.Util.Goals]
BySince [library]
B:10 [binder, in Waterproof.Libs.Negation]
b:100 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:109 [binder, in Waterproof.Libs.Analysis.SupAndInf]
B:109 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
B:11 [binder, in Waterproof.Libs.Sets.Operations]
b:11 [binder, in Waterproof.Libs.Reals.Intervals]
b:110 [binder, in Waterproof.Libs.Analysis.Sequences]
b:110 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:115 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:116 [binder, in Waterproof.Libs.Analysis.Sequences]
b:118 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
B:12 [binder, in Waterproof.Tactics.Either]
b:121 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:122 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:123 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:126 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:128 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:129 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:131 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:134 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:138 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:14 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
b:14 [binder, in Waterproof.Libs.Reals]
B:141 [binder, in Waterproof.Chains.Inequalities]
B:147 [binder, in Waterproof.Chains.Inequalities]
B:15 [binder, in Waterproof.Libs.Sets.Operations]
B:15 [binder, in Waterproof.Tactics.Either]
b:153 [binder, in Waterproof.Libs.Analysis.SupAndInf]
B:153 [binder, in Waterproof.Chains.Inequalities]
b:154 [binder, in Waterproof.Libs.Analysis.SupAndInf]
B:159 [binder, in Waterproof.Chains.Inequalities]
b:169 [binder, in Waterproof.Libs.Analysis.Sequences]
B:17 [binder, in Waterproof.Chains.Inequalities]
B:18 [binder, in Waterproof.Tactics.Either]
b:181 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:182 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:183 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:184 [binder, in Waterproof.Libs.Analysis.SupAndInf]
B:2 [binder, in Waterproof.Libs.Negation]
B:2 [binder, in Waterproof.Tactics.Either]
b:20 [binder, in Waterproof.Libs.Reals.Rational]
B:21 [binder, in Waterproof.Tactics.Either]
b:22 [binder, in Waterproof.Libs.Reals]
B:24 [binder, in Waterproof.Tactics.Either]
b:24 [binder, in Waterproof.Libs.Reals]
b:246 [binder, in Waterproof.Libs.Analysis.Sequences]
B:26 [binder, in Waterproof.Libs.Negation]
b:26 [binder, in Waterproof.Libs.Reals.Rational]
B:29 [binder, in Waterproof.Chains.Inequalities]
B:3 [binder, in Waterproof.Libs.Sets.Operations]
B:30 [binder, in Waterproof.Libs.Negation]
B:34 [binder, in Waterproof.Libs.Negation]
b:34 [binder, in Waterproof.Libs.Reals.Rational]
b:34 [binder, in Waterproof.Libs.Reals]
b:36 [binder, in Waterproof.Libs.Reals]
B:38 [binder, in Waterproof.Libs.Negation]
b:38 [binder, in Waterproof.Libs.Reals.Rational]
B:4 [binder, in Waterproof.Tactics.Either]
b:4 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:40 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:41 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
B:42 [binder, in Waterproof.Libs.Negation]
b:42 [binder, in Waterproof.Libs.Reals.Rational]
b:44 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:45 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
B:45 [binder, in Waterproof.Libs.Negation]
b:46 [binder, in Waterproof.Libs.Analysis.Sequences]
b:46 [binder, in Waterproof.Libs.Reals.Rational]
B:48 [binder, in Waterproof.Libs.Negation]
b:5 [binder, in Waterproof.Libs.Reals.Intervals]
B:51 [binder, in Waterproof.Libs.Negation]
b:511 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:514 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:56 [binder, in Waterproof.Libs.Analysis.Sequences]
B:6 [binder, in Waterproof.Libs.Negation]
B:6 [binder, in Waterproof.Waterprove]
b:6 [binder, in Waterproof.Libs.Reals.RealInequalities]
B:7 [binder, in Waterproof.Libs.Sets.Operations]
b:7 [binder, in Waterproof.Libs.Reals.Intervals]
B:78 [binder, in Waterproof.Libs.Negation]
B:80 [binder, in Waterproof.Libs.Negation]
b:87 [binder, in Waterproof.Libs.Analysis.Sequences]
B:9 [binder, in Waterproof.Tactics.Either]
b:9 [binder, in Waterproof.Libs.Reals.Intervals]
b:90 [binder, in Waterproof.Libs.Functions]
b:91 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:91 [binder, in Waterproof.Libs.Functions]
b:92 [binder, in Waterproof.Libs.Analysis.SupAndInf]
b:92 [binder, in Waterproof.Libs.Functions]
b:93 [binder, in Waterproof.Libs.Functions]
b:98 [binder, in Waterproof.Libs.Functions]
b:99 [binder, in Waterproof.Libs.Analysis.SupAndInf]
C
carrier:19 [binder, in Waterproof.Notations.Sets]carrier:26 [binder, in Waterproof.Notations.Sets]
carrier:33 [binder, in Waterproof.Notations.Sets]
carrier:40 [binder, in Waterproof.Notations.Sets]
carrier:47 [binder, in Waterproof.Notations.Sets]
Case [module, in Waterproof.Util.Goals]
Case.unwrap [definition, in Waterproof.Util.Goals]
Case.wrap [constructor, in Waterproof.Util.Goals]
Case.Wrapper [inductive, in Waterproof.Util.Goals]
ChainBase [record, in Waterproof.Chains.Inequalities]
ChainBase [inductive, in Waterproof.Chains.Inequalities]
ChainLink [record, in Waterproof.Chains.Inequalities]
ChainLink [inductive, in Waterproof.Chains.Inequalities]
Chains [library]
chain_base [projection, in Waterproof.Chains.Inequalities]
chain_base [constructor, in Waterproof.Chains.Inequalities]
chain_link [projection, in Waterproof.Chains.Inequalities]
chain_link [constructor, in Waterproof.Chains.Inequalities]
chain_ge [constructor, in Waterproof.Chains.Inequalities]
chain_gt [constructor, in Waterproof.Chains.Inequalities]
chain_le [constructor, in Waterproof.Chains.Inequalities]
chain_lt [constructor, in Waterproof.Chains.Inequalities]
chain_eq [constructor, in Waterproof.Chains.Inequalities]
Choose [library]
Claims [library]
classic_strong_ind_index_seq_with_prop_with_element_notation [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
classic_strong_ind_index_seq_with_prop [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Closed [constructor, in Waterproof.Libs.Reals.Intervals]
Closed_Open [constructor, in Waterproof.Libs.Reals.Intervals]
Common [library]
complement [definition, in Waterproof.Libs.Analysis.OpenAndClosed]
composition [definition, in Waterproof.Libs.Functions]
Conclusion [library]
constant_sequence [definition, in Waterproof.Libs.Analysis.Sequences]
Constr [library]
Construction [section, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
ConstructiveLogic [library]
const_seq_from [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
const_seq [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
ContinuityDomainNat [library]
ContinuityDomainR [library]
Contradiction [library]
conv [definition, in Waterproof.Notations.Sets]
convergence [definition, in Waterproof.Libs.Analysis.SequencesMetric]
convergence_opp [lemma, in Waterproof.Libs.Analysis.Sequences]
convergence_minus [lemma, in Waterproof.Libs.Analysis.Sequences]
convergence_plus [lemma, in Waterproof.Libs.Analysis.Sequences]
convergence_equivalence [lemma, in Waterproof.Libs.Analysis.Sequences]
converges_to [definition, in Waterproof.Notations.Reals]
conv_evt_eq_seq [lemma, in Waterproof.Libs.Analysis.Sequences]
created_seq_is_index_seq [lemma, in Waterproof.Libs.Analysis.Subsequences]
create_seq [definition, in Waterproof.Libs.Analysis.Subsequences]
cv_implies_cv_abs_to_l_abs [definition, in Waterproof.Notations.Reals]
C:10 [binder, in Waterproof.Tactics.Either]
c:100 [binder, in Waterproof.Chains.Inequalities]
c:103 [binder, in Waterproof.Chains.Inequalities]
c:106 [binder, in Waterproof.Chains.Inequalities]
C:11 [binder, in Waterproof.Libs.Negation]
C:110 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:113 [binder, in Waterproof.Chains.Inequalities]
c:116 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:116 [binder, in Waterproof.Chains.Inequalities]
c:119 [binder, in Waterproof.Chains.Inequalities]
c:123 [binder, in Waterproof.Libs.Analysis.Sequences]
c:125 [binder, in Waterproof.Libs.Analysis.Sequences]
C:13 [binder, in Waterproof.Tactics.Either]
c:143 [binder, in Waterproof.Chains.Inequalities]
c:149 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:149 [binder, in Waterproof.Chains.Inequalities]
c:151 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:155 [binder, in Waterproof.Chains.Inequalities]
C:16 [binder, in Waterproof.Tactics.Either]
C:160 [binder, in Waterproof.Chains.Inequalities]
c:170 [binder, in Waterproof.Libs.Analysis.Sequences]
C:18 [binder, in Waterproof.Chains.Inequalities]
C:19 [binder, in Waterproof.Tactics.Either]
c:2 [binder, in Waterproof.Notations.Reals]
c:21 [binder, in Waterproof.Libs.Reals.Rational]
C:22 [binder, in Waterproof.Tactics.Either]
C:25 [binder, in Waterproof.Tactics.Either]
C:27 [binder, in Waterproof.Libs.Negation]
c:27 [binder, in Waterproof.Libs.Reals.Rational]
C:3 [binder, in Waterproof.Libs.Negation]
c:3 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
C:30 [binder, in Waterproof.Chains.Inequalities]
C:31 [binder, in Waterproof.Libs.Negation]
C:35 [binder, in Waterproof.Libs.Negation]
c:37 [binder, in Waterproof.Chains.Inequalities]
C:39 [binder, in Waterproof.Libs.Negation]
c:41 [binder, in Waterproof.Chains.Inequalities]
C:43 [binder, in Waterproof.Libs.Negation]
c:45 [binder, in Waterproof.Chains.Inequalities]
C:46 [binder, in Waterproof.Libs.Negation]
C:49 [binder, in Waterproof.Libs.Negation]
c:49 [binder, in Waterproof.Chains.Inequalities]
C:5 [binder, in Waterproof.Tactics.Either]
c:5 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
C:52 [binder, in Waterproof.Libs.Negation]
c:52 [binder, in Waterproof.Chains.Inequalities]
c:55 [binder, in Waterproof.Chains.Inequalities]
C:58 [binder, in Waterproof.Chains.Inequalities]
C:7 [binder, in Waterproof.Libs.Negation]
C:7 [binder, in Waterproof.Waterprove]
c:7 [binder, in Waterproof.Libs.Reals.RealInequalities]
c:72 [binder, in Waterproof.Chains.Inequalities]
c:75 [binder, in Waterproof.Chains.Inequalities]
c:87 [binder, in Waterproof.Chains.Inequalities]
c:91 [binder, in Waterproof.Chains.Inequalities]
D
d [definition, in Waterproof.Libs.Analysis.Sequences]Define [library]
Definitions [section, in Waterproof.Libs.Analysis.MetricSpaces]
dep_choice [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
dep_only_on_start_index_seq_prop_family [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
dep_only_on_start [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
diff_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
dist_reflexive [definition, in Waterproof.Libs.Analysis.MetricSpaces]
dist_triangle_inequality [definition, in Waterproof.Libs.Analysis.MetricSpaces]
dist_symmetric [definition, in Waterproof.Libs.Analysis.MetricSpaces]
dist_non_degenerate [definition, in Waterproof.Libs.Analysis.MetricSpaces]
dist_positive [definition, in Waterproof.Libs.Analysis.MetricSpaces]
diverges_to_minus_infinity [definition, in Waterproof.Libs.Analysis.Sequences]
diverges_to_plus_infinity [definition, in Waterproof.Libs.Analysis.Sequences]
divide_char_inv [lemma, in Waterproof.Libs.Integers.Divisibility]
divide_char [lemma, in Waterproof.Libs.Integers.Divisibility]
Divisibility [library]
div_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
div_one_neq_zero [lemma, in Waterproof.Libs.Reals]
div_non_zero [lemma, in Waterproof.Libs.Reals]
div_pos [lemma, in Waterproof.Libs.Reals]
div_sign_flip [lemma, in Waterproof.Libs.Reals]
double_sumbool_sumtriad_cba [lemma, in Waterproof.Tactics.Either]
double_sumbool_sumtriad_cab [lemma, in Waterproof.Tactics.Either]
double_sumbool_sumtriad_bca [lemma, in Waterproof.Tactics.Either]
double_sumbool_sumtriad_bac [lemma, in Waterproof.Tactics.Either]
double_sumbool_sumtriad_acb [lemma, in Waterproof.Tactics.Either]
double_sumbool_sumtriad_abc [lemma, in Waterproof.Tactics.Either]
double_is_even [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
d_discrete_R [definition, in Waterproof.Libs.Analysis.MetricSpaces]
d'_eq_3 [lemma, in Waterproof.Libs.Analysis.MetricSpaces]
d'_eq_0 [lemma, in Waterproof.Libs.Analysis.MetricSpaces]
D:111 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
D:12 [binder, in Waterproof.Libs.Negation]
d:122 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:127 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:132 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:136 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:140 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:142 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:145 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:22 [binder, in Waterproof.Libs.Reals.Rational]
D:28 [binder, in Waterproof.Libs.Negation]
d:28 [binder, in Waterproof.Libs.Reals.Rational]
D:32 [binder, in Waterproof.Libs.Negation]
D:36 [binder, in Waterproof.Libs.Negation]
D:4 [binder, in Waterproof.Libs.Negation]
D:40 [binder, in Waterproof.Libs.Negation]
D:8 [binder, in Waterproof.Libs.Negation]
E
ecn:167 [binder, in Waterproof.Chains.Inequalities]ecn:175 [binder, in Waterproof.Chains.Inequalities]
ecn:191 [binder, in Waterproof.Chains.Inequalities]
ecn:207 [binder, in Waterproof.Chains.Inequalities]
ecn:215 [binder, in Waterproof.Chains.Inequalities]
ecn:231 [binder, in Waterproof.Chains.Inequalities]
ecx:169 [binder, in Waterproof.Chains.Inequalities]
ecx:177 [binder, in Waterproof.Chains.Inequalities]
ecx:193 [binder, in Waterproof.Chains.Inequalities]
ecx:209 [binder, in Waterproof.Chains.Inequalities]
ecx:217 [binder, in Waterproof.Chains.Inequalities]
ecx:233 [binder, in Waterproof.Chains.Inequalities]
ec_map [definition, in Waterproof.Chains.Inequalities]
ec_interpretable [instance, in Waterproof.Chains.Inequalities]
ec_total_statement [definition, in Waterproof.Chains.Inequalities]
ec_global_statement [definition, in Waterproof.Chains.Inequalities]
ec_tail [definition, in Waterproof.Chains.Inequalities]
ec_head [definition, in Waterproof.Chains.Inequalities]
Either [library]
elements_le_seq_of_max [lemma, in Waterproof.Libs.Analysis.Subsequences]
elements_le_seq_of_max_pre [lemma, in Waterproof.Libs.Analysis.Subsequences]
empty [definition, in Waterproof.Notations.Sets]
empty_set_characterization [lemma, in Waterproof.Libs.Sets]
eps:219 [binder, in Waterproof.Libs.Analysis.Sequences]
eps:220 [binder, in Waterproof.Libs.Analysis.Sequences]
eps:257 [binder, in Waterproof.Libs.Analysis.Sequences]
eps:258 [binder, in Waterproof.Libs.Analysis.Sequences]
eps:265 [binder, in Waterproof.Libs.Analysis.Sequences]
eps:266 [binder, in Waterproof.Libs.Analysis.Sequences]
EqualChain [inductive, in Waterproof.Chains.Inequalities]
EqualInterpretation [record, in Waterproof.Chains.Inequalities]
EqualInterpretation0:71 [binder, in Waterproof.Chains.Inequalities]
EqualInterpretation0:74 [binder, in Waterproof.Chains.Inequalities]
EqualInterpretation0:79 [binder, in Waterproof.Chains.Inequalities]
EqualRel [inductive, in Waterproof.Chains.Inequalities]
equal_interpretation [instance, in Waterproof.Chains.Inequalities]
equivalent_subsequence_convergence [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
eq_seq_conv_to_same_lim [lemma, in Waterproof.Libs.Analysis.Sequences]
eq_rel_to_pred [projection, in Waterproof.Chains.Inequalities]
Evars [library]
Even [library]
even_or_odd [lemma, in Waterproof.Libs.Integers.Even]
even_of [lemma, in Waterproof.Libs.Integers.Even]
every_point_in_R_acc_point_R [lemma, in Waterproof.Libs.Analysis.ContinuityDomainR]
evt_eq_sequences [definition, in Waterproof.Libs.Analysis.Sequences]
existence_next_el_to_fun [lemma, in Waterproof.Libs.Analysis.Subsequences]
exists_subseq_to_limsup_bdd [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
exists_almost_lim_sup [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
exists_good_subseq [lemma, in Waterproof.Libs.Analysis.Subsequences]
exists_almost_lim_sup_aux [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_minimizer_ε [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_maximizer_ε [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_minimizer [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_maximizer [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_inf [lemma, in Waterproof.Libs.Analysis.SupAndInf]
exists_exists_in_iff [lemma, in Waterproof.Notations.Sets]
ex_not_all_func [lemma, in Waterproof.Libs.Negation]
ex_func [lemma, in Waterproof.Libs.Negation]
E:112 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:123 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:128 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:133 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:137 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:141 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:144 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:147 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:148 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:150 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
F
false_Req [lemma, in Waterproof.Libs.Reals]finite_or_find_one [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
finite_triangle_inequalty [definition, in Waterproof.Notations.Reals]
first_satisfying_element [definition, in Waterproof.Libs.Analysis.Subsequences]
first_satisfying_element_helper [definition, in Waterproof.Libs.Analysis.Subsequences]
fix_earlier_warning [inductive, in Waterproof.Util.Goals]
forall_forall_in_iff [lemma, in Waterproof.Notations.Sets]
full [definition, in Waterproof.Notations.Sets]
Functions [library]
Functions [library]
f:10 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:101 [binder, in Waterproof.Libs.Functions]
f:110 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:112 [binder, in Waterproof.Libs.Functions]
f:119 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:120 [binder, in Waterproof.Libs.Functions]
f:123 [binder, in Waterproof.Libs.Functions]
f:125 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:126 [binder, in Waterproof.Libs.Functions]
f:129 [binder, in Waterproof.Libs.Functions]
f:130 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:133 [binder, in Waterproof.Libs.Functions]
f:135 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:138 [binder, in Waterproof.Libs.Functions]
f:139 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:142 [binder, in Waterproof.Libs.Functions]
f:142 [binder, in Waterproof.Chains.Inequalities]
f:143 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:146 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:147 [binder, in Waterproof.Libs.Functions]
f:148 [binder, in Waterproof.Chains.Inequalities]
f:151 [binder, in Waterproof.Libs.Functions]
f:154 [binder, in Waterproof.Chains.Inequalities]
f:156 [binder, in Waterproof.Libs.Functions]
f:160 [binder, in Waterproof.Libs.Functions]
f:161 [binder, in Waterproof.Chains.Inequalities]
f:165 [binder, in Waterproof.Libs.Functions]
f:169 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:170 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:173 [binder, in Waterproof.Libs.Functions]
f:175 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:181 [binder, in Waterproof.Libs.Functions]
f:186 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:189 [binder, in Waterproof.Libs.Functions]
f:19 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
f:193 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:197 [binder, in Waterproof.Libs.Functions]
f:201 [binder, in Waterproof.Libs.Functions]
f:205 [binder, in Waterproof.Libs.Functions]
f:213 [binder, in Waterproof.Libs.Functions]
f:221 [binder, in Waterproof.Libs.Functions]
f:30 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
f:34 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
f:38 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:39 [binder, in Waterproof.Libs.Functions]
f:45 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
f:48 [binder, in Waterproof.Libs.Functions]
f:57 [binder, in Waterproof.Libs.Functions]
f:66 [binder, in Waterproof.Libs.Functions]
f:75 [binder, in Waterproof.Libs.Functions]
f:80 [binder, in Waterproof.Libs.Functions]
f:85 [binder, in Waterproof.Libs.Functions]
f:9 [binder, in Waterproof.Libs.Analysis.Subsequences]
f:96 [binder, in Waterproof.Libs.Functions]
G
gcn:195 [binder, in Waterproof.Chains.Inequalities]gcn:199 [binder, in Waterproof.Chains.Inequalities]
gcn:235 [binder, in Waterproof.Chains.Inequalities]
gcn:239 [binder, in Waterproof.Chains.Inequalities]
gcx:197 [binder, in Waterproof.Chains.Inequalities]
gcx:201 [binder, in Waterproof.Chains.Inequalities]
gcx:237 [binder, in Waterproof.Chains.Inequalities]
gcx:241 [binder, in Waterproof.Chains.Inequalities]
gc_map [definition, in Waterproof.Chains.Inequalities]
gc_interpretable [instance, in Waterproof.Chains.Inequalities]
gc_total_statement [definition, in Waterproof.Chains.Inequalities]
gc_weak_global_statement [definition, in Waterproof.Chains.Inequalities]
gc_global_statement [definition, in Waterproof.Chains.Inequalities]
gc_tail [definition, in Waterproof.Chains.Inequalities]
gc_head [definition, in Waterproof.Chains.Inequalities]
ge_zero_gt_one [lemma, in Waterproof.Libs.Reals.Integer]
ge_op [projection, in Waterproof.Notations.Sets]
ge_type [record, in Waterproof.Notations.Sets]
global_grtr_rel [definition, in Waterproof.Chains.Inequalities]
global_less_rel [definition, in Waterproof.Chains.Inequalities]
global_statement [projection, in Waterproof.Chains.Inequalities]
Goals [library]
GreaterChain [inductive, in Waterproof.Chains.Inequalities]
GreaterRel [inductive, in Waterproof.Chains.Inequalities]
grtr_rel_to_pred [projection, in Waterproof.Chains.Inequalities]
grtr_relation_flow [definition, in Waterproof.Chains.Inequalities]
gt_op [projection, in Waterproof.Notations.Sets]
gt_type [record, in Waterproof.Notations.Sets]
g:115 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:12 [binder, in Waterproof.Libs.Functions]
G:12 [binder, in Waterproof.Util.Goals]
g:134 [binder, in Waterproof.Libs.Functions]
g:139 [binder, in Waterproof.Libs.Functions]
g:143 [binder, in Waterproof.Libs.Functions]
g:144 [binder, in Waterproof.Libs.Functions]
g:148 [binder, in Waterproof.Libs.Functions]
G:15 [binder, in Waterproof.Util.Goals]
g:152 [binder, in Waterproof.Libs.Functions]
g:153 [binder, in Waterproof.Libs.Functions]
g:157 [binder, in Waterproof.Libs.Functions]
g:161 [binder, in Waterproof.Libs.Functions]
g:162 [binder, in Waterproof.Libs.Functions]
g:166 [binder, in Waterproof.Libs.Functions]
g:174 [binder, in Waterproof.Libs.Functions]
g:179 [binder, in Waterproof.Libs.Analysis.Subsequences]
G:18 [binder, in Waterproof.Util.Goals]
g:182 [binder, in Waterproof.Libs.Functions]
g:184 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:190 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:190 [binder, in Waterproof.Libs.Functions]
g:197 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:198 [binder, in Waterproof.Libs.Functions]
G:2 [binder, in Waterproof.Util.Goals]
g:202 [binder, in Waterproof.Libs.Functions]
g:206 [binder, in Waterproof.Libs.Functions]
g:21 [binder, in Waterproof.Libs.Functions]
G:21 [binder, in Waterproof.Util.Goals]
g:214 [binder, in Waterproof.Libs.Functions]
g:222 [binder, in Waterproof.Libs.Functions]
g:23 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:24 [binder, in Waterproof.Libs.Analysis.Subsequences]
G:24 [binder, in Waterproof.Util.Goals]
G:27 [binder, in Waterproof.Util.Goals]
g:3 [binder, in Waterproof.Libs.Functions]
g:30 [binder, in Waterproof.Libs.Functions]
G:30 [binder, in Waterproof.Util.Goals]
G:35 [binder, in Waterproof.Util.Goals]
g:35 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
G:40 [binder, in Waterproof.Util.Goals]
g:40 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
g:42 [binder, in Waterproof.Libs.Analysis.Subsequences]
G:44 [binder, in Waterproof.Util.Goals]
G:48 [binder, in Waterproof.Util.Goals]
G:51 [binder, in Waterproof.Util.Goals]
G:54 [binder, in Waterproof.Util.Goals]
g:56 [binder, in Waterproof.Libs.Analysis.Subsequences]
G:57 [binder, in Waterproof.Util.Goals]
G:6 [binder, in Waterproof.Util.Goals]
G:60 [binder, in Waterproof.Util.Goals]
g:86 [binder, in Waterproof.Libs.Analysis.Subsequences]
g:87 [binder, in Waterproof.Libs.Analysis.Subsequences]
G:9 [binder, in Waterproof.Util.Goals]
H
has_inverse [definition, in Waterproof.Libs.Functions]has_right_inverse [definition, in Waterproof.Libs.Functions]
has_left_inverse [definition, in Waterproof.Libs.Functions]
ha:35 [binder, in Waterproof.Libs.Reals.Rational]
ha:39 [binder, in Waterproof.Libs.Reals.Rational]
ha:43 [binder, in Waterproof.Libs.Reals.Rational]
ha:47 [binder, in Waterproof.Libs.Reals.Rational]
ha:50 [binder, in Waterproof.Libs.Reals.Rational]
hb:23 [binder, in Waterproof.Libs.Reals.Rational]
hb:29 [binder, in Waterproof.Libs.Reals.Rational]
hb:36 [binder, in Waterproof.Libs.Reals.Rational]
hb:40 [binder, in Waterproof.Libs.Reals.Rational]
hb:44 [binder, in Waterproof.Libs.Reals.Rational]
hb:48 [binder, in Waterproof.Libs.Reals.Rational]
hd:24 [binder, in Waterproof.Libs.Reals.Rational]
hd:30 [binder, in Waterproof.Libs.Reals.Rational]
Help [library]
HelpNewHyp [module, in Waterproof.Tactics.Help]
help_with_choice [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hints [library]
hm:18 [binder, in Waterproof.Libs.Reals.Rational]
hna:10 [binder, in Waterproof.Libs.Reals.RealInequalities]
hnc:9 [binder, in Waterproof.Libs.Reals.RealInequalities]
hnx:3 [binder, in Waterproof.Libs.Reals.RealInequalities]
hny:4 [binder, in Waterproof.Libs.Reals.RealInequalities]
hn:17 [binder, in Waterproof.Libs.Reals.Rational]
hn:32 [binder, in Waterproof.Libs.Reals.Rational]
hp:23 [binder, in Waterproof.Libs.Integers.Even]
hp:26 [binder, in Waterproof.Libs.Integers.Even]
hp:9 [binder, in Waterproof.Libs.Integers.Square]
hq:15 [binder, in Waterproof.Libs.Reals.Rational]
Hstep:101 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:160 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:189 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:23 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:57 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hypothesis [library]
HypP:17 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
HypP:49 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:154 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:174 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:19 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:51 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:95 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
h:16 [binder, in Waterproof.Libs.Reals.Rational]
h:24 [binder, in Waterproof.Libs.Integers.Divisibility]
h:30 [binder, in Waterproof.Libs.Analysis.Subsequences]
h:34 [binder, in Waterproof.Util.Goals]
h:39 [binder, in Waterproof.Util.Goals]
h:45 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
h:47 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
h:8 [binder, in Waterproof.Libs.Reals.RealInequalities]
I
identity_seal [definition, in Waterproof.Notations.Common]if_almost_minimizer_ε_then_every_low_bd_smaller [lemma, in Waterproof.Libs.Analysis.SupAndInf]
if_almost_maximizer_ε_then_every_upp_bd_larger [lemma, in Waterproof.Libs.Analysis.SupAndInf]
if_almost_minimizer_then_every_low_bd_smaller [lemma, in Waterproof.Libs.Analysis.SupAndInf]
if_almost_maximizer_then_every_upp_bd_larger [lemma, in Waterproof.Libs.Analysis.SupAndInf]
ii:11 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
ii:121 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
ii:20 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
ii:57 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
image [definition, in Waterproof.Libs.Functions]
impl_not_and_func [lemma, in Waterproof.Libs.Negation]
impl_func [lemma, in Waterproof.Libs.Negation]
incr_loc_to_glob [lemma, in Waterproof.Libs.Analysis.Subsequences]
incr_loc_to_glob [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
IndexedOperations [library]
IndexedSets [library]
indexed_union [inductive, in Waterproof.Libs.Sets.IndexedOperations]
indexed_intersection [inductive, in Waterproof.Libs.Sets.IndexedOperations]
index_seq_grows [lemma, in Waterproof.Libs.Analysis.Subsequences]
index_seq_grows_0 [lemma, in Waterproof.Libs.Analysis.Subsequences]
index_seq_strictly_incr [lemma, in Waterproof.Libs.Analysis.Subsequences]
index_union_elim_left [lemma, in Waterproof.Libs.Sets.IndexedOperations]
index_union_elim [lemma, in Waterproof.Libs.Sets.IndexedOperations]
index_union_intro [constructor, in Waterproof.Libs.Sets.IndexedOperations]
index_intersection_elim_left [lemma, in Waterproof.Libs.Sets.IndexedOperations]
index_intersection_elim [lemma, in Waterproof.Libs.Sets.IndexedOperations]
index_intersection_intro [constructor, in Waterproof.Libs.Sets.IndexedOperations]
index_seq_prop_family [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
index_sequence_property2_automation [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property2 [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
index_seq_equiv [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property_automation [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
Induction [library]
induction_principle_elements [lemma, in Waterproof.Tactics.Induction]
ind_seq_with_prop [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
ind_seq_of_seq_and_prop [definition, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Inequalities [library]
InformativeEpsilon [library]
informative_or_lift [lemma, in Waterproof.Libs.Logic.InformativeEpsilon]
inf_el_to_fun [lemma, in Waterproof.Libs.Analysis.Subsequences]
inf_is_low_bd [lemma, in Waterproof.Libs.Analysis.SupAndInf]
Init [library]
injective [definition, in Waterproof.Libs.Functions]
injective_elim [lemma, in Waterproof.Libs.Functions]
INR_0 [lemma, in Waterproof.Libs.Reals.Integer]
INR_1 [lemma, in Waterproof.Libs.Reals.Integer]
Integer [library]
Integers [library]
Integers [library]
InterpretableChain [record, in Waterproof.Chains.Inequalities]
intersection_characterization_left [lemma, in Waterproof.Libs.Sets.Operations]
intersection_characterization [lemma, in Waterproof.Libs.Sets.Operations]
Intervals [library]
int_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
inverse [definition, in Waterproof.Libs.Functions]
inverse_intro [lemma, in Waterproof.Libs.Functions]
inverse_elim_right [lemma, in Waterproof.Libs.Functions]
inverse_elim_left [lemma, in Waterproof.Libs.Functions]
inverse_is_right_inverse [lemma, in Waterproof.Libs.Functions]
inverse_is_left_inverse [lemma, in Waterproof.Libs.Functions]
inv_remove [lemma, in Waterproof.Libs.Reals]
in_preimage_iff [lemma, in Waterproof.Libs.Functions]
in_preimage_elim [lemma, in Waterproof.Libs.Functions]
in_preimage_intro [lemma, in Waterproof.Libs.Functions]
in_image_iff [lemma, in Waterproof.Libs.Functions]
in_image_elim [lemma, in Waterproof.Libs.Functions]
in_image_intro [lemma, in Waterproof.Libs.Functions]
in_implies_not_in_compl [lemma, in Waterproof.Libs.Analysis.OpenAndClosed]
is_square [definition, in Waterproof.Libs.Integers.Square]
is_increasing [definition, in Waterproof.Libs.Analysis.Subsequences]
is_index_seq [definition, in Waterproof.Libs.Analysis.Subsequences]
is_bounded_below [definition, in Waterproof.Libs.Analysis.Sequences]
is_bounded_above [definition, in Waterproof.Libs.Analysis.Sequences]
is_bounded_equivalence [lemma, in Waterproof.Libs.Analysis.Sequences]
is_bounded_equivalent [definition, in Waterproof.Libs.Analysis.Sequences]
is_bounded [definition, in Waterproof.Libs.Analysis.Sequences]
is_continuous_in [definition, in Waterproof.Libs.Analysis.ContinuityDomainR]
is_isolated_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainR]
is_accumulation_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainR]
is_inf_alt_char [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_sup_alt_char [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_inf [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_bounded_below [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_lower_bound [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_max [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_sup_is_lub_iff [lemma, in Waterproof.Libs.Analysis.SupAndInf]
is_upper_bound_Raxioms_is_upper_bound_iff [lemma, in Waterproof.Libs.Analysis.SupAndInf]
is_sup [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_bounded_above [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_upper_bound [definition, in Waterproof.Libs.Analysis.SupAndInf]
is_rational [definition, in Waterproof.Libs.Reals.Rational]
is_seq_acc_pt [definition, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
is_increasing [definition, in Waterproof.Libs.Analysis.SubsequencesMetric]
is_accumulation_point [definition, in Waterproof.Libs.Analysis.SubsequencesMetric]
is_subsequence [definition, in Waterproof.Libs.Analysis.SubsequencesMetric]
is_index_seq [definition, in Waterproof.Libs.Analysis.SubsequencesMetric]
is_index_sequence [definition, in Waterproof.Libs.Analysis.SubsequencesMetric]
is_closed [definition, in Waterproof.Libs.Analysis.OpenAndClosed]
is_open [definition, in Waterproof.Libs.Analysis.OpenAndClosed]
is_interior_point [definition, in Waterproof.Libs.Analysis.OpenAndClosed]
is_interval [inductive, in Waterproof.Libs.Reals.Intervals]
is_continuous_in [definition, in Waterproof.Libs.Analysis.ContinuityDomainNat]
is_isolated_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainNat]
is_accumulation_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ItHolds [library]
ItSuffices [library]
i:1 [binder, in Waterproof.Notations.IndexedSets]
i:10 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:104 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
I:11 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:12 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:120 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:15 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:16 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:17 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:18 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:19 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:2 [binder, in Waterproof.Notations.IndexedSets]
I:21 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:22 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:25 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:26 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:27 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:28 [binder, in Waterproof.Libs.Sets.IndexedOperations]
I:3 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:30 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
I:31 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:36 [binder, in Waterproof.Libs.Sets.IndexedOperations]
I:39 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:40 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:43 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:44 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:45 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:46 [binder, in Waterproof.Libs.Sets.IndexedOperations]
I:49 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:50 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:53 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:54 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:55 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:56 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:56 [binder, in Waterproof.Libs.Sets.IndexedOperations]
i:8 [binder, in Waterproof.Libs.Sets.IndexedOperations]
K
k0:138 [binder, in Waterproof.Libs.Analysis.Subsequences]k0:139 [binder, in Waterproof.Libs.Analysis.Subsequences]
k0:143 [binder, in Waterproof.Libs.Analysis.Subsequences]
k0:144 [binder, in Waterproof.Libs.Analysis.Subsequences]
k0:33 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k0:34 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k1:54 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:55 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:56 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:57 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:67 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:68 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:58 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:59 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:60 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:61 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:69 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:70 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:10 [binder, in Waterproof.Tactics.Induction]
k:10 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:100 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:100 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:100 [binder, in Waterproof.Libs.Analysis.Sequences]
k:101 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:101 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:102 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:102 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:103 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:103 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:105 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:105 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:106 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:107 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:107 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:108 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:109 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:11 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:110 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:110 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:111 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:111 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:111 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:112 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:112 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:112 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:113 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:113 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:114 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:114 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:115 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:116 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:116 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:117 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:117 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:118 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:12 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:12 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:120 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:121 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:121 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:122 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:122 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:123 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:123 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:124 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:124 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:125 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:125 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:126 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:127 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:128 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:128 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:129 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:129 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:130 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:130 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:131 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:131 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:132 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:133 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:133 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:134 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:134 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:135 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:136 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:136 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:137 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:139 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:14 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:141 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:142 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:142 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:146 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:147 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:149 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:15 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:150 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:150 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:151 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:152 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:155 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:156 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:162 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:163 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:164 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:165 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:166 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:166 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:167 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:168 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:168 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:17 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:171 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:172 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:173 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:173 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:174 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:175 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:18 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:18 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:180 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:181 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:182 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:183 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:19 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:19 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:19 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:192 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:194 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:194 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:195 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:196 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:197 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:198 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:199 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:199 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:2 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:2 [binder, in Waterproof.Libs.Analysis.Series]
k:20 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:20 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:20 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:20 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:200 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:201 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:201 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:202 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:203 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:204 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:205 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:21 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:21 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:213 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:214 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:215 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:216 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:22 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:221 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:222 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:223 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:224 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:23 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:23 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:24 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:24 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:24 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:25 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:26 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:26 [binder, in Waterproof.Libs.Analysis.Series]
k:27 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:27 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:27 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:273 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:274 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:275 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:276 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:28 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:28 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:29 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:29 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:299 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:3 [binder, in Waterproof.Tactics.Induction]
k:3 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:3 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:30 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:30 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
K:300 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:301 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:302 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:31 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:31 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:32 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:32 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:32 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
K:325 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:326 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:327 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:328 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:33 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:33 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:34 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:34 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:34 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
K:349 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:35 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:350 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:351 [binder, in Waterproof.Libs.Analysis.SupAndInf]
K:352 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:36 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:36 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:36 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:37 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:37 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:38 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:38 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:39 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:39 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:4 [binder, in Waterproof.Tactics.Induction]
k:4 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:41 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:42 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:42 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:43 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:43 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:44 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:44 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:46 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:46 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:47 [binder, in Waterproof.Libs.Analysis.Sequences]
k:48 [binder, in Waterproof.Libs.Analysis.Sequences]
k:49 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:49 [binder, in Waterproof.Libs.Analysis.Sequences]
k:49 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:5 [binder, in Waterproof.Tactics.Induction]
k:5 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:5 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:50 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:50 [binder, in Waterproof.Libs.Analysis.Sequences]
k:50 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:51 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:51 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:51 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:52 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:52 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:52 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:52 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:523 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:524 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:529 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:53 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:53 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:530 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:536 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:537 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:54 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:54 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:549 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:550 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:561 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:562 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:563 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:564 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:573 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:574 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:575 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:576 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:577 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:578 [binder, in Waterproof.Libs.Analysis.SupAndInf]
k:59 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:6 [binder, in Waterproof.Tactics.Induction]
k:60 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:61 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:62 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:62 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:63 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:63 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:63 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:64 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:64 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:64 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:65 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:67 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:67 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:68 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:69 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:7 [binder, in Waterproof.Tactics.Induction]
k:7 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:7 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:70 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:71 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:72 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:73 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:73 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:74 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:74 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:75 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:75 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:76 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:76 [binder, in Waterproof.Libs.Analysis.Sequences]
k:76 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:77 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:77 [binder, in Waterproof.Libs.Analysis.Sequences]
k:77 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:78 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:78 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:78 [binder, in Waterproof.Libs.Analysis.Sequences]
k:79 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:79 [binder, in Waterproof.Libs.Analysis.Subsequences]
K:79 [binder, in Waterproof.Libs.Analysis.Sequences]
k:79 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:8 [binder, in Waterproof.Tactics.Induction]
k:8 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:8 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:80 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:81 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:82 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:83 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:84 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:84 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:84 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:85 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:85 [binder, in Waterproof.Libs.Analysis.Subsequences]
k:86 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:86 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:87 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:87 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:88 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:88 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:89 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:89 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:9 [binder, in Waterproof.Tactics.Induction]
k:9 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:90 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:94 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:95 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:96 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:96 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:96 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:97 [binder, in Waterproof.Libs.Analysis.Sequences]
k:97 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:98 [binder, in Waterproof.Libs.Analysis.Sequences]
k:98 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
k:99 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:99 [binder, in Waterproof.Libs.Analysis.Sequences]
k:99 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
L
lcn:179 [binder, in Waterproof.Chains.Inequalities]lcn:183 [binder, in Waterproof.Chains.Inequalities]
lcn:219 [binder, in Waterproof.Chains.Inequalities]
lcn:223 [binder, in Waterproof.Chains.Inequalities]
lcx:181 [binder, in Waterproof.Chains.Inequalities]
lcx:185 [binder, in Waterproof.Chains.Inequalities]
lcx:221 [binder, in Waterproof.Chains.Inequalities]
lcx:225 [binder, in Waterproof.Chains.Inequalities]
lc_map [definition, in Waterproof.Chains.Inequalities]
lc_interpretable [instance, in Waterproof.Chains.Inequalities]
lc_total_statement [definition, in Waterproof.Chains.Inequalities]
lc_weak_global_statement [definition, in Waterproof.Chains.Inequalities]
lc_global_statement [definition, in Waterproof.Chains.Inequalities]
lc_tail [definition, in Waterproof.Chains.Inequalities]
lc_head [definition, in Waterproof.Chains.Inequalities]
left [constructor, in Waterproof.Tactics.Either]
left_inverse_intro [lemma, in Waterproof.Libs.Functions]
left_inverse_elim [lemma, in Waterproof.Libs.Functions]
left_inverse [definition, in Waterproof.Libs.Functions]
left_in_closed_open [lemma, in Waterproof.Libs.Reals]
LessChain [inductive, in Waterproof.Chains.Inequalities]
LessRel [inductive, in Waterproof.Chains.Inequalities]
less_rel_to_pred [projection, in Waterproof.Chains.Inequalities]
less_relation_flow [definition, in Waterproof.Chains.Inequalities]
le_op [projection, in Waterproof.Notations.Sets]
le_type [record, in Waterproof.Notations.Sets]
limit_in_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainR]
limit_in_point [definition, in Waterproof.Libs.Analysis.ContinuityDomainNat]
LimsupLiminfBolzano [library]
lim_sup_bdd_is_lub_seq_acc_pts [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
lim_const_min_1_over_n_plus_1 [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
lim_sup_bdd [definition, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
lim_d_0 [lemma, in Waterproof.Libs.Analysis.Sequences]
lim_const_seq [lemma, in Waterproof.Libs.Analysis.Sequences]
link_gc_grtr_R_Z [instance, in Waterproof.Chains.Inequalities]
link_gc_grtr_Z_R [instance, in Waterproof.Chains.Inequalities]
link_gc_eq_R_Z [instance, in Waterproof.Chains.Inequalities]
link_gc_eq_Z_R [instance, in Waterproof.Chains.Inequalities]
link_ec_grtr_R_Z [instance, in Waterproof.Chains.Inequalities]
link_ec_grtr_Z_R [instance, in Waterproof.Chains.Inequalities]
link_lc_less_R_Z [instance, in Waterproof.Chains.Inequalities]
link_lc_less_Z_R [instance, in Waterproof.Chains.Inequalities]
link_lc_eq_R_Z [instance, in Waterproof.Chains.Inequalities]
link_lc_eq_Z_R [instance, in Waterproof.Chains.Inequalities]
link_ec_less_R_Z [instance, in Waterproof.Chains.Inequalities]
link_ec_less_Z_R [instance, in Waterproof.Chains.Inequalities]
link_ec_eq_R_Z [instance, in Waterproof.Chains.Inequalities]
link_ec_eq_Z_R [instance, in Waterproof.Chains.Inequalities]
link_gc_grtr_R_nat [instance, in Waterproof.Chains.Inequalities]
link_gc_grtr_nat_R [instance, in Waterproof.Chains.Inequalities]
link_gc_eq_R_nat [instance, in Waterproof.Chains.Inequalities]
link_gc_eq_nat_R [instance, in Waterproof.Chains.Inequalities]
link_ec_grtr_R_nat [instance, in Waterproof.Chains.Inequalities]
link_ec_grtr_nat_R [instance, in Waterproof.Chains.Inequalities]
link_lc_less_R_nat [instance, in Waterproof.Chains.Inequalities]
link_lc_less_nat_R [instance, in Waterproof.Chains.Inequalities]
link_lc_eq_R_nat [instance, in Waterproof.Chains.Inequalities]
link_lc_eq_nat_R [instance, in Waterproof.Chains.Inequalities]
link_ec_less_R_nat [instance, in Waterproof.Chains.Inequalities]
link_ec_less_nat_R [instance, in Waterproof.Chains.Inequalities]
link_ec_eq_R_nat [instance, in Waterproof.Chains.Inequalities]
link_ec_eq_nat_R [instance, in Waterproof.Chains.Inequalities]
link_gc_grtr_inst [instance, in Waterproof.Chains.Inequalities]
link_gc_eq_inst [instance, in Waterproof.Chains.Inequalities]
link_ec_grtr_inst [instance, in Waterproof.Chains.Inequalities]
link_lc_less_inst [instance, in Waterproof.Chains.Inequalities]
link_lc_eq_inst [instance, in Waterproof.Chains.Inequalities]
link_ec_less_inst [instance, in Waterproof.Chains.Inequalities]
link_ec_eq_inst [instance, in Waterproof.Chains.Inequalities]
link_gc_grtr [constructor, in Waterproof.Chains.Inequalities]
link_gc_eq [constructor, in Waterproof.Chains.Inequalities]
link_ec_grtr [constructor, in Waterproof.Chains.Inequalities]
link_lc_less [constructor, in Waterproof.Chains.Inequalities]
link_lc_eq [constructor, in Waterproof.Chains.Inequalities]
link_ec_less [constructor, in Waterproof.Chains.Inequalities]
link_ec_eq [constructor, in Waterproof.Chains.Inequalities]
ln:166 [binder, in Waterproof.Chains.Inequalities]
ln:170 [binder, in Waterproof.Chains.Inequalities]
ln:174 [binder, in Waterproof.Chains.Inequalities]
ln:178 [binder, in Waterproof.Chains.Inequalities]
ln:182 [binder, in Waterproof.Chains.Inequalities]
ln:186 [binder, in Waterproof.Chains.Inequalities]
ln:190 [binder, in Waterproof.Chains.Inequalities]
ln:194 [binder, in Waterproof.Chains.Inequalities]
ln:198 [binder, in Waterproof.Chains.Inequalities]
ln:202 [binder, in Waterproof.Chains.Inequalities]
ln:206 [binder, in Waterproof.Chains.Inequalities]
ln:210 [binder, in Waterproof.Chains.Inequalities]
ln:214 [binder, in Waterproof.Chains.Inequalities]
ln:218 [binder, in Waterproof.Chains.Inequalities]
ln:222 [binder, in Waterproof.Chains.Inequalities]
ln:226 [binder, in Waterproof.Chains.Inequalities]
ln:230 [binder, in Waterproof.Chains.Inequalities]
ln:234 [binder, in Waterproof.Chains.Inequalities]
ln:238 [binder, in Waterproof.Chains.Inequalities]
ln:242 [binder, in Waterproof.Chains.Inequalities]
Logic [library]
low_bd_seq_is_low_bd_lim [lemma, in Waterproof.Libs.Analysis.Sequences]
low_bd_set_opp_to_upp_bd_set [lemma, in Waterproof.Libs.Analysis.SupAndInf]
low_bd_set_to_upp_bd_set_opp [lemma, in Waterproof.Libs.Analysis.SupAndInf]
lt_op [projection, in Waterproof.Notations.Sets]
lt_type [record, in Waterproof.Notations.Sets]
lx:164 [binder, in Waterproof.Chains.Inequalities]
lx:168 [binder, in Waterproof.Chains.Inequalities]
lx:172 [binder, in Waterproof.Chains.Inequalities]
lx:176 [binder, in Waterproof.Chains.Inequalities]
lx:184 [binder, in Waterproof.Chains.Inequalities]
lx:188 [binder, in Waterproof.Chains.Inequalities]
lx:192 [binder, in Waterproof.Chains.Inequalities]
lx:200 [binder, in Waterproof.Chains.Inequalities]
lx:204 [binder, in Waterproof.Chains.Inequalities]
lx:208 [binder, in Waterproof.Chains.Inequalities]
lx:212 [binder, in Waterproof.Chains.Inequalities]
lx:216 [binder, in Waterproof.Chains.Inequalities]
lx:224 [binder, in Waterproof.Chains.Inequalities]
lx:228 [binder, in Waterproof.Chains.Inequalities]
lx:232 [binder, in Waterproof.Chains.Inequalities]
lx:240 [binder, in Waterproof.Chains.Inequalities]
l:112 [binder, in Waterproof.Libs.Analysis.Sequences]
l:118 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:118 [binder, in Waterproof.Libs.Analysis.Sequences]
l:119 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:126 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:127 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:139 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:14 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:14 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:140 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:141 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:142 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:144 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
l:147 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:148 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:148 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:149 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:149 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:15 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:150 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:153 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:154 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:157 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:158 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
L:16 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:161 [binder, in Waterproof.Libs.Analysis.Subsequences]
L:17 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:17 [binder, in Waterproof.Libs.Analysis.Series]
l:171 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:171 [binder, in Waterproof.Libs.Analysis.Sequences]
l:172 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:174 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:176 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:177 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:178 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:179 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:180 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:181 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:182 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:183 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:184 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:187 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:19 [binder, in Waterproof.Libs.Analysis.Series]
L:195 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:196 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:197 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:198 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:209 [binder, in Waterproof.Libs.Analysis.Sequences]
l:210 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:219 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:220 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:221 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:222 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:23 [binder, in Waterproof.Libs.Analysis.Series]
L:233 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:234 [binder, in Waterproof.Libs.Analysis.Sequences]
L:234 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:248 [binder, in Waterproof.Libs.Analysis.Sequences]
L:249 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:250 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:251 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:252 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:267 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:268 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:27 [binder, in Waterproof.Libs.Analysis.Series]
L:277 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:278 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:28 [binder, in Waterproof.Libs.Analysis.Subsequences]
L:28 [binder, in Waterproof.Libs.Analysis.Series]
L:291 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:292 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:293 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:294 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:3 [binder, in Waterproof.Libs.Analysis.Series]
L:303 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:304 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:32 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
l:36 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:39 [binder, in Waterproof.Libs.Analysis.Subsequences]
l:4 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
l:40 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:45 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:45 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
l:455 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:456 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:457 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:458 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:459 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:46 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
l:460 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:461 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:462 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:47 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
l:479 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:48 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
l:480 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:481 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:482 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:483 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:484 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:485 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:486 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:487 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:488 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:489 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:490 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:51 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:52 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:53 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:54 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:54 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
L:55 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:56 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:56 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:57 [binder, in Waterproof.Libs.Analysis.Sequences]
L:57 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:58 [binder, in Waterproof.Libs.Analysis.SupAndInf]
L:59 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:6 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
L:60 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:62 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:65 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:79 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:80 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:81 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:81 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:82 [binder, in Waterproof.Libs.Analysis.SupAndInf]
l:82 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:86 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:88 [binder, in Waterproof.Libs.Analysis.Sequences]
l:88 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:89 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:9 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:90 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:91 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:92 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:94 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
l:95 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
l:98 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
l:99 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
M
make_sumtriad_uninformative_6 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]make_sumtriad_uninformative_5 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_4 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_3 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_2 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_1 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumbool_uninformative_2 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumbool_uninformative_1 [lemma, in Waterproof.Libs.Logic.ConstructiveLogic]
Manipulation [library]
max_or_strict [lemma, in Waterproof.Libs.Analysis.SupAndInf]
mem_of_preimage [lemma, in Waterproof.Libs.Functions]
mem_subset_full_set [lemma, in Waterproof.Notations.Sets]
MessagesToUser [library]
metricspace [section, in Waterproof.Libs.Analysis.ContinuityDomainNat]
MetricSpaces [library]
metricspace.X [variable, in Waterproof.Libs.Analysis.ContinuityDomainNat]
middle [constructor, in Waterproof.Tactics.Either]
minus_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
min_1_over_n_plus_1_to_0 [lemma, in Waterproof.Libs.Analysis.Sequences]
min_frac [lemma, in Waterproof.Libs.Reals.Rational]
mouse_tail [lemma, in Waterproof.Libs.Analysis.Series]
mult_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
mult_neq_zero [lemma, in Waterproof.Libs.Reals.RealInequalities]
mult_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
my_section.X [variable, in Waterproof.Libs.Analysis.SubsequencesMetric]
my_section [section, in Waterproof.Libs.Analysis.SubsequencesMetric]
m_seq:66 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m_seq:65 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M0:135 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:136 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:137 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:138 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:151 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:152 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:185 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:186 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:187 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:188 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:199 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:200 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:201 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:202 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:209 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:210 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:211 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:212 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:223 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:224 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:225 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:226 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:413 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:414 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:415 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:416 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:417 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:418 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:419 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:420 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:433 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:434 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:435 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:436 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:437 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:438 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:439 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M0:440 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M1:312 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:313 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:314 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:315 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:320 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:321 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:340 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:341 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:342 [binder, in Waterproof.Libs.Analysis.Sequences]
M1:343 [binder, in Waterproof.Libs.Analysis.Sequences]
M:1 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
M:10 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:10 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:10 [binder, in Waterproof.Libs.Integers.Even]
m:10 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
m:103 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:103 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
m:104 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:104 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:104 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
m:105 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:105 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:106 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:106 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:106 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:107 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:107 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:108 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:109 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:11 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:11 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:111 [binder, in Waterproof.Libs.Analysis.Sequences]
M:113 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:114 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:115 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:116 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:117 [binder, in Waterproof.Libs.Analysis.Sequences]
m:12 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:12 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:12 [binder, in Waterproof.Libs.Integers.Even]
m:12 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
M:121 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:122 [binder, in Waterproof.Libs.Analysis.Sequences]
M:122 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:123 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:124 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:125 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:126 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:126 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:127 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:127 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:128 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:13 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:13 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:13 [binder, in Waterproof.Libs.Integers.Even]
M:131 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:132 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:133 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:134 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:14 [binder, in Waterproof.Libs.Reals.Rational]
M:14 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:14 [binder, in Waterproof.Libs.Integers.Even]
m:15 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:15 [binder, in Waterproof.Libs.Integers.Even]
m:151 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:152 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:153 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:154 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:16 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:16 [binder, in Waterproof.Libs.Integers.Divisibility]
m:16 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
m:161 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:162 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:163 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:164 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:167 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:168 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:169 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:17 [binder, in Waterproof.Libs.Integers.Divisibility]
m:17 [binder, in Waterproof.Libs.Integers.Even]
m:17 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
m:170 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:171 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:172 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:173 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:174 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:175 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:176 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:177 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:177 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:178 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:178 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:179 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:18 [binder, in Waterproof.Libs.Integers.Divisibility]
m:18 [binder, in Waterproof.Libs.Integers.Even]
M:180 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:19 [binder, in Waterproof.Libs.Integers.Divisibility]
M:19 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:19 [binder, in Waterproof.Libs.Integers.Even]
M:191 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:192 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:193 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:194 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:2 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:2 [binder, in Waterproof.Libs.Integers.Even]
m:2 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
m:20 [binder, in Waterproof.Libs.Integers.Even]
m:205 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:206 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:207 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:208 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:21 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:21 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:210 [binder, in Waterproof.Libs.Analysis.Sequences]
m:215 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:216 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:217 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:218 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:22 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:22 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:22 [binder, in Waterproof.Libs.Integers.Even]
M:22 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
M:229 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:23 [binder, in Waterproof.Libs.Integers.Divisibility]
M:23 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:23 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
M:230 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:231 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:232 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:235 [binder, in Waterproof.Libs.Analysis.Sequences]
M:24 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:24 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
M:24 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
m:245 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:246 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:247 [binder, in Waterproof.Libs.Analysis.Sequences]
m:247 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:248 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:25 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
m:25 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:25 [binder, in Waterproof.Libs.Integers.Even]
m:25 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
M:25 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
m:26 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:263 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:264 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:265 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:266 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:28 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:287 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:288 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:289 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:29 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:290 [binder, in Waterproof.Libs.Analysis.Sequences]
m:290 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:291 [binder, in Waterproof.Libs.Analysis.Sequences]
M:292 [binder, in Waterproof.Libs.Analysis.Sequences]
M:293 [binder, in Waterproof.Libs.Analysis.Sequences]
M:299 [binder, in Waterproof.Libs.Analysis.Sequences]
m:3 [binder, in Waterproof.Libs.Integers.Square]
m:3 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:3 [binder, in Waterproof.Libs.Integers.Even]
m:3 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
M:300 [binder, in Waterproof.Libs.Analysis.Sequences]
M:301 [binder, in Waterproof.Libs.Analysis.Sequences]
M:302 [binder, in Waterproof.Libs.Analysis.Sequences]
M:313 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:314 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:315 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:316 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:328 [binder, in Waterproof.Libs.Analysis.Sequences]
M:329 [binder, in Waterproof.Libs.Analysis.Sequences]
M:330 [binder, in Waterproof.Libs.Analysis.Sequences]
M:331 [binder, in Waterproof.Libs.Analysis.Sequences]
m:337 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:338 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:339 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:340 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:356 [binder, in Waterproof.Libs.Analysis.Sequences]
M:357 [binder, in Waterproof.Libs.Analysis.Sequences]
M:358 [binder, in Waterproof.Libs.Analysis.Sequences]
M:359 [binder, in Waterproof.Libs.Analysis.Sequences]
M:36 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:361 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:362 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:363 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:364 [binder, in Waterproof.Libs.Analysis.Sequences]
M:364 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:365 [binder, in Waterproof.Libs.Analysis.Sequences]
M:366 [binder, in Waterproof.Libs.Analysis.Sequences]
M:367 [binder, in Waterproof.Libs.Analysis.Sequences]
M:37 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:375 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:376 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:377 [binder, in Waterproof.Libs.Analysis.Sequences]
m:377 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:378 [binder, in Waterproof.Libs.Analysis.Sequences]
m:378 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:379 [binder, in Waterproof.Libs.Analysis.Sequences]
M:38 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:38 [binder, in Waterproof.Libs.Analysis.Series]
M:380 [binder, in Waterproof.Libs.Analysis.Sequences]
m:386 [binder, in Waterproof.Libs.Analysis.Sequences]
m:387 [binder, in Waterproof.Libs.Analysis.Sequences]
m:388 [binder, in Waterproof.Libs.Analysis.Sequences]
M:388 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:389 [binder, in Waterproof.Libs.Analysis.Sequences]
M:39 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:39 [binder, in Waterproof.Libs.Analysis.Series]
M:395 [binder, in Waterproof.Libs.Analysis.Sequences]
M:396 [binder, in Waterproof.Libs.Analysis.Sequences]
M:397 [binder, in Waterproof.Libs.Analysis.Sequences]
M:398 [binder, in Waterproof.Libs.Analysis.Sequences]
m:398 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:4 [binder, in Waterproof.Libs.Integers.Square]
m:4 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:4 [binder, in Waterproof.Libs.Reals.Integer]
m:4 [binder, in Waterproof.Libs.Integers.Even]
M:4 [binder, in Waterproof.Libs.Analysis.Series]
M:40 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:40 [binder, in Waterproof.Libs.Analysis.Series]
M:408 [binder, in Waterproof.Libs.Analysis.Sequences]
M:408 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:409 [binder, in Waterproof.Libs.Analysis.Sequences]
M:41 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:41 [binder, in Waterproof.Libs.Analysis.Series]
M:410 [binder, in Waterproof.Libs.Analysis.Sequences]
M:411 [binder, in Waterproof.Libs.Analysis.Sequences]
M:42 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:43 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:43 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:44 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:450 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:46 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:47 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:47 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:48 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:493 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:494 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:495 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:496 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:5 [binder, in Waterproof.Libs.Integers.Square]
m:5 [binder, in Waterproof.Libs.Integers.Even]
m:5 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
M:50 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:510 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:513 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:547 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:548 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:553 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:554 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:555 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:556 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:565 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:566 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:567 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:568 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:58 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:59 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:6 [binder, in Waterproof.Libs.Integers.Square]
m:6 [binder, in Waterproof.Libs.Reals.Integer]
m:6 [binder, in Waterproof.Libs.Reals.Rational]
M:60 [binder, in Waterproof.Libs.Analysis.Series]
m:61 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:61 [binder, in Waterproof.Libs.Analysis.Series]
m:62 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:62 [binder, in Waterproof.Libs.Analysis.Series]
M:63 [binder, in Waterproof.Libs.Analysis.Series]
m:64 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:65 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:65 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:67 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:7 [binder, in Waterproof.Libs.Reals.Rational]
m:7 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:7 [binder, in Waterproof.Libs.Integers.Even]
m:70 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:71 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:73 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:74 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:75 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:76 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:78 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:8 [binder, in Waterproof.Libs.Integers.Square]
m:8 [binder, in Waterproof.Libs.Reals.Integer]
M:8 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:8 [binder, in Waterproof.Libs.Reals.Rational]
m:8 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:8 [binder, in Waterproof.Libs.Integers.Even]
m:8 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
m:80 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:81 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:87 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:88 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:88 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:89 [binder, in Waterproof.Libs.Analysis.Subsequences]
M:89 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:9 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:9 [binder, in Waterproof.Libs.Reals.Rational]
m:9 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:9 [binder, in Waterproof.Libs.Integers.Even]
M:90 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:92 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:93 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:95 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:96 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:96 [binder, in Waterproof.Libs.Analysis.SupAndInf]
m:97 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:97 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:98 [binder, in Waterproof.Libs.Analysis.Subsequences]
m:98 [binder, in Waterproof.Libs.Analysis.SupAndInf]
M:99 [binder, in Waterproof.Libs.Analysis.Subsequences]
N
NaturalInduction [module, in Waterproof.Util.Goals]NaturalInduction.Base [module, in Waterproof.Util.Goals]
NaturalInduction.Base.unwrap [definition, in Waterproof.Util.Goals]
NaturalInduction.Base.wrap [constructor, in Waterproof.Util.Goals]
NaturalInduction.Base.Wrapper [inductive, in Waterproof.Util.Goals]
NaturalInduction.Step [module, in Waterproof.Util.Goals]
NaturalInduction.Step.unwrap [definition, in Waterproof.Util.Goals]
NaturalInduction.Step.wrap [constructor, in Waterproof.Util.Goals]
NaturalInduction.Step.Wrapper [inductive, in Waterproof.Util.Goals]
nat_ne_type [instance, in Waterproof.Notations.Sets]
nat_lt_type [instance, in Waterproof.Notations.Sets]
nat_le_type [instance, in Waterproof.Notations.Sets]
nat_gt_type [instance, in Waterproof.Notations.Sets]
nat_ge_type [instance, in Waterproof.Notations.Sets]
nat_dist_less_than_one_iff_equal [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
nat_dist_larger_zero_not_equal [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
nat_not_equal_dist_larger_one [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Na:192 [binder, in Waterproof.Libs.Analysis.Sequences]
Na:193 [binder, in Waterproof.Libs.Analysis.Sequences]
Na:194 [binder, in Waterproof.Libs.Analysis.Sequences]
Na:195 [binder, in Waterproof.Libs.Analysis.Sequences]
Nc:198 [binder, in Waterproof.Libs.Analysis.Sequences]
Nc:199 [binder, in Waterproof.Libs.Analysis.Sequences]
Nc:200 [binder, in Waterproof.Libs.Analysis.Sequences]
Nc:201 [binder, in Waterproof.Libs.Analysis.Sequences]
Negation [library]
neg_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
neg_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
ne_op [projection, in Waterproof.Notations.Sets]
ne_type [record, in Waterproof.Notations.Sets]
Nn:227 [binder, in Waterproof.Libs.Analysis.Sequences]
Nn:228 [binder, in Waterproof.Libs.Analysis.Sequences]
Nn:229 [binder, in Waterproof.Libs.Analysis.Sequences]
Nn:230 [binder, in Waterproof.Libs.Analysis.Sequences]
Nn:29 [binder, in Waterproof.Libs.Analysis.Series]
Nn:30 [binder, in Waterproof.Libs.Analysis.Series]
Nn:31 [binder, in Waterproof.Libs.Analysis.Series]
Nn:32 [binder, in Waterproof.Libs.Analysis.Series]
Nn:33 [binder, in Waterproof.Libs.Analysis.Series]
Nn:35 [binder, in Waterproof.Libs.Analysis.Series]
Nn:36 [binder, in Waterproof.Libs.Analysis.Series]
Nn:37 [binder, in Waterproof.Libs.Analysis.Series]
Nn:48 [binder, in Waterproof.Libs.Analysis.Series]
Nn:49 [binder, in Waterproof.Libs.Analysis.Series]
Nn:50 [binder, in Waterproof.Libs.Analysis.Series]
Nn:51 [binder, in Waterproof.Libs.Analysis.Series]
Nn:52 [binder, in Waterproof.Libs.Analysis.Series]
Nn:53 [binder, in Waterproof.Libs.Analysis.Series]
Nn:54 [binder, in Waterproof.Libs.Analysis.Series]
Nn:55 [binder, in Waterproof.Libs.Analysis.Series]
Nn:569 [binder, in Waterproof.Libs.Analysis.SupAndInf]
Nn:570 [binder, in Waterproof.Libs.Analysis.SupAndInf]
Nn:571 [binder, in Waterproof.Libs.Analysis.SupAndInf]
Nn:572 [binder, in Waterproof.Libs.Analysis.SupAndInf]
Nn:58 [binder, in Waterproof.Libs.Analysis.Series]
Nn:59 [binder, in Waterproof.Libs.Analysis.Series]
Notations [library]
not_neg_pos_func [lemma, in Waterproof.Libs.Negation]
not_ex_all_func [lemma, in Waterproof.Libs.Negation]
not_all_ex_func [lemma, in Waterproof.Libs.Negation]
not_impl_and_func [lemma, in Waterproof.Libs.Negation]
not_and_impl_func [lemma, in Waterproof.Libs.Negation]
not_and_or_func [lemma, in Waterproof.Libs.Negation]
not_or_and_func [lemma, in Waterproof.Libs.Negation]
not_even_and_odd [lemma, in Waterproof.Libs.Integers.Even]
not_in_empty [lemma, in Waterproof.Libs.Sets]
not_in_compl_implies_in [lemma, in Waterproof.Libs.Analysis.OpenAndClosed]
n_kplus1:209 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:208 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:207 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:206 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:205 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:204 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:203 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:202 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:188 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:187 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:186 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:185 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:173 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:172 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:171 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:170 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:159 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:153 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:100 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:94 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:87 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:83 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_ge_k:34 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
n0:163 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n0:164 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n0:97 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n0:98 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N1:10 [binder, in Waterproof.Notations.Reals]
N1:10 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
N1:11 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
N1:130 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:131 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:132 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:133 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:147 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:148 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:149 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:15 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:150 [binder, in Waterproof.Libs.Analysis.Sequences]
n1:155 [binder, in Waterproof.Libs.Analysis.Sequences]
n1:156 [binder, in Waterproof.Libs.Analysis.Sequences]
n1:157 [binder, in Waterproof.Libs.Analysis.Sequences]
n1:158 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:16 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:17 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:18 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:184 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:185 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:186 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:187 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:27 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:273 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:274 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:275 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:276 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:28 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:29 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:30 [binder, in Waterproof.Libs.Analysis.Sequences]
N1:399 [binder, in Waterproof.Libs.Analysis.Sequences]
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n:418 [binder, in Waterproof.Libs.Analysis.Sequences]
n:419 [binder, in Waterproof.Libs.Analysis.Sequences]
n:42 [binder, in Waterproof.Libs.Analysis.Sequences]
n:42 [binder, in Waterproof.Libs.Analysis.Series]
n:42 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:43 [binder, in Waterproof.Libs.Analysis.Sequences]
n:43 [binder, in Waterproof.Libs.Analysis.Series]
n:43 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:44 [binder, in Waterproof.Libs.Analysis.Sequences]
n:44 [binder, in Waterproof.Libs.Analysis.Series]
n:44 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:45 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:45 [binder, in Waterproof.Libs.Analysis.Series]
N:46 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:46 [binder, in Waterproof.Libs.Analysis.Series]
n:47 [binder, in Waterproof.Libs.Analysis.Series]
N:49 [binder, in Waterproof.Libs.Analysis.Subsequences]
N:5 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:5 [binder, in Waterproof.Libs.Reals.Integer]
n:5 [binder, in Waterproof.Libs.Reals.Rational]
N:50 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:51 [binder, in Waterproof.Libs.Analysis.Sequences]
n:52 [binder, in Waterproof.Libs.Analysis.Sequences]
n:53 [binder, in Waterproof.Libs.Analysis.Sequences]
n:53 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:54 [binder, in Waterproof.Libs.Analysis.Sequences]
n:541 [binder, in Waterproof.Libs.Analysis.SupAndInf]
n:542 [binder, in Waterproof.Libs.Analysis.SupAndInf]
N:557 [binder, in Waterproof.Libs.Analysis.SupAndInf]
N:558 [binder, in Waterproof.Libs.Analysis.SupAndInf]
N:559 [binder, in Waterproof.Libs.Analysis.SupAndInf]
N:56 [binder, in Waterproof.Libs.Analysis.Series]
N:560 [binder, in Waterproof.Libs.Analysis.SupAndInf]
N:57 [binder, in Waterproof.Libs.Analysis.Series]
n:58 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:59 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:6 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:6 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:6 [binder, in Waterproof.Libs.Reals.ArchimedN]
n:6 [binder, in Waterproof.Libs.Integers.Even]
n:6 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:6 [binder, in Waterproof.Libs.Analysis.Series]
n:6 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:60 [binder, in Waterproof.Libs.Analysis.Subsequences]
N:61 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:64 [binder, in Waterproof.Libs.Analysis.Series]
n:65 [binder, in Waterproof.Libs.Analysis.Series]
N:66 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:66 [binder, in Waterproof.Libs.Analysis.Sequences]
n:66 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:66 [binder, in Waterproof.Libs.Analysis.Series]
N:67 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:67 [binder, in Waterproof.Libs.Analysis.Sequences]
n:67 [binder, in Waterproof.Libs.Analysis.Series]
n:68 [binder, in Waterproof.Libs.Analysis.Sequences]
n:68 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:68 [binder, in Waterproof.Libs.Analysis.Series]
n:69 [binder, in Waterproof.Libs.Analysis.Sequences]
n:69 [binder, in Waterproof.Libs.Analysis.Series]
n:7 [binder, in Waterproof.Libs.Integers.Square]
n:7 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:7 [binder, in Waterproof.Libs.Reals.ArchimedN]
n:7 [binder, in Waterproof.Libs.Reals.Integer]
n:7 [binder, in Waterproof.Libs.Analysis.Series]
n:7 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:70 [binder, in Waterproof.Libs.Analysis.Series]
n:71 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:71 [binder, in Waterproof.Libs.Analysis.Series]
n:72 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:72 [binder, in Waterproof.Libs.Analysis.Series]
N:73 [binder, in Waterproof.Libs.Analysis.Series]
n:74 [binder, in Waterproof.Libs.Analysis.Sequences]
n:74 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:75 [binder, in Waterproof.Libs.Analysis.Sequences]
n:75 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:75 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:76 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:76 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:77 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:77 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
n:8 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:8 [binder, in Waterproof.Libs.Reals.ArchimedN]
n:8 [binder, in Waterproof.Libs.Analysis.Series]
n:80 [binder, in Waterproof.Libs.Analysis.Sequences]
n:80 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:81 [binder, in Waterproof.Libs.Analysis.Sequences]
N:82 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:82 [binder, in Waterproof.Libs.Analysis.Sequences]
N:83 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:83 [binder, in Waterproof.Libs.Analysis.Sequences]
n:84 [binder, in Waterproof.Libs.Analysis.Sequences]
n:85 [binder, in Waterproof.Libs.Analysis.Sequences]
n:85 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:89 [binder, in Waterproof.Libs.Analysis.Sequences]
n:9 [binder, in Waterproof.Libs.Reals.ArchimedN]
n:9 [binder, in Waterproof.Libs.Reals.Integer]
n:9 [binder, in Waterproof.Libs.Analysis.Series]
n:9 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:90 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:90 [binder, in Waterproof.Libs.Analysis.Sequences]
N:91 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:91 [binder, in Waterproof.Libs.Analysis.Sequences]
n:92 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:92 [binder, in Waterproof.Libs.Analysis.Sequences]
n:93 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:93 [binder, in Waterproof.Libs.Analysis.Sequences]
N:94 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:94 [binder, in Waterproof.Libs.Analysis.Sequences]
N:95 [binder, in Waterproof.Libs.Analysis.Subsequences]
n:95 [binder, in Waterproof.Libs.Analysis.Sequences]
n:96 [binder, in Waterproof.Libs.Analysis.Sequences]
n:97 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N₀:13 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N₀:31 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N₀:72 [binder, in Waterproof.Libs.Analysis.Subsequences]
N₀:73 [binder, in Waterproof.Libs.Analysis.Subsequences]
O
Obtain [library]odd_of [lemma, in Waterproof.Libs.Integers.Even]
one_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
one_in_complement_interval_closed_zero_open_one [lemma, in Waterproof.Libs.Analysis.OpenAndClosed]
Open [constructor, in Waterproof.Libs.Reals.Intervals]
OpenAndClosed [library]
open_ball [definition, in Waterproof.Libs.Analysis.OpenAndClosed]
Open_Closed [constructor, in Waterproof.Libs.Reals.Intervals]
Operations [library]
OrderInterpretation [record, in Waterproof.Chains.Inequalities]
OrderInterpretation0:102 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:105 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:110 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:112 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:115 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:118 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:123 [binder, in Waterproof.Chains.Inequalities]
OrderInterpretation0:99 [binder, in Waterproof.Chains.Inequalities]
order_interpretation_R [instance, in Waterproof.Chains.Inequalities]
order_interpretation_nat [instance, in Waterproof.Chains.Inequalities]
or_not_and_func [lemma, in Waterproof.Libs.Negation]
or_func [lemma, in Waterproof.Libs.Negation]
P
partial_sums_pos_incr [lemma, in Waterproof.Libs.Analysis.Series]partial_sums [abbreviation, in Waterproof.Libs.Analysis.Series]
pat:1 [binder, in Waterproof.Tactics.Help]
pat:1 [binder, in Waterproof.Waterprove]
pat:10 [binder, in Waterproof.Tactics.Help]
pat:11 [binder, in Waterproof.Tactics.Induction]
pat:11 [binder, in Waterproof.Tactics.Help]
pat:12 [binder, in Waterproof.Tactics.Induction]
pat:12 [binder, in Waterproof.Tactics.Help]
pat:13 [binder, in Waterproof.Tactics.Help]
pat:14 [binder, in Waterproof.Tactics.Help]
pat:15 [binder, in Waterproof.Tactics.Help]
pat:16 [binder, in Waterproof.Tactics.Help]
pat:17 [binder, in Waterproof.Tactics.Help]
pat:18 [binder, in Waterproof.Tactics.Help]
pat:19 [binder, in Waterproof.Tactics.Help]
pat:2 [binder, in Waterproof.Tactics.Help]
pat:2 [binder, in Waterproof.Waterprove]
pat:20 [binder, in Waterproof.Tactics.Help]
pat:21 [binder, in Waterproof.Tactics.Help]
pat:22 [binder, in Waterproof.Tactics.Help]
pat:23 [binder, in Waterproof.Tactics.Help]
pat:24 [binder, in Waterproof.Tactics.Help]
pat:25 [binder, in Waterproof.Tactics.Help]
pat:26 [binder, in Waterproof.Tactics.Help]
pat:27 [binder, in Waterproof.Tactics.Help]
pat:28 [binder, in Waterproof.Tactics.Help]
pat:29 [binder, in Waterproof.Tactics.Help]
pat:3 [binder, in Waterproof.Tactics.Help]
pat:3 [binder, in Waterproof.Waterprove]
pat:30 [binder, in Waterproof.Tactics.Help]
pat:33 [binder, in Waterproof.Tactics.Help]
pat:34 [binder, in Waterproof.Tactics.Help]
pat:35 [binder, in Waterproof.Tactics.Help]
pat:36 [binder, in Waterproof.Tactics.Help]
pat:37 [binder, in Waterproof.Tactics.Help]
pat:38 [binder, in Waterproof.Tactics.Help]
pat:39 [binder, in Waterproof.Tactics.Help]
pat:4 [binder, in Waterproof.Tactics.Help]
pat:4 [binder, in Waterproof.Waterprove]
pat:40 [binder, in Waterproof.Tactics.Help]
pat:41 [binder, in Waterproof.Tactics.Help]
pat:42 [binder, in Waterproof.Tactics.Help]
pat:43 [binder, in Waterproof.Tactics.Help]
pat:44 [binder, in Waterproof.Tactics.Help]
pat:45 [binder, in Waterproof.Tactics.Help]
pat:46 [binder, in Waterproof.Tactics.Help]
pat:47 [binder, in Waterproof.Tactics.Help]
pat:48 [binder, in Waterproof.Tactics.Help]
pat:49 [binder, in Waterproof.Tactics.Help]
pat:5 [binder, in Waterproof.Tactics.Help]
pat:50 [binder, in Waterproof.Tactics.Help]
pat:51 [binder, in Waterproof.Tactics.Help]
pat:52 [binder, in Waterproof.Tactics.Help]
pat:53 [binder, in Waterproof.Tactics.Help]
pat:54 [binder, in Waterproof.Tactics.Help]
pat:55 [binder, in Waterproof.Tactics.Help]
pat:56 [binder, in Waterproof.Tactics.Help]
pat:57 [binder, in Waterproof.Tactics.Help]
pat:58 [binder, in Waterproof.Tactics.Help]
pat:59 [binder, in Waterproof.Tactics.Help]
pat:6 [binder, in Waterproof.Tactics.Help]
pat:60 [binder, in Waterproof.Tactics.Help]
pat:61 [binder, in Waterproof.Tactics.Help]
pat:62 [binder, in Waterproof.Tactics.Help]
pat:63 [binder, in Waterproof.Tactics.Help]
pat:64 [binder, in Waterproof.Tactics.Help]
pat:65 [binder, in Waterproof.Tactics.Help]
pat:66 [binder, in Waterproof.Tactics.Help]
pat:67 [binder, in Waterproof.Tactics.Help]
pat:68 [binder, in Waterproof.Tactics.Help]
pat:69 [binder, in Waterproof.Tactics.Help]
pat:7 [binder, in Waterproof.Tactics.Help]
pat:70 [binder, in Waterproof.Tactics.Help]
pat:71 [binder, in Waterproof.Tactics.Help]
pat:72 [binder, in Waterproof.Tactics.Help]
pat:8 [binder, in Waterproof.Tactics.Help]
pat:9 [binder, in Waterproof.Tactics.Help]
perfect_square_of [lemma, in Waterproof.Libs.Integers.Square]
plus_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
plus_frac [lemma, in Waterproof.Libs.Reals.Rational]
pos_not_neg_func [lemma, in Waterproof.Libs.Negation]
power_set_characterization_alt [lemma, in Waterproof.Libs.Sets]
power_set_characterization [lemma, in Waterproof.Libs.Sets]
preimage [definition, in Waterproof.Libs.Functions]
preimage_of_mem [lemma, in Waterproof.Libs.Functions]
prev:21 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
prev:53 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
pr1:2 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
pr2:3 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
pr:517 [binder, in Waterproof.Libs.Analysis.SupAndInf]
pr:518 [binder, in Waterproof.Libs.Analysis.SupAndInf]
pr:545 [binder, in Waterproof.Libs.Analysis.SupAndInf]
pr:546 [binder, in Waterproof.Libs.Analysis.SupAndInf]
pr:552 [binder, in Waterproof.Libs.Analysis.SupAndInf]
P:1 [binder, in Waterproof.Libs.Logic.InformativeEpsilon]
P:1 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
p:1 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
p:102 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
P:11 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
P:113 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:14 [binder, in Waterproof.Libs.Negation]
P:14 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
P:16 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:164 [binder, in Waterproof.Libs.Analysis.Subsequences]
P:17 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
P:2 [binder, in Waterproof.Tactics.Induction]
P:2 [binder, in Waterproof.Libs.Analysis.Subsequences]
P:2 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:20 [binder, in Waterproof.Libs.Negation]
P:20 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
p:22 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
P:3 [binder, in Waterproof.Libs.Logic.Quantification]
P:3 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
P:33 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:38 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:42 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:48 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:5 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
P:54 [binder, in Waterproof.Libs.Negation]
P:57 [binder, in Waterproof.Libs.Analysis.Subsequences]
P:60 [binder, in Waterproof.Libs.Negation]
P:66 [binder, in Waterproof.Libs.Negation]
P:69 [binder, in Waterproof.Libs.Analysis.Subsequences]
P:72 [binder, in Waterproof.Libs.Negation]
P:72 [binder, in Waterproof.Notations.Sets]
p:73 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
P:8 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
Q
Quantification [library]Quantifiers [module, in Waterproof.Notations.Common]
∃ _ .. _ , _ (type_scope) [notation, in Waterproof.Notations.Common]
there exists _ .. _ , _ (type_scope) [notation, in Waterproof.Notations.Common]
∀ _ .. _ , _ (type_scope) [notation, in Waterproof.Notations.Common]
for all _ .. _ , _ (type_scope) [notation, in Waterproof.Notations.Common]
quant_over_start_dep_only_on_start [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q_in_R [definition, in Waterproof.Libs.Reals.Rational]
q:1 [binder, in Waterproof.Libs.Reals.Rational]
q:12 [binder, in Waterproof.Libs.Reals.Rational]
Q:12 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
q:14 [binder, in Waterproof.Libs.Integers.Divisibility]
Q:15 [binder, in Waterproof.Libs.Negation]
Q:15 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
Q:152 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:169 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:17 [binder, in Waterproof.Notations.Sets]
Q:18 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
q:18 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
q:19 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
Q:2 [binder, in Waterproof.Libs.Logic.InformativeEpsilon]
Q:2 [binder, in Waterproof.Notations.Sets]
Q:2 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
q:20 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
Q:21 [binder, in Waterproof.Libs.Negation]
q:21 [binder, in Waterproof.Libs.Integers.Divisibility]
q:21 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
Q:21 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
q:21 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
q:286 [binder, in Waterproof.Libs.Analysis.Sequences]
q:287 [binder, in Waterproof.Libs.Analysis.Sequences]
q:288 [binder, in Waterproof.Libs.Analysis.Sequences]
q:289 [binder, in Waterproof.Libs.Analysis.Sequences]
q:308 [binder, in Waterproof.Libs.Analysis.Sequences]
q:309 [binder, in Waterproof.Libs.Analysis.Sequences]
q:310 [binder, in Waterproof.Libs.Analysis.Sequences]
q:311 [binder, in Waterproof.Libs.Analysis.Sequences]
q:352 [binder, in Waterproof.Libs.Analysis.Sequences]
q:353 [binder, in Waterproof.Libs.Analysis.Sequences]
q:354 [binder, in Waterproof.Libs.Analysis.Sequences]
q:355 [binder, in Waterproof.Libs.Analysis.Sequences]
q:4 [binder, in Waterproof.Libs.Analysis.Sequences]
Q:4 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
Q:55 [binder, in Waterproof.Libs.Negation]
Q:6 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
Q:61 [binder, in Waterproof.Libs.Negation]
Q:66 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:67 [binder, in Waterproof.Libs.Negation]
Q:70 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:71 [binder, in Waterproof.Notations.Sets]
Q:71 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:73 [binder, in Waterproof.Libs.Negation]
Q:74 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:78 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:87 [binder, in Waterproof.Notations.Sets]
Q:9 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
Q:93 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:95 [binder, in Waterproof.Notations.Sets]
R
Rabs_left1_with_minus [lemma, in Waterproof.Libs.Reals]Rabs_zero [lemma, in Waterproof.Libs.Reals]
Rabs_m_lt_n [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Rabs_n_min_m [lemma, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Rational [library]
rational_of [lemma, in Waterproof.Libs.Reals.Rational]
Rdivid_ineq_interchange [lemma, in Waterproof.Libs.Reals.RealInequalities]
RealInequalities [library]
Reals [library]
Reals [library]
RealsWithSubsets [library]
reformulate_step_prop_index [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_final_prop_index [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_base_prop_index [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_final_prop_strong [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_base_prop_strong [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
relation_shift [lemma, in Waterproof.Libs.Analysis.SequencesMetric]
rel1:80 [binder, in Waterproof.Chains.Inequalities]
rel1:83 [binder, in Waterproof.Chains.Inequalities]
rel2:81 [binder, in Waterproof.Chains.Inequalities]
rel2:84 [binder, in Waterproof.Chains.Inequalities]
rel:124 [binder, in Waterproof.Chains.Inequalities]
rel:128 [binder, in Waterproof.Chains.Inequalities]
rel:132 [binder, in Waterproof.Chains.Inequalities]
rel:136 [binder, in Waterproof.Chains.Inequalities]
rel:155 [binder, in Waterproof.Libs.Analysis.Subsequences]
rel:160 [binder, in Waterproof.Libs.Analysis.Subsequences]
rel:67 [binder, in Waterproof.Chains.Inequalities]
remainder [definition, in Waterproof.Libs.Integers.Divisibility]
remainder_of [lemma, in Waterproof.Libs.Integers.Divisibility]
Req_false [lemma, in Waterproof.Libs.Reals]
Req_true [lemma, in Waterproof.Libs.Reals]
Rge_lt_or_eq_dec [lemma, in Waterproof.Libs.Reals]
Rge_le_dec [lemma, in Waterproof.Libs.Reals]
Rge_min_abs [lemma, in Waterproof.Libs.Reals]
right [constructor, in Waterproof.Tactics.Either]
right_inverse_intro [lemma, in Waterproof.Libs.Functions]
right_inverse_elim [lemma, in Waterproof.Libs.Functions]
right_inverse [definition, in Waterproof.Libs.Functions]
right_in_open_closed [lemma, in Waterproof.Libs.Reals]
Rle_ge_dec [lemma, in Waterproof.Libs.Reals]
Rle_abs_min [lemma, in Waterproof.Libs.Reals]
Rlt_ge_dec [lemma, in Waterproof.Libs.Reals]
Rmax_abs [lemma, in Waterproof.Libs.Reals]
R_complete_unsealed [lemma, in Waterproof.Libs.Analysis.SupAndInf]
R_complete [lemma, in Waterproof.Libs.Analysis.SupAndInf]
R_ne_type [instance, in Waterproof.Notations.Sets]
R_lt_type [instance, in Waterproof.Notations.Sets]
R_le_type [instance, in Waterproof.Notations.Sets]
R_gt_type [instance, in Waterproof.Notations.Sets]
R_ge_type [instance, in Waterproof.Notations.Sets]
r1:11 [binder, in Waterproof.Libs.Reals]
r1:17 [binder, in Waterproof.Libs.Reals]
r1:25 [binder, in Waterproof.Libs.Reals]
r1:27 [binder, in Waterproof.Libs.Reals]
r1:29 [binder, in Waterproof.Libs.Reals]
r1:31 [binder, in Waterproof.Libs.Reals]
r1:9 [binder, in Waterproof.Libs.Reals]
r2:10 [binder, in Waterproof.Libs.Reals]
r2:12 [binder, in Waterproof.Libs.Reals]
r2:18 [binder, in Waterproof.Libs.Reals]
r2:26 [binder, in Waterproof.Libs.Reals]
r2:28 [binder, in Waterproof.Libs.Reals]
r2:30 [binder, in Waterproof.Libs.Reals]
r2:32 [binder, in Waterproof.Libs.Reals]
r:1 [binder, in Waterproof.Libs.Reals.ArchimedN]
r:1 [binder, in Waterproof.Libs.Reals.Integer]
R:10 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
R:13 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
r:15 [binder, in Waterproof.Libs.Integers.Divisibility]
R:16 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
r:16 [binder, in Waterproof.Libs.Reals]
R:19 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
r:2 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
r:22 [binder, in Waterproof.Libs.Integers.Divisibility]
R:22 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
r:37 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
r:38 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
r:39 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
r:40 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
r:5 [binder, in Waterproof.Libs.Reals.ArchimedN]
r:6 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
R:7 [binder, in Waterproof.Libs.Logic.ConstructiveLogic]
r:7 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
r:8 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
r:9 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
S
seal [definition, in Waterproof.Notations.Sets]Sequences [library]
SequencesMetric [library]
sequence_ub_bds [lemma, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
SequentialAccumulationPoints [library]
seq_of_max_is_increasing [lemma, in Waterproof.Libs.Analysis.Subsequences]
seq_of_max [definition, in Waterproof.Libs.Analysis.Subsequences]
seq_ordered_lim_ordered [lemma, in Waterproof.Libs.Analysis.Sequences]
seq_ex_almost_maximizer_m [lemma, in Waterproof.Libs.Analysis.SupAndInf]
seq_ex_almost_maximizer_ε [lemma, in Waterproof.Libs.Analysis.SupAndInf]
seq_bdd_seq_acc_pts_bdd [lemma, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
seq:13 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:25 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:28 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:35 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:39 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:43 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:58 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:60 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:63 [binder, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Series [library]
series_cv_abs_to [definition, in Waterproof.Libs.Analysis.Series]
series_cv_abs [definition, in Waterproof.Libs.Analysis.Series]
series_cv [definition, in Waterproof.Libs.Analysis.Series]
series_cv_to [definition, in Waterproof.Libs.Analysis.Series]
Sets [library]
Sets [library]
set_opp [definition, in Waterproof.Libs.Analysis.SupAndInf]
set_difference_elim [lemma, in Waterproof.Libs.Sets]
sigma_split_v2 [lemma, in Waterproof.Libs.Analysis.Series]
snd_map [definition, in Waterproof.Chains.Inequalities]
Sn_eq_nplus1 [lemma, in Waterproof.Tactics.Induction]
Specialize [library]
square [definition, in Waterproof.Libs.Integers.Square]
Square [library]
squeeze_theorem [lemma, in Waterproof.Libs.Analysis.Sequences]
StateGoal [module, in Waterproof.Util.Goals]
StateGoal.unwrap [definition, in Waterproof.Util.Goals]
StateGoal.wrap [constructor, in Waterproof.Util.Goals]
StateGoal.Wrapper [inductive, in Waterproof.Util.Goals]
StateHyp [module, in Waterproof.Util.Goals]
StateHyp.unwrap [definition, in Waterproof.Util.Goals]
StateHyp.wrap [constructor, in Waterproof.Util.Goals]
StateHyp.Wrapper [inductive, in Waterproof.Util.Goals]
StrongIndIndxSeq [module, in Waterproof.Util.Goals]
StrongIndIndxSeq.Base [module, in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.unwrap [definition, in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.wrap [constructor, in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.Wrapper [inductive, in Waterproof.Util.Goals]
StrongIndIndxSeq.Step [module, in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.unwrap [definition, in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.wrap [constructor, in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.Wrapper [inductive, in Waterproof.Util.Goals]
StrongInduction [section, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
StrongInductionIndexSequence [section, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
StrongInductionIndexSequence [library]
strong_ind_index_seq_with_prop [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
strong_ind_seq_with_prop [lemma, in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Subsequences [library]
SubsequencesMetric [library]
subsequence_of_convergent_sequence [lemma, in Waterproof.Libs.Analysis.SubsequencesMetric]
subseq_sat_rel [lemma, in Waterproof.Libs.Analysis.Subsequences]
subset_in [definition, in Waterproof.Notations.Sets]
subset_type [definition, in Waterproof.Notations.Sets]
sumbool_comm [lemma, in Waterproof.Tactics.Either]
sumtriad [inductive, in Waterproof.Tactics.Either]
sum_is_rational [lemma, in Waterproof.Libs.Reals.Rational]
SupAndInf [library]
sup_is_upp_bd [lemma, in Waterproof.Libs.Analysis.SupAndInf]
sup_set_opp_is_inf_set [lemma, in Waterproof.Libs.Analysis.SupAndInf]
surjective [definition, in Waterproof.Libs.Functions]
surjective_elim [lemma, in Waterproof.Libs.Functions]
T
Tactics [library]Take [library]
ToShow [library]
total_statement [projection, in Waterproof.Chains.Inequalities]
true_Req [lemma, in Waterproof.Libs.Reals]
two_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]
TypeCorrector [library]
type_of_test_aux [definition, in Waterproof.Util.Assertions]
type_of [definition, in Waterproof.Util.Init]
T:1 [binder, in Waterproof.Libs.Logic.Quantification]
T:1 [binder, in Waterproof.Util.Assertions]
T:1 [binder, in Waterproof.Util.Init]
T:10 [binder, in Waterproof.Chains.Inequalities]
T:101 [binder, in Waterproof.Chains.Inequalities]
T:104 [binder, in Waterproof.Chains.Inequalities]
T:109 [binder, in Waterproof.Chains.Inequalities]
T:11 [binder, in Waterproof.Notations.Common]
T:111 [binder, in Waterproof.Chains.Inequalities]
T:114 [binder, in Waterproof.Chains.Inequalities]
T:117 [binder, in Waterproof.Chains.Inequalities]
T:122 [binder, in Waterproof.Chains.Inequalities]
T:13 [binder, in Waterproof.Chains.Inequalities]
T:14 [binder, in Waterproof.Notations.Sets]
T:16 [binder, in Waterproof.Notations.Sets]
T:21 [binder, in Waterproof.Chains.Inequalities]
T:22 [binder, in Waterproof.Chains.Inequalities]
T:23 [binder, in Waterproof.Chains.Inequalities]
T:24 [binder, in Waterproof.Chains.Inequalities]
T:25 [binder, in Waterproof.Chains.Inequalities]
T:26 [binder, in Waterproof.Chains.Inequalities]
T:27 [binder, in Waterproof.Chains.Inequalities]
T:33 [binder, in Waterproof.Chains.Inequalities]
T:34 [binder, in Waterproof.Chains.Inequalities]
T:35 [binder, in Waterproof.Chains.Inequalities]
T:36 [binder, in Waterproof.Chains.Inequalities]
T:40 [binder, in Waterproof.Chains.Inequalities]
T:44 [binder, in Waterproof.Chains.Inequalities]
T:48 [binder, in Waterproof.Chains.Inequalities]
T:51 [binder, in Waterproof.Chains.Inequalities]
T:54 [binder, in Waterproof.Chains.Inequalities]
T:57 [binder, in Waterproof.Chains.Inequalities]
T:63 [binder, in Waterproof.Chains.Inequalities]
T:66 [binder, in Waterproof.Notations.Sets]
T:66 [binder, in Waterproof.Chains.Inequalities]
T:7 [binder, in Waterproof.Chains.Inequalities]
T:70 [binder, in Waterproof.Notations.Sets]
T:70 [binder, in Waterproof.Chains.Inequalities]
T:73 [binder, in Waterproof.Chains.Inequalities]
T:78 [binder, in Waterproof.Chains.Inequalities]
T:86 [binder, in Waterproof.Notations.Sets]
T:86 [binder, in Waterproof.Chains.Inequalities]
T:90 [binder, in Waterproof.Chains.Inequalities]
T:94 [binder, in Waterproof.Notations.Sets]
T:94 [binder, in Waterproof.Chains.Inequalities]
T:98 [binder, in Waterproof.Chains.Inequalities]
U
Unfold [library]union_characterization_left [lemma, in Waterproof.Libs.Sets.Operations]
union_characterization [lemma, in Waterproof.Libs.Sets.Operations]
unique_exists [definition, in Waterproof.Notations.Sets]
upp_bd_seq_is_upp_bd_lim [lemma, in Waterproof.Libs.Analysis.Sequences]
upp_bd_set_opp_to_low_bd_set [lemma, in Waterproof.Libs.Analysis.SupAndInf]
upp_bd_set_to_low_bd_set_opp [lemma, in Waterproof.Libs.Analysis.SupAndInf]
U:1 [binder, in Waterproof.Libs.Sets.Operations]
U:1 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:1 [binder, in Waterproof.Libs.Sets]
U:10 [binder, in Waterproof.Libs.Sets]
U:13 [binder, in Waterproof.Libs.Sets.Operations]
U:13 [binder, in Waterproof.Libs.Functions]
U:14 [binder, in Waterproof.Libs.Sets]
U:19 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:2 [binder, in Waterproof.Libs.Logic.Quantification]
U:22 [binder, in Waterproof.Libs.Functions]
U:29 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:31 [binder, in Waterproof.Libs.Functions]
U:37 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:4 [binder, in Waterproof.Libs.Functions]
U:4 [binder, in Waterproof.Libs.Sets]
U:47 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:5 [binder, in Waterproof.Libs.Sets.Operations]
U:7 [binder, in Waterproof.Libs.Sets]
U:8 [binder, in Waterproof.Notations.Sets]
U:9 [binder, in Waterproof.Libs.Sets.Operations]
U:9 [binder, in Waterproof.Libs.Sets.IndexedOperations]
U:9 [binder, in Waterproof.Notations.Sets]
V
VerifyGoal [module, in Waterproof.Util.Goals]VerifyGoal.unwrap [definition, in Waterproof.Util.Goals]
VerifyGoal.wrap [constructor, in Waterproof.Util.Goals]
VerifyGoal.Wrapper [inductive, in Waterproof.Util.Goals]
Version [library]
V:10 [binder, in Waterproof.Libs.Sets.IndexedOperations]
V:2 [binder, in Waterproof.Libs.Sets.IndexedOperations]
V:20 [binder, in Waterproof.Libs.Sets.IndexedOperations]
V:30 [binder, in Waterproof.Libs.Sets.IndexedOperations]
v:31 [binder, in Waterproof.Tactics.Help]
v:32 [binder, in Waterproof.Tactics.Help]
V:38 [binder, in Waterproof.Libs.Sets.IndexedOperations]
V:40 [binder, in Waterproof.Libs.Functions]
V:48 [binder, in Waterproof.Libs.Sets.IndexedOperations]
V:49 [binder, in Waterproof.Libs.Functions]
V:58 [binder, in Waterproof.Libs.Functions]
V:67 [binder, in Waterproof.Libs.Functions]
V:76 [binder, in Waterproof.Libs.Functions]
V:81 [binder, in Waterproof.Libs.Functions]
W
Waterproof [library]Waterprove [library]
weak_global_statement [projection, in Waterproof.Chains.Inequalities]
X
x0:27 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]x0:28 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x0:29 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x0:30 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x:1 [binder, in Waterproof.Util.Constr]
x:1 [binder, in Waterproof.Libs.Integers.Divisibility]
X:1 [binder, in Waterproof.Libs.Functions]
x:1 [binder, in Waterproof.Libs.Reals.RealInequalities]
x:1 [binder, in Waterproof.Notations.Common]
X:1 [binder, in Waterproof.Notations.Sets]
x:1 [binder, in Waterproof.Libs.Reals]
X:1 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:10 [binder, in Waterproof.Libs.Functions]
x:10 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:10 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:100 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:100 [binder, in Waterproof.Notations.Sets]
x:100 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
x:100 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:101 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:101 [binder, in Waterproof.Notations.Sets]
x:102 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:102 [binder, in Waterproof.Notations.Sets]
x:103 [binder, in Waterproof.Notations.Sets]
x:105 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:106 [binder, in Waterproof.Libs.Functions]
x:107 [binder, in Waterproof.Libs.Functions]
x:108 [binder, in Waterproof.Libs.Functions]
x:109 [binder, in Waterproof.Libs.Functions]
x:11 [binder, in Waterproof.Libs.Reals.Rational]
x:11 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
X:11 [binder, in Waterproof.Libs.Sets]
x:11 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:11 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:110 [binder, in Waterproof.Libs.Functions]
x:111 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:112 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:113 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:114 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:114 [binder, in Waterproof.Libs.Functions]
x:115 [binder, in Waterproof.Libs.Functions]
x:116 [binder, in Waterproof.Libs.Functions]
x:117 [binder, in Waterproof.Libs.Functions]
X:118 [binder, in Waterproof.Libs.Functions]
x:12 [binder, in Waterproof.Libs.Sets.Operations]
x:12 [binder, in Waterproof.Notations.Common]
x:12 [binder, in Waterproof.Notations.Sets]
x:12 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x:12 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:12 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:121 [binder, in Waterproof.Libs.Functions]
x:124 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
X:124 [binder, in Waterproof.Libs.Functions]
x:125 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:125 [binder, in Waterproof.Chains.Inequalities]
X:127 [binder, in Waterproof.Libs.Functions]
x:129 [binder, in Waterproof.Chains.Inequalities]
X:13 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:13 [binder, in Waterproof.Util.Goals]
x:13 [binder, in Waterproof.Notations.Sets]
x:13 [binder, in Waterproof.Libs.Sets]
x:13 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:13 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:130 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
X:130 [binder, in Waterproof.Libs.Functions]
x:131 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:132 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:133 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:133 [binder, in Waterproof.Chains.Inequalities]
x:135 [binder, in Waterproof.Libs.Functions]
X:136 [binder, in Waterproof.Libs.Functions]
x:137 [binder, in Waterproof.Chains.Inequalities]
x:14 [binder, in Waterproof.Libs.Sets.IndexedOperations]
X:140 [binder, in Waterproof.Libs.Functions]
x:145 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:145 [binder, in Waterproof.Libs.Functions]
x:146 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:149 [binder, in Waterproof.Libs.Functions]
x:15 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:15 [binder, in Waterproof.Libs.Functions]
x:15 [binder, in Waterproof.Notations.Reals]
x:15 [binder, in Waterproof.Notations.Sets]
x:15 [binder, in Waterproof.Libs.Sets]
x:15 [binder, in Waterproof.Libs.Reals]
X:154 [binder, in Waterproof.Libs.Functions]
x:157 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:158 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:158 [binder, in Waterproof.Libs.Functions]
x:159 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:16 [binder, in Waterproof.Libs.Sets.Operations]
x:16 [binder, in Waterproof.Libs.Negation]
x:16 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:16 [binder, in Waterproof.Libs.Functions]
x:16 [binder, in Waterproof.Notations.Reals]
X:16 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
x:160 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:163 [binder, in Waterproof.Libs.Functions]
x:165 [binder, in Waterproof.Chains.Inequalities]
x:167 [binder, in Waterproof.Libs.Functions]
x:168 [binder, in Waterproof.Libs.Functions]
x:169 [binder, in Waterproof.Libs.Functions]
x:17 [binder, in Waterproof.Libs.Negation]
x:17 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:17 [binder, in Waterproof.Libs.Functions]
x:17 [binder, in Waterproof.Notations.Reals]
x:170 [binder, in Waterproof.Libs.Functions]
X:171 [binder, in Waterproof.Libs.Functions]
x:173 [binder, in Waterproof.Chains.Inequalities]
x:175 [binder, in Waterproof.Libs.Functions]
x:176 [binder, in Waterproof.Libs.Functions]
x:177 [binder, in Waterproof.Libs.Functions]
x:178 [binder, in Waterproof.Libs.Functions]
X:179 [binder, in Waterproof.Libs.Functions]
x:18 [binder, in Waterproof.Libs.Negation]
x:18 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:18 [binder, in Waterproof.Libs.Functions]
x:18 [binder, in Waterproof.Notations.Reals]
x:18 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:180 [binder, in Waterproof.Chains.Inequalities]
X:187 [binder, in Waterproof.Libs.Functions]
x:189 [binder, in Waterproof.Chains.Inequalities]
X:19 [binder, in Waterproof.Libs.Functions]
x:19 [binder, in Waterproof.Util.Goals]
x:19 [binder, in Waterproof.Notations.Reals]
x:19 [binder, in Waterproof.Libs.Reals]
x:19 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:195 [binder, in Waterproof.Libs.Functions]
x:196 [binder, in Waterproof.Chains.Inequalities]
X:199 [binder, in Waterproof.Libs.Functions]
x:2 [binder, in Waterproof.Util.Assertions]
x:2 [binder, in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
X:2 [binder, in Waterproof.Libs.Sets]
x:2 [binder, in Waterproof.Util.Init]
x:2 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:20 [binder, in Waterproof.Notations.Reals]
x:20 [binder, in Waterproof.Libs.Reals]
x:20 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:20 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:203 [binder, in Waterproof.Libs.Functions]
x:205 [binder, in Waterproof.Chains.Inequalities]
x:207 [binder, in Waterproof.Libs.Functions]
x:208 [binder, in Waterproof.Libs.Functions]
x:209 [binder, in Waterproof.Libs.Functions]
x:21 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:210 [binder, in Waterproof.Libs.Functions]
X:211 [binder, in Waterproof.Libs.Functions]
x:213 [binder, in Waterproof.Chains.Inequalities]
X:219 [binder, in Waterproof.Libs.Functions]
x:22 [binder, in Waterproof.Libs.Negation]
x:220 [binder, in Waterproof.Chains.Inequalities]
x:223 [binder, in Waterproof.Libs.Functions]
x:224 [binder, in Waterproof.Libs.Functions]
x:225 [binder, in Waterproof.Libs.Functions]
x:226 [binder, in Waterproof.Libs.Functions]
x:229 [binder, in Waterproof.Chains.Inequalities]
x:23 [binder, in Waterproof.Libs.Negation]
X:23 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:23 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:236 [binder, in Waterproof.Chains.Inequalities]
x:24 [binder, in Waterproof.Libs.Negation]
x:24 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:24 [binder, in Waterproof.Libs.Functions]
x:241 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:242 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:25 [binder, in Waterproof.Libs.Functions]
x:25 [binder, in Waterproof.Util.Goals]
x:25 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:259 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:26 [binder, in Waterproof.Libs.Functions]
x:26 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:260 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:27 [binder, in Waterproof.Libs.Functions]
x:27 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:28 [binder, in Waterproof.Libs.Functions]
x:28 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:29 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:3 [binder, in Waterproof.Notations.Common]
X:3 [binder, in Waterproof.Notations.Sets]
x:3 [binder, in Waterproof.Libs.Reals]
x:3 [binder, in Waterproof.Libs.Analysis.OpenAndClosed]
x:3 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:30 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:30 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:30 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
x:31 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:31 [binder, in Waterproof.Util.Goals]
X:32 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:32 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:33 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:33 [binder, in Waterproof.Libs.Functions]
x:34 [binder, in Waterproof.Libs.Functions]
x:35 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:35 [binder, in Waterproof.Libs.Functions]
x:36 [binder, in Waterproof.Libs.Functions]
X:37 [binder, in Waterproof.Libs.Functions]
x:38 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:39 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:4 [binder, in Waterproof.Libs.Sets.Operations]
X:4 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:4 [binder, in Waterproof.Libs.Logic.Quantification]
x:4 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:40 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
X:41 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:41 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:41 [binder, in Waterproof.Libs.Functions]
x:41 [binder, in Waterproof.Util.Goals]
x:41 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:42 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:42 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:42 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:43 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:44 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:44 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:44 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:45 [binder, in Waterproof.Libs.Analysis.SupAndInf]
X:46 [binder, in Waterproof.Libs.Functions]
x:46 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:47 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:48 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:48 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:49 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:49 [binder, in Waterproof.Util.Goals]
x:5 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:5 [binder, in Waterproof.Notations.Common]
x:5 [binder, in Waterproof.Libs.Logic.Quantification]
X:5 [binder, in Waterproof.Notations.Sets]
X:5 [binder, in Waterproof.Libs.Sets]
x:5 [binder, in Waterproof.Libs.Reals]
x:5 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
x:50 [binder, in Waterproof.Libs.Functions]
X:51 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:52 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:54 [binder, in Waterproof.Notations.Sets]
x:55 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
X:55 [binder, in Waterproof.Libs.Functions]
x:55 [binder, in Waterproof.Util.Goals]
x:55 [binder, in Waterproof.Notations.Sets]
x:56 [binder, in Waterproof.Libs.Negation]
x:56 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:56 [binder, in Waterproof.Notations.Sets]
x:57 [binder, in Waterproof.Libs.Negation]
x:57 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:57 [binder, in Waterproof.Notations.Sets]
x:57 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:58 [binder, in Waterproof.Libs.Negation]
x:58 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:58 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:59 [binder, in Waterproof.Libs.Functions]
x:59 [binder, in Waterproof.Notations.Sets]
x:59 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:6 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:6 [binder, in Waterproof.Libs.Functions]
x:6 [binder, in Waterproof.Libs.Logic.Quantification]
x:60 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:61 [binder, in Waterproof.Util.Goals]
x:61 [binder, in Waterproof.Notations.Sets]
x:62 [binder, in Waterproof.Libs.Negation]
x:63 [binder, in Waterproof.Libs.Negation]
x:63 [binder, in Waterproof.Notations.Sets]
x:64 [binder, in Waterproof.Libs.Negation]
X:64 [binder, in Waterproof.Libs.Functions]
x:65 [binder, in Waterproof.Notations.Sets]
x:67 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:67 [binder, in Waterproof.Notations.Sets]
x:68 [binder, in Waterproof.Libs.Negation]
x:68 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:68 [binder, in Waterproof.Libs.Functions]
x:68 [binder, in Waterproof.Notations.Sets]
x:68 [binder, in Waterproof.Chains.Inequalities]
x:69 [binder, in Waterproof.Libs.Negation]
x:69 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:69 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:7 [binder, in Waterproof.Libs.Sets.IndexedOperations]
x:7 [binder, in Waterproof.Libs.Integers.Divisibility]
x:7 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:7 [binder, in Waterproof.Libs.Functions]
x:7 [binder, in Waterproof.Notations.Common]
x:7 [binder, in Waterproof.Libs.Logic.Quantification]
x:7 [binder, in Waterproof.Util.Goals]
x:7 [binder, in Waterproof.Notations.Sets]
x:7 [binder, in Waterproof.Libs.Reals]
x:70 [binder, in Waterproof.Libs.Negation]
x:70 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:70 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:71 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:72 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
X:73 [binder, in Waterproof.Libs.Functions]
x:73 [binder, in Waterproof.Notations.Sets]
x:73 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:74 [binder, in Waterproof.Libs.Negation]
x:74 [binder, in Waterproof.Notations.Sets]
x:74 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:75 [binder, in Waterproof.Libs.Negation]
x:75 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:75 [binder, in Waterproof.Notations.Sets]
x:75 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:76 [binder, in Waterproof.Libs.Negation]
x:76 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:76 [binder, in Waterproof.Notations.Sets]
x:76 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:77 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:77 [binder, in Waterproof.Libs.Functions]
x:77 [binder, in Waterproof.Notations.Sets]
x:78 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
X:78 [binder, in Waterproof.Libs.Functions]
x:78 [binder, in Waterproof.Notations.Sets]
x:79 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:79 [binder, in Waterproof.Notations.Sets]
x:8 [binder, in Waterproof.Libs.Sets.Operations]
x:8 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:8 [binder, in Waterproof.Libs.Functions]
x:8 [binder, in Waterproof.Libs.Logic.Quantification]
X:8 [binder, in Waterproof.Libs.Sets]
x:80 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:80 [binder, in Waterproof.Notations.Sets]
x:81 [binder, in Waterproof.Libs.Negation]
x:81 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:82 [binder, in Waterproof.Libs.Negation]
x:82 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:82 [binder, in Waterproof.Libs.Functions]
x:83 [binder, in Waterproof.Libs.Negation]
X:83 [binder, in Waterproof.Libs.Functions]
x:84 [binder, in Waterproof.Libs.Negation]
x:84 [binder, in Waterproof.Libs.Analysis.SupAndInf]
x:85 [binder, in Waterproof.Libs.Negation]
x:85 [binder, in Waterproof.Notations.Sets]
x:85 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:86 [binder, in Waterproof.Libs.Negation]
x:86 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:87 [binder, in Waterproof.Libs.Negation]
x:87 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:87 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:88 [binder, in Waterproof.Libs.Negation]
x:88 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:88 [binder, in Waterproof.Notations.Sets]
x:88 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:89 [binder, in Waterproof.Libs.Negation]
x:89 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:89 [binder, in Waterproof.Notations.Sets]
x:9 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:9 [binder, in Waterproof.Libs.Functions]
x:9 [binder, in Waterproof.Notations.Common]
x:9 [binder, in Waterproof.Libs.Logic.Quantification]
x:9 [binder, in Waterproof.Libs.Sets]
x:90 [binder, in Waterproof.Libs.Negation]
x:90 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
x:90 [binder, in Waterproof.Notations.Sets]
x:91 [binder, in Waterproof.Libs.Negation]
x:91 [binder, in Waterproof.Notations.Sets]
x:92 [binder, in Waterproof.Libs.Negation]
x:92 [binder, in Waterproof.Notations.Sets]
x:93 [binder, in Waterproof.Notations.Sets]
X:94 [binder, in Waterproof.Libs.Functions]
x:96 [binder, in Waterproof.Notations.Sets]
x:97 [binder, in Waterproof.Notations.Sets]
x:97 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:98 [binder, in Waterproof.Notations.Sets]
x:98 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:99 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
X:99 [binder, in Waterproof.Libs.Functions]
x:99 [binder, in Waterproof.Notations.Sets]
x:99 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Y
y_seq [definition, in Waterproof.Libs.Analysis.Sequences]y:10 [binder, in Waterproof.Notations.Common]
y:10 [binder, in Waterproof.Libs.Logic.Quantification]
y:10 [binder, in Waterproof.Libs.Reals.Rational]
Y:100 [binder, in Waterproof.Libs.Functions]
y:101 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
y:102 [binder, in Waterproof.Libs.Functions]
y:103 [binder, in Waterproof.Libs.Functions]
y:104 [binder, in Waterproof.Libs.Functions]
y:105 [binder, in Waterproof.Libs.Functions]
Y:11 [binder, in Waterproof.Libs.Functions]
y:11 [binder, in Waterproof.Libs.Logic.Quantification]
Y:111 [binder, in Waterproof.Libs.Functions]
y:113 [binder, in Waterproof.Libs.Functions]
Y:119 [binder, in Waterproof.Libs.Functions]
y:12 [binder, in Waterproof.Libs.Logic.Quantification]
Y:12 [binder, in Waterproof.Libs.Sets]
Y:122 [binder, in Waterproof.Libs.Functions]
Y:125 [binder, in Waterproof.Libs.Functions]
y:126 [binder, in Waterproof.Chains.Inequalities]
Y:128 [binder, in Waterproof.Libs.Functions]
y:13 [binder, in Waterproof.Libs.Logic.Quantification]
y:130 [binder, in Waterproof.Chains.Inequalities]
Y:131 [binder, in Waterproof.Libs.Functions]
y:134 [binder, in Waterproof.Chains.Inequalities]
Y:137 [binder, in Waterproof.Libs.Functions]
y:138 [binder, in Waterproof.Chains.Inequalities]
y:14 [binder, in Waterproof.Libs.Functions]
y:14 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:141 [binder, in Waterproof.Libs.Functions]
Y:146 [binder, in Waterproof.Libs.Functions]
y:15 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:150 [binder, in Waterproof.Libs.Functions]
Y:155 [binder, in Waterproof.Libs.Functions]
Y:159 [binder, in Waterproof.Libs.Functions]
y:16 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:164 [binder, in Waterproof.Libs.Functions]
y:17 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:172 [binder, in Waterproof.Libs.Functions]
y:18 [binder, in Waterproof.Notations.Sets]
Y:180 [binder, in Waterproof.Libs.Functions]
y:183 [binder, in Waterproof.Libs.Functions]
y:184 [binder, in Waterproof.Libs.Functions]
y:185 [binder, in Waterproof.Libs.Functions]
y:186 [binder, in Waterproof.Libs.Functions]
Y:188 [binder, in Waterproof.Libs.Functions]
y:191 [binder, in Waterproof.Libs.Functions]
y:192 [binder, in Waterproof.Libs.Functions]
y:193 [binder, in Waterproof.Libs.Functions]
y:194 [binder, in Waterproof.Libs.Functions]
Y:196 [binder, in Waterproof.Libs.Functions]
y:2 [binder, in Waterproof.Libs.Integers.Divisibility]
Y:2 [binder, in Waterproof.Libs.Functions]
y:2 [binder, in Waterproof.Libs.Reals.RealInequalities]
y:2 [binder, in Waterproof.Notations.Common]
y:2 [binder, in Waterproof.Libs.Reals]
Y:20 [binder, in Waterproof.Libs.Functions]
Y:200 [binder, in Waterproof.Libs.Functions]
Y:204 [binder, in Waterproof.Libs.Functions]
Y:212 [binder, in Waterproof.Libs.Functions]
y:215 [binder, in Waterproof.Libs.Functions]
y:216 [binder, in Waterproof.Libs.Functions]
y:217 [binder, in Waterproof.Libs.Functions]
y:218 [binder, in Waterproof.Libs.Functions]
y:22 [binder, in Waterproof.Notations.Sets]
y:22 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:220 [binder, in Waterproof.Libs.Functions]
y:227 [binder, in Waterproof.Libs.Functions]
y:228 [binder, in Waterproof.Libs.Functions]
y:229 [binder, in Waterproof.Libs.Functions]
y:23 [binder, in Waterproof.Libs.Functions]
y:23 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:230 [binder, in Waterproof.Libs.Functions]
y:24 [binder, in Waterproof.Notations.Sets]
y:24 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:25 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:26 [binder, in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
Y:29 [binder, in Waterproof.Libs.Functions]
y:29 [binder, in Waterproof.Notations.Sets]
Y:3 [binder, in Waterproof.Libs.Sets]
y:30 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:31 [binder, in Waterproof.Notations.Sets]
y:31 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:32 [binder, in Waterproof.Libs.Functions]
y:32 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:33 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:36 [binder, in Waterproof.Notations.Sets]
Y:38 [binder, in Waterproof.Libs.Functions]
y:38 [binder, in Waterproof.Notations.Sets]
y:4 [binder, in Waterproof.Notations.Common]
y:4 [binder, in Waterproof.Libs.Reals]
y:42 [binder, in Waterproof.Libs.Functions]
y:43 [binder, in Waterproof.Libs.Functions]
y:43 [binder, in Waterproof.Notations.Sets]
y:43 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:44 [binder, in Waterproof.Libs.Functions]
y:45 [binder, in Waterproof.Libs.Functions]
y:45 [binder, in Waterproof.Notations.Sets]
y:45 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:47 [binder, in Waterproof.Libs.Functions]
y:47 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:5 [binder, in Waterproof.Libs.Functions]
y:50 [binder, in Waterproof.Notations.Sets]
y:51 [binder, in Waterproof.Libs.Functions]
y:52 [binder, in Waterproof.Libs.Functions]
y:52 [binder, in Waterproof.Notations.Sets]
y:53 [binder, in Waterproof.Libs.Functions]
y:539 [binder, in Waterproof.Libs.Analysis.SupAndInf]
y:54 [binder, in Waterproof.Libs.Functions]
y:540 [binder, in Waterproof.Libs.Analysis.SupAndInf]
Y:56 [binder, in Waterproof.Libs.Functions]
y:6 [binder, in Waterproof.Notations.Common]
Y:6 [binder, in Waterproof.Libs.Sets]
y:6 [binder, in Waterproof.Libs.Reals]
y:6 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:60 [binder, in Waterproof.Libs.Functions]
y:61 [binder, in Waterproof.Libs.Functions]
y:62 [binder, in Waterproof.Libs.Functions]
y:63 [binder, in Waterproof.Libs.Functions]
Y:65 [binder, in Waterproof.Libs.Functions]
y:69 [binder, in Waterproof.Libs.Functions]
y:69 [binder, in Waterproof.Chains.Inequalities]
y:7 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:70 [binder, in Waterproof.Libs.Functions]
y:71 [binder, in Waterproof.Libs.Functions]
y:72 [binder, in Waterproof.Libs.Functions]
Y:74 [binder, in Waterproof.Libs.Functions]
Y:79 [binder, in Waterproof.Libs.Functions]
y:8 [binder, in Waterproof.Libs.Integers.Divisibility]
y:8 [binder, in Waterproof.Notations.Common]
y:8 [binder, in Waterproof.Libs.Reals]
y:8 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
y:81 [binder, in Waterproof.Notations.Sets]
y:82 [binder, in Waterproof.Notations.Sets]
y:83 [binder, in Waterproof.Notations.Sets]
Y:84 [binder, in Waterproof.Libs.Functions]
y:84 [binder, in Waterproof.Notations.Sets]
y:9 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
Y:95 [binder, in Waterproof.Libs.Functions]
Z
zero_Z_in_R [lemma, in Waterproof.Libs.Reals.Integer]zero_in_interval_closed_zero_open_one [lemma, in Waterproof.Libs.Analysis.OpenAndClosed]
Zeven_char_inv [lemma, in Waterproof.Libs.Integers.Even]
Zeven_char [lemma, in Waterproof.Libs.Integers.Even]
Zodd_char_inv [lemma, in Waterproof.Libs.Integers.Even]
Zodd_char [lemma, in Waterproof.Libs.Integers.Even]
Z_in_R [definition, in Waterproof.Libs.Reals.Integer]
z:10 [binder, in Waterproof.Libs.Integers.Divisibility]
z:11 [binder, in Waterproof.Libs.Integers.Divisibility]
z:12 [binder, in Waterproof.Libs.Integers.Divisibility]
Z:132 [binder, in Waterproof.Libs.Functions]
z:162 [binder, in Waterproof.Chains.Inequalities]
z:165 [binder, in Waterproof.Libs.Analysis.SupAndInf]
z:166 [binder, in Waterproof.Libs.Analysis.SupAndInf]
z:2 [binder, in Waterproof.Libs.Reals.Integer]
z:23 [binder, in Waterproof.Notations.Sets]
z:25 [binder, in Waterproof.Notations.Sets]
z:3 [binder, in Waterproof.Libs.Reals.ArchimedN]
z:3 [binder, in Waterproof.Libs.Integers.Divisibility]
z:30 [binder, in Waterproof.Notations.Sets]
z:32 [binder, in Waterproof.Notations.Sets]
z:34 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
z:35 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
z:36 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
z:37 [binder, in Waterproof.Notations.Sets]
z:37 [binder, in Waterproof.Libs.Analysis.MetricSpaces]
z:39 [binder, in Waterproof.Notations.Sets]
z:4 [binder, in Waterproof.Libs.Reals.ArchimedN]
z:4 [binder, in Waterproof.Libs.Integers.Divisibility]
z:44 [binder, in Waterproof.Notations.Sets]
z:46 [binder, in Waterproof.Notations.Sets]
z:5 [binder, in Waterproof.Libs.Integers.Divisibility]
z:51 [binder, in Waterproof.Notations.Sets]
z:53 [binder, in Waterproof.Notations.Sets]
z:58 [binder, in Waterproof.Notations.Sets]
z:6 [binder, in Waterproof.Libs.Integers.Divisibility]
z:60 [binder, in Waterproof.Notations.Sets]
z:62 [binder, in Waterproof.Notations.Sets]
z:64 [binder, in Waterproof.Notations.Sets]
z:9 [binder, in Waterproof.Libs.Integers.Divisibility]
_
_and_assoc1 [lemma, in Waterproof.Waterprove]other
& _ _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]≥ _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
>= _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
> _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
= _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
≤ _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
<= _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
< _ (chain_scope) [notation, in Waterproof.Chains.Inequalities]
_ is an inverse of _ (function_scope) [notation, in Waterproof.Notations.Functions]
_ has an inverse (function_scope) [notation, in Waterproof.Notations.Functions]
_ is a right inverse of _ (function_scope) [notation, in Waterproof.Notations.Functions]
_ has a right inverse (function_scope) [notation, in Waterproof.Notations.Functions]
_ is a left inverse of _ (function_scope) [notation, in Waterproof.Notations.Functions]
_ has a left inverse (function_scope) [notation, in Waterproof.Notations.Functions]
_ is bijective (function_scope) [notation, in Waterproof.Notations.Functions]
_ is surjective (function_scope) [notation, in Waterproof.Notations.Functions]
_ is injective (function_scope) [notation, in Waterproof.Notations.Functions]
_ ∘ _ (function_scope) [notation, in Waterproof.Notations.Functions]
_ ⁻¹ [ _ ] (function_scope) [notation, in Waterproof.Notations.Functions]
_ [ _ ] (function_scope) [notation, in Waterproof.Notations.Functions]
_ is an accumulation point of _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an _accumulation point_ of _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a subsequence of _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a _subsequence_ of _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an index sequence (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an _index sequence_ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
index sequence (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_index sequence_ (metric_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ converges to _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SequencesMetric]
_ _converges to_ _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SequencesMetric]
_ ⟶ _ (metric_scope) [notation, in Waterproof.Libs.Analysis.SequencesMetric]
_ ≥ _ (nat_scope) [notation, in Waterproof.Notations.Reals]
_ ≤ _ (nat_scope) [notation, in Waterproof.Notations.Reals]
≠ _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
≥ _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
> _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
≤ _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
< _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
∈ _ (pred_for_subset_scope) [notation, in Waterproof.Notations.Sets]
index sequence (pred_for_subset_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_index sequence_ (pred_for_subset_scope) [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a single interval (R_scope) [notation, in Waterproof.Notations.RealsWithSubsets]
[ _ , ∞ ) (R_scope) [notation, in Waterproof.Notations.Reals]
( _ , ∞ ) (R_scope) [notation, in Waterproof.Notations.Reals]
( _ , _ ) (R_scope) [notation, in Waterproof.Notations.Reals]
( _ , _ ] (R_scope) [notation, in Waterproof.Notations.Reals]
[ _ , _ ) (R_scope) [notation, in Waterproof.Notations.Reals]
[ _ , _ ] (R_scope) [notation, in Waterproof.Notations.Reals]
_ ³ (R_scope) [notation, in Waterproof.Notations.Reals]
｜ _ - _ ｜ (R_scope) [notation, in Waterproof.Notations.Reals]
|- _ | (R_scope) [notation, in Waterproof.Notations.Reals]
| _ | (R_scope) [notation, in Waterproof.Notations.Reals]
_ ≥ _ (R_scope) [notation, in Waterproof.Notations.Reals]
_ ≤ _ (R_scope) [notation, in Waterproof.Notations.Reals]
_ is irrational (R2_scope) [notation, in Waterproof.Notations.RealsWithSubsets]
_ is rational (R2_scope) [notation, in Waterproof.Notations.RealsWithSubsets]
ℚ (R2_scope) [notation, in Waterproof.Notations.RealsWithSubsets]
ℤ (R2_scope) [notation, in Waterproof.Notations.RealsWithSubsets]
∃! _ _ , _ (subset_scope) [notation, in Waterproof.Notations.Sets]
{ _ , _ } (subset_scope) [notation, in Waterproof.Notations.Sets]
{ _ ∈ _ | _ } (subset_scope) [notation, in Waterproof.Notations.Sets]
for all _ _ , _ (subset_scope) [notation, in Waterproof.Notations.Sets]
∀ _ _ , _ (subset_scope) [notation, in Waterproof.Notations.Sets]
there exists _ _ , _ (subset_scope) [notation, in Waterproof.Notations.Sets]
∃ _ _ , _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ < _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ≤ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ > _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ≥ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
𝒫( _ ) (subset_scope) [notation, in Waterproof.Notations.Sets]
[ _ ] (subset_scope) [notation, in Waterproof.Notations.Sets]
｛ _ : _ | _ ｝ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ is inhabited (subset_scope) [notation, in Waterproof.Notations.Sets]
_ is empty (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ⊂ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ∉ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ \ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ∪ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
_ ∩ _ (subset_scope) [notation, in Waterproof.Notations.Sets]
Ω (subset_scope) [notation, in Waterproof.Notations.Sets]
∅ (subset_scope) [notation, in Waterproof.Notations.Sets]
⋂_{ _ _ } _ (subset_scope) [notation, in Waterproof.Notations.IndexedSets]
_ ≠ _ (type_scope) [notation, in Waterproof.Notations.Common]
¬ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ⇔ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ↔ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ⇨ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ⇒ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ → _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ∧ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ∨ _ (type_scope) [notation, in Waterproof.Notations.Common]
fun _ .. _ ↦ _ (type_scope) [notation, in Waterproof.Notations.Common]
_ ( _ , .. , _ ) (type_scope) [notation, in Waterproof.Notations.Common]
for all _ , _ (type_scope) [notation, in Waterproof.Notations.Sets]
∀ _ , _ (type_scope) [notation, in Waterproof.Notations.Sets]
there exists _ , _ (type_scope) [notation, in Waterproof.Notations.Sets]
∃ _ , _ (type_scope) [notation, in Waterproof.Notations.Sets]
_ ∈ _ (type_scope) [notation, in Waterproof.Notations.Sets]
_ ³ (Z_scope) [notation, in Waterproof.Notations.Integers]
_ leaves a remainder of _ when divided by _ (Z_scope) [notation, in Waterproof.Notations.Integers]
_ is a perfect square (Z_scope) [notation, in Waterproof.Notations.Integers]
_ ² (Z_scope) [notation, in Waterproof.Notations.Integers]
_ is odd (Z_scope) [notation, in Waterproof.Notations.Integers]
_ is even (Z_scope) [notation, in Waterproof.Notations.Integers]
_ is divisible by _ (Z_scope) [notation, in Waterproof.Notations.Integers]
_ | _ (Z_scope) [notation, in Waterproof.Notations.Integers]
_ diverges to -∞ [notation, in Waterproof.Libs.Analysis.Sequences]
_ _diverges to -∞_ [notation, in Waterproof.Libs.Analysis.Sequences]
_ ⟶ -∞ [notation, in Waterproof.Libs.Analysis.Sequences]
_ diverges to ∞ [notation, in Waterproof.Libs.Analysis.Sequences]
_ _diverges to ∞_ [notation, in Waterproof.Libs.Analysis.Sequences]
_ ⟶ ∞ [notation, in Waterproof.Libs.Analysis.Sequences]
_ is bounded below [notation, in Waterproof.Libs.Analysis.Sequences]
_ is _bounded below_ [notation, in Waterproof.Libs.Analysis.Sequences]
_ is bounded above [notation, in Waterproof.Libs.Analysis.Sequences]
_ is _bounded above_ [notation, in Waterproof.Libs.Analysis.Sequences]
_ is bounded [notation, in Waterproof.Libs.Analysis.Sequences]
_ is _bounded_ [notation, in Waterproof.Libs.Analysis.Sequences]
_ is continuous in _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is _continuous_ in _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an isolated point [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an _isolated point_ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an accumulation point [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an _accumulation point_ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is a lower bound for _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is a _lower bound_ for _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is bounded from below [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is _bounded from below_ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the infimum of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the _infimum_ of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the maximum of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the _maximum_ of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is an upper bound for _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is an _upper bound_ for _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is bounded from above [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is _bounded from above_ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the supremum of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ is the _supremum_ of _ [notation, in Waterproof.Libs.Analysis.SupAndInf]
_ ? [notation, in Waterproof.Notations.Common]
_ ⟶ _ [notation, in Waterproof.Notations.Reals]
_ is empty [notation, in Waterproof.Notations.Sets]
_ is disjoint from _ [notation, in Waterproof.Notations.Sets]
_ ◦ _ ◦ _ [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ ◦ _ [notation, in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is closed [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is _closed_ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is open [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is _open_ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is an interior point of _ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is an _interior point_ of _ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
_ is continuous in _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is _continuous_ in _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an isolated point [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an _isolated point_ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an accumulation point [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an _accumulation point_ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
Add the following line to the proof: Take k ∈ ℕ and assume n_0,...,n_k are defined. [notation, in Waterproof.Util.Goals]
Add the following line to the proof: - We first define n_0 . [notation, in Waterproof.Util.Goals]
Add the following line to the proof: Assume that _ . [notation, in Waterproof.Util.Goals]
Add the following line to the proof: It holds that _ . [notation, in Waterproof.Util.Goals]
Add the following line to the proof: { Indeed, _ . } or write: { We need to verify that _ . } if intermediary proof steps are required. [notation, in Waterproof.Util.Goals]
Add the following line to the proof: We need to show that _ . or write: We conclude that _ . if no intermediary proof steps are required. [notation, in Waterproof.Util.Goals]
Add the following line to the proof: We now show the induction step. [notation, in Waterproof.Util.Goals]
Add the following line to the proof: - We first show the base case _ . [notation, in Waterproof.Util.Goals]
Add the following line to the proof: - Case _ . [notation, in Waterproof.Util.Goals]
B( _ , _ ) [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
Derive a contradiction. [notation, in Waterproof.Notations.Common]
Fix an earlier warning [notation, in Waterproof.Util.Goals]
limit of _ in _ is _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
limit of _ in _ is _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
set_of_subsets _ [notation, in Waterproof.Notations.Sets]
subset _ [notation, in Waterproof.Notations.Sets]
the Archimedean property [notation, in Waterproof.Libs.Reals.ArchimedN]
_limit_ of _ in _ is _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainR]
_limit_ of _ in _ is _ [notation, in Waterproof.Libs.Analysis.ContinuityDomainNat]
& _ _ _ .. _ [notation, in Waterproof.Chains.Inequalities]
[ ( % @ < _ holds [notation, in Waterproof.Tactics.Because]
[ ( % @ < _ hold [notation, in Waterproof.Tactics.Because]
[ ( % @ < _ as [notation, in Waterproof.Tactics.Assume]
[ ( % @ < _ and [notation, in Waterproof.Tactics.Assume]
[ ( % @ < _ or [notation, in Waterproof.Tactics.Either]
[ ( % @ < _ it [notation, in Waterproof.Tactics.ItHolds]
[ ( % @ < _ we [notation, in Waterproof.Tactics.Conclusion]
Σ _ equals _ [notation, in Waterproof.Notations.Reals]
ℕ [notation, in Waterproof.Notations.Reals]
ℚ [notation, in Waterproof.Notations.Reals]
ℝ [notation, in Waterproof.Notations.Reals]
ℝ \ _ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
ℝ\ _ [notation, in Waterproof.Libs.Analysis.OpenAndClosed]
ℤ [notation, in Waterproof.Notations.Reals]
⋃_{ _ _ } _ [notation, in Waterproof.Notations.IndexedSets]
δ1:71 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ1:72 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ1:73 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ1:74 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:107 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:108 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:109 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:110 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:26 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:27 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:28 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:29 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:37 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:38 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:39 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:40 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:51 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:52 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:53 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:53 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:54 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:54 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:55 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:56 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:63 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:64 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:65 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:65 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:66 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:66 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:67 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:68 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:81 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:82 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:83 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:84 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:93 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:94 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:95 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:95 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:96 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:96 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:97 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:98 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε1:5 [binder, in Waterproof.Libs.Analysis.Sequences]
ε1:6 [binder, in Waterproof.Libs.Analysis.Sequences]
ε1:7 [binder, in Waterproof.Libs.Analysis.Sequences]
ε1:8 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:101 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:102 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:103 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:103 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:104 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:104 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:105 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:106 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:11 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:113 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:114 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:115 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:116 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:12 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:126 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:127 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:128 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:129 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:13 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:14 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:143 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:144 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:145 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:146 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:15 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:16 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:17 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:18 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:180 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:181 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:182 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:183 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:2 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:22 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:22 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:23 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:23 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:23 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:24 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:24 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:24 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:25 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:25 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:25 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:26 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:3 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:3 [binder, in Waterproof.Notations.Reals]
ε:317 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:318 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:319 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:320 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:329 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:33 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:330 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:34 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:341 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:342 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:343 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:344 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:35 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:353 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:354 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:36 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:365 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:366 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:367 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:368 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:379 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:380 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:381 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:382 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:389 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:390 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:391 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:392 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:399 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:4 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:4 [binder, in Waterproof.Notations.Reals]
ε:4 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
ε:400 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:401 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:402 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:409 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:410 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:421 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:422 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:425 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:426 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:429 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:430 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:441 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:442 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:443 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:444 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:451 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:452 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:463 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:464 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:467 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:468 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:47 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:471 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:472 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:475 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:476 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:48 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:49 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:49 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:5 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:5 [binder, in Waterproof.Notations.Reals]
ε:5 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
ε:50 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:50 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:51 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:519 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:52 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:520 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:521 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:522 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:525 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:526 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:527 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:528 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:532 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:533 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:534 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:535 [binder, in Waterproof.Libs.Analysis.SupAndInf]
ε:58 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:59 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:59 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:6 [binder, in Waterproof.Notations.Reals]
ε:6 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
ε:60 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:60 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:61 [binder, in Waterproof.Libs.Analysis.Sequences]
ε:61 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:61 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:62 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:62 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:63 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:64 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:7 [binder, in Waterproof.Libs.Analysis.SequencesMetric]
ε:77 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:78 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:78 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:79 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:79 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:80 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:80 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:81 [binder, in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:83 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:84 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:85 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:86 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:89 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:90 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:91 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:91 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:92 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:92 [binder, in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:93 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:94 [binder, in Waterproof.Libs.Analysis.ContinuityDomainR]
Notation Index
Q
∃ _ .. _ , _ (type_scope) [in Waterproof.Notations.Common]there exists _ .. _ , _ (type_scope) [in Waterproof.Notations.Common]
∀ _ .. _ , _ (type_scope) [in Waterproof.Notations.Common]
for all _ .. _ , _ (type_scope) [in Waterproof.Notations.Common]
other
& _ _ (chain_scope) [in Waterproof.Chains.Inequalities]≥ _ (chain_scope) [in Waterproof.Chains.Inequalities]
>= _ (chain_scope) [in Waterproof.Chains.Inequalities]
> _ (chain_scope) [in Waterproof.Chains.Inequalities]
= _ (chain_scope) [in Waterproof.Chains.Inequalities]
≤ _ (chain_scope) [in Waterproof.Chains.Inequalities]
<= _ (chain_scope) [in Waterproof.Chains.Inequalities]
< _ (chain_scope) [in Waterproof.Chains.Inequalities]
_ is an inverse of _ (function_scope) [in Waterproof.Notations.Functions]
_ has an inverse (function_scope) [in Waterproof.Notations.Functions]
_ is a right inverse of _ (function_scope) [in Waterproof.Notations.Functions]
_ has a right inverse (function_scope) [in Waterproof.Notations.Functions]
_ is a left inverse of _ (function_scope) [in Waterproof.Notations.Functions]
_ has a left inverse (function_scope) [in Waterproof.Notations.Functions]
_ is bijective (function_scope) [in Waterproof.Notations.Functions]
_ is surjective (function_scope) [in Waterproof.Notations.Functions]
_ is injective (function_scope) [in Waterproof.Notations.Functions]
_ ∘ _ (function_scope) [in Waterproof.Notations.Functions]
_ ⁻¹ [ _ ] (function_scope) [in Waterproof.Notations.Functions]
_ [ _ ] (function_scope) [in Waterproof.Notations.Functions]
_ is an accumulation point of _ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an _accumulation point_ of _ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a subsequence of _ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a _subsequence_ of _ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an index sequence (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is an _index sequence_ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
index sequence (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_index sequence_ (metric_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ converges to _ (metric_scope) [in Waterproof.Libs.Analysis.SequencesMetric]
_ _converges to_ _ (metric_scope) [in Waterproof.Libs.Analysis.SequencesMetric]
_ ⟶ _ (metric_scope) [in Waterproof.Libs.Analysis.SequencesMetric]
_ ≥ _ (nat_scope) [in Waterproof.Notations.Reals]
_ ≤ _ (nat_scope) [in Waterproof.Notations.Reals]
≠ _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
≥ _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
> _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
≤ _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
< _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
∈ _ (pred_for_subset_scope) [in Waterproof.Notations.Sets]
index sequence (pred_for_subset_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_index sequence_ (pred_for_subset_scope) [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is a single interval (R_scope) [in Waterproof.Notations.RealsWithSubsets]
[ _ , ∞ ) (R_scope) [in Waterproof.Notations.Reals]
( _ , ∞ ) (R_scope) [in Waterproof.Notations.Reals]
( _ , _ ) (R_scope) [in Waterproof.Notations.Reals]
( _ , _ ] (R_scope) [in Waterproof.Notations.Reals]
[ _ , _ ) (R_scope) [in Waterproof.Notations.Reals]
[ _ , _ ] (R_scope) [in Waterproof.Notations.Reals]
_ ³ (R_scope) [in Waterproof.Notations.Reals]
｜ _ - _ ｜ (R_scope) [in Waterproof.Notations.Reals]
|- _ | (R_scope) [in Waterproof.Notations.Reals]
| _ | (R_scope) [in Waterproof.Notations.Reals]
_ ≥ _ (R_scope) [in Waterproof.Notations.Reals]
_ ≤ _ (R_scope) [in Waterproof.Notations.Reals]
_ is irrational (R2_scope) [in Waterproof.Notations.RealsWithSubsets]
_ is rational (R2_scope) [in Waterproof.Notations.RealsWithSubsets]
ℚ (R2_scope) [in Waterproof.Notations.RealsWithSubsets]
ℤ (R2_scope) [in Waterproof.Notations.RealsWithSubsets]
∃! _ _ , _ (subset_scope) [in Waterproof.Notations.Sets]
{ _ , _ } (subset_scope) [in Waterproof.Notations.Sets]
{ _ ∈ _ | _ } (subset_scope) [in Waterproof.Notations.Sets]
for all _ _ , _ (subset_scope) [in Waterproof.Notations.Sets]
∀ _ _ , _ (subset_scope) [in Waterproof.Notations.Sets]
there exists _ _ , _ (subset_scope) [in Waterproof.Notations.Sets]
∃ _ _ , _ (subset_scope) [in Waterproof.Notations.Sets]
_ < _ (subset_scope) [in Waterproof.Notations.Sets]
_ ≤ _ (subset_scope) [in Waterproof.Notations.Sets]
_ > _ (subset_scope) [in Waterproof.Notations.Sets]
_ ≥ _ (subset_scope) [in Waterproof.Notations.Sets]
𝒫( _ ) (subset_scope) [in Waterproof.Notations.Sets]
[ _ ] (subset_scope) [in Waterproof.Notations.Sets]
｛ _ : _ | _ ｝ (subset_scope) [in Waterproof.Notations.Sets]
_ is inhabited (subset_scope) [in Waterproof.Notations.Sets]
_ is empty (subset_scope) [in Waterproof.Notations.Sets]
_ ⊂ _ (subset_scope) [in Waterproof.Notations.Sets]
_ ∉ _ (subset_scope) [in Waterproof.Notations.Sets]
_ \ _ (subset_scope) [in Waterproof.Notations.Sets]
_ ∪ _ (subset_scope) [in Waterproof.Notations.Sets]
_ ∩ _ (subset_scope) [in Waterproof.Notations.Sets]
Ω (subset_scope) [in Waterproof.Notations.Sets]
∅ (subset_scope) [in Waterproof.Notations.Sets]
⋂_{ _ _ } _ (subset_scope) [in Waterproof.Notations.IndexedSets]
_ ≠ _ (type_scope) [in Waterproof.Notations.Common]
¬ _ (type_scope) [in Waterproof.Notations.Common]
_ ⇔ _ (type_scope) [in Waterproof.Notations.Common]
_ ↔ _ (type_scope) [in Waterproof.Notations.Common]
_ ⇨ _ (type_scope) [in Waterproof.Notations.Common]
_ ⇒ _ (type_scope) [in Waterproof.Notations.Common]
_ → _ (type_scope) [in Waterproof.Notations.Common]
_ ∧ _ (type_scope) [in Waterproof.Notations.Common]
_ ∨ _ (type_scope) [in Waterproof.Notations.Common]
fun _ .. _ ↦ _ (type_scope) [in Waterproof.Notations.Common]
_ ( _ , .. , _ ) (type_scope) [in Waterproof.Notations.Common]
for all _ , _ (type_scope) [in Waterproof.Notations.Sets]
∀ _ , _ (type_scope) [in Waterproof.Notations.Sets]
there exists _ , _ (type_scope) [in Waterproof.Notations.Sets]
∃ _ , _ (type_scope) [in Waterproof.Notations.Sets]
_ ∈ _ (type_scope) [in Waterproof.Notations.Sets]
_ ³ (Z_scope) [in Waterproof.Notations.Integers]
_ leaves a remainder of _ when divided by _ (Z_scope) [in Waterproof.Notations.Integers]
_ is a perfect square (Z_scope) [in Waterproof.Notations.Integers]
_ ² (Z_scope) [in Waterproof.Notations.Integers]
_ is odd (Z_scope) [in Waterproof.Notations.Integers]
_ is even (Z_scope) [in Waterproof.Notations.Integers]
_ is divisible by _ (Z_scope) [in Waterproof.Notations.Integers]
_ | _ (Z_scope) [in Waterproof.Notations.Integers]
_ diverges to -∞ [in Waterproof.Libs.Analysis.Sequences]
_ _diverges to -∞_ [in Waterproof.Libs.Analysis.Sequences]
_ ⟶ -∞ [in Waterproof.Libs.Analysis.Sequences]
_ diverges to ∞ [in Waterproof.Libs.Analysis.Sequences]
_ _diverges to ∞_ [in Waterproof.Libs.Analysis.Sequences]
_ ⟶ ∞ [in Waterproof.Libs.Analysis.Sequences]
_ is bounded below [in Waterproof.Libs.Analysis.Sequences]
_ is _bounded below_ [in Waterproof.Libs.Analysis.Sequences]
_ is bounded above [in Waterproof.Libs.Analysis.Sequences]
_ is _bounded above_ [in Waterproof.Libs.Analysis.Sequences]
_ is bounded [in Waterproof.Libs.Analysis.Sequences]
_ is _bounded_ [in Waterproof.Libs.Analysis.Sequences]
_ is continuous in _ [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is _continuous_ in _ [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an isolated point [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an _isolated point_ [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an accumulation point [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is an _accumulation point_ [in Waterproof.Libs.Analysis.ContinuityDomainR]
_ is a lower bound for _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is a _lower bound_ for _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is bounded from below [in Waterproof.Libs.Analysis.SupAndInf]
_ is _bounded from below_ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the infimum of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the _infimum_ of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the maximum of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the _maximum_ of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is an upper bound for _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is an _upper bound_ for _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is bounded from above [in Waterproof.Libs.Analysis.SupAndInf]
_ is _bounded from above_ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the supremum of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ is the _supremum_ of _ [in Waterproof.Libs.Analysis.SupAndInf]
_ ? [in Waterproof.Notations.Common]
_ ⟶ _ [in Waterproof.Notations.Reals]
_ is empty [in Waterproof.Notations.Sets]
_ is disjoint from _ [in Waterproof.Notations.Sets]
_ ◦ _ ◦ _ [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ ◦ _ [in Waterproof.Libs.Analysis.SubsequencesMetric]
_ is closed [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is _closed_ [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is open [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is _open_ [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is an interior point of _ [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is an _interior point_ of _ [in Waterproof.Libs.Analysis.OpenAndClosed]
_ is continuous in _ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is _continuous_ in _ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an isolated point [in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an _isolated point_ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an accumulation point [in Waterproof.Libs.Analysis.ContinuityDomainNat]
_ is an _accumulation point_ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
Add the following line to the proof: Take k ∈ ℕ and assume n_0,...,n_k are defined. [in Waterproof.Util.Goals]
Add the following line to the proof: - We first define n_0 . [in Waterproof.Util.Goals]
Add the following line to the proof: Assume that _ . [in Waterproof.Util.Goals]
Add the following line to the proof: It holds that _ . [in Waterproof.Util.Goals]
Add the following line to the proof: { Indeed, _ . } or write: { We need to verify that _ . } if intermediary proof steps are required. [in Waterproof.Util.Goals]
Add the following line to the proof: We need to show that _ . or write: We conclude that _ . if no intermediary proof steps are required. [in Waterproof.Util.Goals]
Add the following line to the proof: We now show the induction step. [in Waterproof.Util.Goals]
Add the following line to the proof: - We first show the base case _ . [in Waterproof.Util.Goals]
Add the following line to the proof: - Case _ . [in Waterproof.Util.Goals]
B( _ , _ ) [in Waterproof.Libs.Analysis.OpenAndClosed]
Derive a contradiction. [in Waterproof.Notations.Common]
Fix an earlier warning [in Waterproof.Util.Goals]
limit of _ in _ is _ [in Waterproof.Libs.Analysis.ContinuityDomainR]
limit of _ in _ is _ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
set_of_subsets _ [in Waterproof.Notations.Sets]
subset _ [in Waterproof.Notations.Sets]
the Archimedean property [in Waterproof.Libs.Reals.ArchimedN]
_limit_ of _ in _ is _ [in Waterproof.Libs.Analysis.ContinuityDomainR]
_limit_ of _ in _ is _ [in Waterproof.Libs.Analysis.ContinuityDomainNat]
& _ _ _ .. _ [in Waterproof.Chains.Inequalities]
[ ( % @ < _ holds [in Waterproof.Tactics.Because]
[ ( % @ < _ hold [in Waterproof.Tactics.Because]
[ ( % @ < _ as [in Waterproof.Tactics.Assume]
[ ( % @ < _ and [in Waterproof.Tactics.Assume]
[ ( % @ < _ or [in Waterproof.Tactics.Either]
[ ( % @ < _ it [in Waterproof.Tactics.ItHolds]
[ ( % @ < _ we [in Waterproof.Tactics.Conclusion]
Σ _ equals _ [in Waterproof.Notations.Reals]
ℕ [in Waterproof.Notations.Reals]
ℚ [in Waterproof.Notations.Reals]
ℝ [in Waterproof.Notations.Reals]
ℝ \ _ [in Waterproof.Libs.Analysis.OpenAndClosed]
ℝ\ _ [in Waterproof.Libs.Analysis.OpenAndClosed]
ℤ [in Waterproof.Notations.Reals]
⋃_{ _ _ } _ [in Waterproof.Notations.IndexedSets]
Binder Index
A
a0:18 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]a0:35 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a0:37 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a0:50 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a0:531 [in Waterproof.Libs.Analysis.SupAndInf]
a0:538 [in Waterproof.Libs.Analysis.SupAndInf]
a:1 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:1 [in Waterproof.Libs.Negation]
a:1 [in Waterproof.Libs.Analysis.Subsequences]
a:1 [in Waterproof.Libs.Analysis.ContinuityDomainR]
A:1 [in Waterproof.Libs.Analysis.SupAndInf]
A:1 [in Waterproof.Tactics.Either]
A:1 [in Waterproof.Util.Goals]
a:1 [in Waterproof.Notations.Reals]
A:1 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:1 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
a:1 [in Waterproof.Libs.Analysis.Series]
A:1 [in Waterproof.Libs.Reals.Intervals]
A:10 [in Waterproof.Libs.Sets.Operations]
a:10 [in Waterproof.Libs.Analysis.ContinuityDomainR]
a:10 [in Waterproof.Notations.Sets]
A:10 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:10 [in Waterproof.Libs.Reals.Intervals]
A:101 [in Waterproof.Libs.Analysis.SupAndInf]
A:102 [in Waterproof.Libs.Analysis.SupAndInf]
a:103 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:107 [in Waterproof.Libs.Analysis.SupAndInf]
a:108 [in Waterproof.Libs.Analysis.SupAndInf]
A:108 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:109 [in Waterproof.Libs.Analysis.Sequences]
A:11 [in Waterproof.Tactics.Either]
a:11 [in Waterproof.Notations.Sets]
a:11 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:111 [in Waterproof.Libs.Analysis.SupAndInf]
A:112 [in Waterproof.Libs.Analysis.SupAndInf]
a:114 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:115 [in Waterproof.Libs.Analysis.Sequences]
a:117 [in Waterproof.Libs.Analysis.SupAndInf]
a:117 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:118 [in Waterproof.Libs.Analysis.SupAndInf]
a:119 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:119 [in Waterproof.Libs.Analysis.SupAndInf]
A:12 [in Waterproof.Libs.Analysis.SupAndInf]
A:120 [in Waterproof.Libs.Analysis.SupAndInf]
a:120 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:121 [in Waterproof.Libs.Analysis.Sequences]
a:124 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:129 [in Waterproof.Libs.Analysis.SupAndInf]
a:129 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
A:13 [in Waterproof.Libs.Negation]
a:13 [in Waterproof.Libs.Reals]
A:130 [in Waterproof.Libs.Analysis.SupAndInf]
A:14 [in Waterproof.Libs.Sets.Operations]
A:14 [in Waterproof.Tactics.Either]
A:14 [in Waterproof.Libs.Analysis.OpenAndClosed]
a:14 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
A:140 [in Waterproof.Chains.Inequalities]
a:143 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:143 [in Waterproof.Libs.Analysis.SupAndInf]
a:144 [in Waterproof.Libs.Analysis.SupAndInf]
A:146 [in Waterproof.Chains.Inequalities]
A:15 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:15 [in Waterproof.Libs.Analysis.SubsequencesMetric]
a:15 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:152 [in Waterproof.Chains.Inequalities]
A:155 [in Waterproof.Libs.Analysis.SupAndInf]
A:156 [in Waterproof.Libs.Analysis.SupAndInf]
A:158 [in Waterproof.Chains.Inequalities]
A:16 [in Waterproof.Chains.Inequalities]
a:16 [in Waterproof.Libs.Analysis.Series]
a:16 [in Waterproof.Libs.Analysis.OpenAndClosed]
a:163 [in Waterproof.Libs.Analysis.Subsequences]
a:168 [in Waterproof.Libs.Analysis.Sequences]
A:17 [in Waterproof.Tactics.Either]
a:17 [in Waterproof.Libs.Analysis.SequencesMetric]
a:17 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:175 [in Waterproof.Libs.Analysis.SupAndInf]
A:176 [in Waterproof.Libs.Analysis.SupAndInf]
a:18 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:18 [in Waterproof.Libs.Analysis.SupAndInf]
a:18 [in Waterproof.Libs.Analysis.Series]
a:18 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:189 [in Waterproof.Libs.Analysis.SupAndInf]
A:19 [in Waterproof.Libs.Negation]
a:19 [in Waterproof.Libs.Reals.Rational]
A:19 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:190 [in Waterproof.Libs.Analysis.SupAndInf]
A:2 [in Waterproof.Libs.Sets.Operations]
a:2 [in Waterproof.Libs.Analysis.SequencesMetric]
a:20 [in Waterproof.Libs.Analysis.ContinuityDomainR]
A:20 [in Waterproof.Libs.Analysis.SupAndInf]
A:20 [in Waterproof.Tactics.Either]
a:20 [in Waterproof.Libs.Analysis.Series]
A:203 [in Waterproof.Libs.Analysis.SupAndInf]
A:204 [in Waterproof.Libs.Analysis.SupAndInf]
a:208 [in Waterproof.Libs.Analysis.Sequences]
a:21 [in Waterproof.Libs.Reals]
A:21 [in Waterproof.Libs.Analysis.OpenAndClosed]
a:21 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
A:213 [in Waterproof.Libs.Analysis.SupAndInf]
A:214 [in Waterproof.Libs.Analysis.SupAndInf]
a:22 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:22 [in Waterproof.Libs.Analysis.Series]
A:22 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:227 [in Waterproof.Libs.Analysis.SupAndInf]
A:228 [in Waterproof.Libs.Analysis.SupAndInf]
A:23 [in Waterproof.Tactics.Either]
a:23 [in Waterproof.Libs.Analysis.SubsequencesMetric]
a:23 [in Waterproof.Libs.Reals]
a:233 [in Waterproof.Libs.Analysis.Sequences]
a:235 [in Waterproof.Libs.Analysis.SupAndInf]
a:236 [in Waterproof.Libs.Analysis.SupAndInf]
a:237 [in Waterproof.Libs.Analysis.SupAndInf]
a:238 [in Waterproof.Libs.Analysis.SupAndInf]
a:239 [in Waterproof.Libs.Analysis.SupAndInf]
A:24 [in Waterproof.Libs.Analysis.OpenAndClosed]
a:240 [in Waterproof.Libs.Analysis.SupAndInf]
A:243 [in Waterproof.Libs.Analysis.SupAndInf]
A:244 [in Waterproof.Libs.Analysis.SupAndInf]
a:245 [in Waterproof.Libs.Analysis.Sequences]
A:25 [in Waterproof.Libs.Negation]
a:25 [in Waterproof.Libs.Reals.Rational]
a:25 [in Waterproof.Libs.Analysis.Series]
a:253 [in Waterproof.Libs.Analysis.SupAndInf]
a:254 [in Waterproof.Libs.Analysis.SupAndInf]
a:255 [in Waterproof.Libs.Analysis.SupAndInf]
a:256 [in Waterproof.Libs.Analysis.SupAndInf]
a:257 [in Waterproof.Libs.Analysis.SupAndInf]
a:258 [in Waterproof.Libs.Analysis.SupAndInf]
A:261 [in Waterproof.Libs.Analysis.SupAndInf]
A:262 [in Waterproof.Libs.Analysis.SupAndInf]
a:269 [in Waterproof.Libs.Analysis.SupAndInf]
A:27 [in Waterproof.Libs.Analysis.SupAndInf]
a:270 [in Waterproof.Libs.Analysis.SupAndInf]
a:271 [in Waterproof.Libs.Analysis.SupAndInf]
a:272 [in Waterproof.Libs.Analysis.SupAndInf]
a:279 [in Waterproof.Libs.Analysis.SupAndInf]
A:28 [in Waterproof.Chains.Inequalities]
a:280 [in Waterproof.Libs.Analysis.SupAndInf]
a:281 [in Waterproof.Libs.Analysis.SupAndInf]
a:282 [in Waterproof.Libs.Analysis.SupAndInf]
a:283 [in Waterproof.Libs.Analysis.SupAndInf]
a:284 [in Waterproof.Libs.Analysis.SupAndInf]
a:285 [in Waterproof.Libs.Analysis.Sequences]
A:285 [in Waterproof.Libs.Analysis.SupAndInf]
A:286 [in Waterproof.Libs.Analysis.SupAndInf]
a:29 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:29 [in Waterproof.Libs.Negation]
A:29 [in Waterproof.Libs.Analysis.SupAndInf]
a:295 [in Waterproof.Libs.Analysis.SupAndInf]
a:296 [in Waterproof.Libs.Analysis.SupAndInf]
a:297 [in Waterproof.Libs.Analysis.SupAndInf]
a:298 [in Waterproof.Libs.Analysis.Sequences]
a:298 [in Waterproof.Libs.Analysis.SupAndInf]
a:3 [in Waterproof.Libs.Analysis.Sequences]
a:3 [in Waterproof.Libs.Analysis.SupAndInf]
A:3 [in Waterproof.Tactics.Either]
a:305 [in Waterproof.Libs.Analysis.SupAndInf]
a:306 [in Waterproof.Libs.Analysis.SupAndInf]
a:307 [in Waterproof.Libs.Analysis.Sequences]
a:307 [in Waterproof.Libs.Analysis.SupAndInf]
a:308 [in Waterproof.Libs.Analysis.SupAndInf]
a:309 [in Waterproof.Libs.Analysis.SupAndInf]
A:31 [in Waterproof.Libs.Analysis.SupAndInf]
a:31 [in Waterproof.Libs.Analysis.SequencesMetric]
a:31 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:310 [in Waterproof.Libs.Analysis.SupAndInf]
A:311 [in Waterproof.Libs.Analysis.SupAndInf]
A:312 [in Waterproof.Libs.Analysis.SupAndInf]
a:32 [in Waterproof.Libs.Analysis.SupAndInf]
A:32 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:321 [in Waterproof.Libs.Analysis.SupAndInf]
a:322 [in Waterproof.Libs.Analysis.SupAndInf]
a:323 [in Waterproof.Libs.Analysis.SupAndInf]
a:324 [in Waterproof.Libs.Analysis.SupAndInf]
A:33 [in Waterproof.Libs.Negation]
a:33 [in Waterproof.Libs.Analysis.SupAndInf]
a:33 [in Waterproof.Libs.Reals.Rational]
A:33 [in Waterproof.Util.Goals]
a:33 [in Waterproof.Libs.Reals]
a:331 [in Waterproof.Libs.Analysis.SupAndInf]
a:332 [in Waterproof.Libs.Analysis.SupAndInf]
a:333 [in Waterproof.Libs.Analysis.SupAndInf]
a:334 [in Waterproof.Libs.Analysis.SupAndInf]
A:335 [in Waterproof.Libs.Analysis.SupAndInf]
A:336 [in Waterproof.Libs.Analysis.SupAndInf]
a:34 [in Waterproof.Libs.Analysis.SupAndInf]
a:345 [in Waterproof.Libs.Analysis.SupAndInf]
a:346 [in Waterproof.Libs.Analysis.SupAndInf]
a:347 [in Waterproof.Libs.Analysis.SupAndInf]
a:348 [in Waterproof.Libs.Analysis.SupAndInf]
a:35 [in Waterproof.Libs.Analysis.ContinuityDomainR]
a:35 [in Waterproof.Libs.Analysis.SupAndInf]
a:35 [in Waterproof.Libs.Reals]
a:355 [in Waterproof.Libs.Analysis.SupAndInf]
a:356 [in Waterproof.Libs.Analysis.SupAndInf]
a:357 [in Waterproof.Libs.Analysis.SupAndInf]
a:358 [in Waterproof.Libs.Analysis.SupAndInf]
A:359 [in Waterproof.Libs.Analysis.SupAndInf]
a:36 [in Waterproof.Libs.Analysis.ContinuityDomainR]
A:360 [in Waterproof.Libs.Analysis.SupAndInf]
a:369 [in Waterproof.Libs.Analysis.SupAndInf]
A:37 [in Waterproof.Libs.Negation]
a:37 [in Waterproof.Libs.Reals.Rational]
A:37 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:370 [in Waterproof.Libs.Analysis.SupAndInf]
a:371 [in Waterproof.Libs.Analysis.SupAndInf]
a:372 [in Waterproof.Libs.Analysis.SupAndInf]
A:373 [in Waterproof.Libs.Analysis.SupAndInf]
A:374 [in Waterproof.Libs.Analysis.SupAndInf]
a:376 [in Waterproof.Libs.Analysis.Sequences]
A:38 [in Waterproof.Util.Goals]
a:383 [in Waterproof.Libs.Analysis.SupAndInf]
a:384 [in Waterproof.Libs.Analysis.SupAndInf]
a:385 [in Waterproof.Libs.Analysis.Sequences]
a:385 [in Waterproof.Libs.Analysis.SupAndInf]
a:386 [in Waterproof.Libs.Analysis.SupAndInf]
A:387 [in Waterproof.Libs.Analysis.SupAndInf]
a:393 [in Waterproof.Libs.Analysis.SupAndInf]
a:394 [in Waterproof.Libs.Analysis.Sequences]
a:394 [in Waterproof.Libs.Analysis.SupAndInf]
a:395 [in Waterproof.Libs.Analysis.SupAndInf]
a:396 [in Waterproof.Libs.Analysis.SupAndInf]
A:397 [in Waterproof.Libs.Analysis.SupAndInf]
a:4 [in Waterproof.Libs.Analysis.SupAndInf]
A:4 [in Waterproof.Notations.Sets]
a:4 [in Waterproof.Libs.Analysis.OpenAndClosed]
a:4 [in Waterproof.Libs.Reals.Intervals]
a:403 [in Waterproof.Libs.Analysis.SupAndInf]
a:404 [in Waterproof.Libs.Analysis.SupAndInf]
a:405 [in Waterproof.Libs.Analysis.SupAndInf]
a:406 [in Waterproof.Libs.Analysis.SupAndInf]
a:407 [in Waterproof.Libs.Analysis.Sequences]
A:407 [in Waterproof.Libs.Analysis.SupAndInf]
A:41 [in Waterproof.Libs.Negation]
a:41 [in Waterproof.Libs.Reals.Rational]
A:41 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:411 [in Waterproof.Libs.Analysis.SupAndInf]
a:412 [in Waterproof.Libs.Analysis.SupAndInf]
a:423 [in Waterproof.Libs.Analysis.SupAndInf]
a:424 [in Waterproof.Libs.Analysis.SupAndInf]
a:427 [in Waterproof.Libs.Analysis.SupAndInf]
a:428 [in Waterproof.Libs.Analysis.SupAndInf]
A:43 [in Waterproof.Util.Goals]
a:431 [in Waterproof.Libs.Analysis.SupAndInf]
a:432 [in Waterproof.Libs.Analysis.SupAndInf]
A:44 [in Waterproof.Libs.Negation]
a:445 [in Waterproof.Libs.Analysis.SupAndInf]
a:446 [in Waterproof.Libs.Analysis.SupAndInf]
a:447 [in Waterproof.Libs.Analysis.SupAndInf]
a:448 [in Waterproof.Libs.Analysis.SupAndInf]
A:449 [in Waterproof.Libs.Analysis.SupAndInf]
a:45 [in Waterproof.Libs.Analysis.Sequences]
a:45 [in Waterproof.Libs.Reals.Rational]
a:453 [in Waterproof.Libs.Analysis.SupAndInf]
a:454 [in Waterproof.Libs.Analysis.SupAndInf]
a:46 [in Waterproof.Libs.Analysis.ContinuityDomainR]
a:46 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:465 [in Waterproof.Libs.Analysis.SupAndInf]
a:466 [in Waterproof.Libs.Analysis.SupAndInf]
a:469 [in Waterproof.Libs.Analysis.SupAndInf]
A:47 [in Waterproof.Libs.Negation]
A:47 [in Waterproof.Util.Goals]
A:47 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:470 [in Waterproof.Libs.Analysis.SupAndInf]
a:473 [in Waterproof.Libs.Analysis.SupAndInf]
a:474 [in Waterproof.Libs.Analysis.SupAndInf]
a:477 [in Waterproof.Libs.Analysis.SupAndInf]
a:478 [in Waterproof.Libs.Analysis.SupAndInf]
a:48 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
a:49 [in Waterproof.Libs.Reals.Rational]
A:491 [in Waterproof.Libs.Analysis.SupAndInf]
A:492 [in Waterproof.Libs.Analysis.SupAndInf]
a:497 [in Waterproof.Libs.Analysis.SupAndInf]
a:498 [in Waterproof.Libs.Analysis.SupAndInf]
a:499 [in Waterproof.Libs.Analysis.SupAndInf]
A:5 [in Waterproof.Libs.Negation]
a:5 [in Waterproof.Libs.Analysis.SupAndInf]
A:5 [in Waterproof.Waterprove]
a:5 [in Waterproof.Libs.Reals.RealInequalities]
A:5 [in Waterproof.Util.Goals]
a:5 [in Waterproof.Libs.Analysis.Series]
A:5 [in Waterproof.Libs.Analysis.OpenAndClosed]
A:50 [in Waterproof.Libs.Negation]
a:500 [in Waterproof.Libs.Analysis.SupAndInf]
a:501 [in Waterproof.Libs.Analysis.SupAndInf]
a:502 [in Waterproof.Libs.Analysis.SupAndInf]
a:503 [in Waterproof.Libs.Analysis.SupAndInf]
a:504 [in Waterproof.Libs.Analysis.SupAndInf]
a:505 [in Waterproof.Libs.Analysis.SupAndInf]
a:506 [in Waterproof.Libs.Analysis.SupAndInf]
a:507 [in Waterproof.Libs.Analysis.SupAndInf]
a:508 [in Waterproof.Libs.Analysis.SupAndInf]
A:509 [in Waterproof.Libs.Analysis.SupAndInf]
A:512 [in Waterproof.Libs.Analysis.SupAndInf]
a:515 [in Waterproof.Libs.Analysis.SupAndInf]
a:516 [in Waterproof.Libs.Analysis.SupAndInf]
A:53 [in Waterproof.Libs.Negation]
a:543 [in Waterproof.Libs.Analysis.SupAndInf]
a:544 [in Waterproof.Libs.Analysis.SupAndInf]
a:55 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
a:55 [in Waterproof.Libs.Analysis.Subsequences]
a:55 [in Waterproof.Libs.Analysis.Sequences]
a:55 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:551 [in Waterproof.Libs.Analysis.SupAndInf]
A:59 [in Waterproof.Libs.Negation]
A:6 [in Waterproof.Libs.Sets.Operations]
a:6 [in Waterproof.Libs.Analysis.SupAndInf]
A:6 [in Waterproof.Notations.Sets]
a:6 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
a:6 [in Waterproof.Libs.Reals.Intervals]
A:61 [in Waterproof.Libs.Analysis.SupAndInf]
A:62 [in Waterproof.Libs.Analysis.SupAndInf]
a:63 [in Waterproof.Libs.Analysis.SupAndInf]
a:64 [in Waterproof.Libs.Analysis.SupAndInf]
A:65 [in Waterproof.Libs.Negation]
A:66 [in Waterproof.Libs.Analysis.SupAndInf]
a:68 [in Waterproof.Libs.Analysis.Subsequences]
a:68 [in Waterproof.Libs.Analysis.SupAndInf]
a:69 [in Waterproof.Libs.Analysis.SupAndInf]
a:69 [in Waterproof.Notations.Sets]
A:7 [in Waterproof.Libs.Analysis.SupAndInf]
A:7 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:70 [in Waterproof.Libs.Analysis.SupAndInf]
A:71 [in Waterproof.Libs.Negation]
a:71 [in Waterproof.Libs.Analysis.SupAndInf]
A:72 [in Waterproof.Libs.Analysis.SupAndInf]
a:72 [in Waterproof.Libs.Analysis.SubsequencesMetric]
A:77 [in Waterproof.Libs.Negation]
A:77 [in Waterproof.Libs.Analysis.SupAndInf]
A:79 [in Waterproof.Libs.Negation]
A:8 [in Waterproof.Tactics.Either]
a:8 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
a:8 [in Waterproof.Libs.Reals.Intervals]
A:83 [in Waterproof.Libs.Analysis.SupAndInf]
A:85 [in Waterproof.Libs.Analysis.SupAndInf]
a:86 [in Waterproof.Libs.Analysis.Sequences]
A:86 [in Waterproof.Libs.Analysis.SupAndInf]
a:86 [in Waterproof.Libs.Functions]
a:87 [in Waterproof.Libs.Functions]
a:88 [in Waterproof.Libs.Functions]
a:89 [in Waterproof.Libs.Functions]
a:9 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:9 [in Waterproof.Libs.Negation]
a:91 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
A:93 [in Waterproof.Libs.Analysis.SupAndInf]
A:94 [in Waterproof.Libs.Analysis.SupAndInf]
a:97 [in Waterproof.Libs.Functions]
B
B:10 [in Waterproof.Libs.Negation]b:100 [in Waterproof.Libs.Analysis.SupAndInf]
b:109 [in Waterproof.Libs.Analysis.SupAndInf]
B:109 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
B:11 [in Waterproof.Libs.Sets.Operations]
b:11 [in Waterproof.Libs.Reals.Intervals]
b:110 [in Waterproof.Libs.Analysis.Sequences]
b:110 [in Waterproof.Libs.Analysis.SupAndInf]
b:115 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:116 [in Waterproof.Libs.Analysis.Sequences]
b:118 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
B:12 [in Waterproof.Tactics.Either]
b:121 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:122 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:123 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:126 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:128 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:129 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:131 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:134 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:138 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:14 [in Waterproof.Libs.Analysis.SubsequencesMetric]
b:14 [in Waterproof.Libs.Reals]
B:141 [in Waterproof.Chains.Inequalities]
B:147 [in Waterproof.Chains.Inequalities]
B:15 [in Waterproof.Libs.Sets.Operations]
B:15 [in Waterproof.Tactics.Either]
b:153 [in Waterproof.Libs.Analysis.SupAndInf]
B:153 [in Waterproof.Chains.Inequalities]
b:154 [in Waterproof.Libs.Analysis.SupAndInf]
B:159 [in Waterproof.Chains.Inequalities]
b:169 [in Waterproof.Libs.Analysis.Sequences]
B:17 [in Waterproof.Chains.Inequalities]
B:18 [in Waterproof.Tactics.Either]
b:181 [in Waterproof.Libs.Analysis.SupAndInf]
b:182 [in Waterproof.Libs.Analysis.SupAndInf]
b:183 [in Waterproof.Libs.Analysis.SupAndInf]
b:184 [in Waterproof.Libs.Analysis.SupAndInf]
B:2 [in Waterproof.Libs.Negation]
B:2 [in Waterproof.Tactics.Either]
b:20 [in Waterproof.Libs.Reals.Rational]
B:21 [in Waterproof.Tactics.Either]
b:22 [in Waterproof.Libs.Reals]
B:24 [in Waterproof.Tactics.Either]
b:24 [in Waterproof.Libs.Reals]
b:246 [in Waterproof.Libs.Analysis.Sequences]
B:26 [in Waterproof.Libs.Negation]
b:26 [in Waterproof.Libs.Reals.Rational]
B:29 [in Waterproof.Chains.Inequalities]
B:3 [in Waterproof.Libs.Sets.Operations]
B:30 [in Waterproof.Libs.Negation]
B:34 [in Waterproof.Libs.Negation]
b:34 [in Waterproof.Libs.Reals.Rational]
b:34 [in Waterproof.Libs.Reals]
b:36 [in Waterproof.Libs.Reals]
B:38 [in Waterproof.Libs.Negation]
b:38 [in Waterproof.Libs.Reals.Rational]
B:4 [in Waterproof.Tactics.Either]
b:4 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
b:40 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:41 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
B:42 [in Waterproof.Libs.Negation]
b:42 [in Waterproof.Libs.Reals.Rational]
b:44 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
b:45 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
B:45 [in Waterproof.Libs.Negation]
b:46 [in Waterproof.Libs.Analysis.Sequences]
b:46 [in Waterproof.Libs.Reals.Rational]
B:48 [in Waterproof.Libs.Negation]
b:5 [in Waterproof.Libs.Reals.Intervals]
B:51 [in Waterproof.Libs.Negation]
b:511 [in Waterproof.Libs.Analysis.SupAndInf]
b:514 [in Waterproof.Libs.Analysis.SupAndInf]
b:56 [in Waterproof.Libs.Analysis.Sequences]
B:6 [in Waterproof.Libs.Negation]
B:6 [in Waterproof.Waterprove]
b:6 [in Waterproof.Libs.Reals.RealInequalities]
B:7 [in Waterproof.Libs.Sets.Operations]
b:7 [in Waterproof.Libs.Reals.Intervals]
B:78 [in Waterproof.Libs.Negation]
B:80 [in Waterproof.Libs.Negation]
b:87 [in Waterproof.Libs.Analysis.Sequences]
B:9 [in Waterproof.Tactics.Either]
b:9 [in Waterproof.Libs.Reals.Intervals]
b:90 [in Waterproof.Libs.Functions]
b:91 [in Waterproof.Libs.Analysis.SupAndInf]
b:91 [in Waterproof.Libs.Functions]
b:92 [in Waterproof.Libs.Analysis.SupAndInf]
b:92 [in Waterproof.Libs.Functions]
b:93 [in Waterproof.Libs.Functions]
b:98 [in Waterproof.Libs.Functions]
b:99 [in Waterproof.Libs.Analysis.SupAndInf]
C
carrier:19 [in Waterproof.Notations.Sets]carrier:26 [in Waterproof.Notations.Sets]
carrier:33 [in Waterproof.Notations.Sets]
carrier:40 [in Waterproof.Notations.Sets]
carrier:47 [in Waterproof.Notations.Sets]
C:10 [in Waterproof.Tactics.Either]
c:100 [in Waterproof.Chains.Inequalities]
c:103 [in Waterproof.Chains.Inequalities]
c:106 [in Waterproof.Chains.Inequalities]
C:11 [in Waterproof.Libs.Negation]
C:110 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:113 [in Waterproof.Chains.Inequalities]
c:116 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:116 [in Waterproof.Chains.Inequalities]
c:119 [in Waterproof.Chains.Inequalities]
c:123 [in Waterproof.Libs.Analysis.Sequences]
c:125 [in Waterproof.Libs.Analysis.Sequences]
C:13 [in Waterproof.Tactics.Either]
c:143 [in Waterproof.Chains.Inequalities]
c:149 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:149 [in Waterproof.Chains.Inequalities]
c:151 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
c:155 [in Waterproof.Chains.Inequalities]
C:16 [in Waterproof.Tactics.Either]
C:160 [in Waterproof.Chains.Inequalities]
c:170 [in Waterproof.Libs.Analysis.Sequences]
C:18 [in Waterproof.Chains.Inequalities]
C:19 [in Waterproof.Tactics.Either]
c:2 [in Waterproof.Notations.Reals]
c:21 [in Waterproof.Libs.Reals.Rational]
C:22 [in Waterproof.Tactics.Either]
C:25 [in Waterproof.Tactics.Either]
C:27 [in Waterproof.Libs.Negation]
c:27 [in Waterproof.Libs.Reals.Rational]
C:3 [in Waterproof.Libs.Negation]
c:3 [in Waterproof.Libs.Analysis.SequencesMetric]
C:30 [in Waterproof.Chains.Inequalities]
C:31 [in Waterproof.Libs.Negation]
C:35 [in Waterproof.Libs.Negation]
c:37 [in Waterproof.Chains.Inequalities]
C:39 [in Waterproof.Libs.Negation]
c:41 [in Waterproof.Chains.Inequalities]
C:43 [in Waterproof.Libs.Negation]
c:45 [in Waterproof.Chains.Inequalities]
C:46 [in Waterproof.Libs.Negation]
C:49 [in Waterproof.Libs.Negation]
c:49 [in Waterproof.Chains.Inequalities]
C:5 [in Waterproof.Tactics.Either]
c:5 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
C:52 [in Waterproof.Libs.Negation]
c:52 [in Waterproof.Chains.Inequalities]
c:55 [in Waterproof.Chains.Inequalities]
C:58 [in Waterproof.Chains.Inequalities]
C:7 [in Waterproof.Libs.Negation]
C:7 [in Waterproof.Waterprove]
c:7 [in Waterproof.Libs.Reals.RealInequalities]
c:72 [in Waterproof.Chains.Inequalities]
c:75 [in Waterproof.Chains.Inequalities]
c:87 [in Waterproof.Chains.Inequalities]
c:91 [in Waterproof.Chains.Inequalities]
D
D:111 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]D:12 [in Waterproof.Libs.Negation]
d:122 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:127 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:132 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:136 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:140 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:142 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:145 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
d:22 [in Waterproof.Libs.Reals.Rational]
D:28 [in Waterproof.Libs.Negation]
d:28 [in Waterproof.Libs.Reals.Rational]
D:32 [in Waterproof.Libs.Negation]
D:36 [in Waterproof.Libs.Negation]
D:4 [in Waterproof.Libs.Negation]
D:40 [in Waterproof.Libs.Negation]
D:8 [in Waterproof.Libs.Negation]
E
ecn:167 [in Waterproof.Chains.Inequalities]ecn:175 [in Waterproof.Chains.Inequalities]
ecn:191 [in Waterproof.Chains.Inequalities]
ecn:207 [in Waterproof.Chains.Inequalities]
ecn:215 [in Waterproof.Chains.Inequalities]
ecn:231 [in Waterproof.Chains.Inequalities]
ecx:169 [in Waterproof.Chains.Inequalities]
ecx:177 [in Waterproof.Chains.Inequalities]
ecx:193 [in Waterproof.Chains.Inequalities]
ecx:209 [in Waterproof.Chains.Inequalities]
ecx:217 [in Waterproof.Chains.Inequalities]
ecx:233 [in Waterproof.Chains.Inequalities]
eps:219 [in Waterproof.Libs.Analysis.Sequences]
eps:220 [in Waterproof.Libs.Analysis.Sequences]
eps:257 [in Waterproof.Libs.Analysis.Sequences]
eps:258 [in Waterproof.Libs.Analysis.Sequences]
eps:265 [in Waterproof.Libs.Analysis.Sequences]
eps:266 [in Waterproof.Libs.Analysis.Sequences]
EqualInterpretation0:71 [in Waterproof.Chains.Inequalities]
EqualInterpretation0:74 [in Waterproof.Chains.Inequalities]
EqualInterpretation0:79 [in Waterproof.Chains.Inequalities]
E:112 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:123 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:128 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:133 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:137 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:141 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:144 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:147 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:148 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
e:150 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
F
f:10 [in Waterproof.Libs.Analysis.Subsequences]f:101 [in Waterproof.Libs.Functions]
f:110 [in Waterproof.Libs.Analysis.Subsequences]
f:112 [in Waterproof.Libs.Functions]
f:119 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:120 [in Waterproof.Libs.Functions]
f:123 [in Waterproof.Libs.Functions]
f:125 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:126 [in Waterproof.Libs.Functions]
f:129 [in Waterproof.Libs.Functions]
f:130 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:133 [in Waterproof.Libs.Functions]
f:135 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:138 [in Waterproof.Libs.Functions]
f:139 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:142 [in Waterproof.Libs.Functions]
f:142 [in Waterproof.Chains.Inequalities]
f:143 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:146 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
f:147 [in Waterproof.Libs.Functions]
f:148 [in Waterproof.Chains.Inequalities]
f:151 [in Waterproof.Libs.Functions]
f:154 [in Waterproof.Chains.Inequalities]
f:156 [in Waterproof.Libs.Functions]
f:160 [in Waterproof.Libs.Functions]
f:161 [in Waterproof.Chains.Inequalities]
f:165 [in Waterproof.Libs.Functions]
f:169 [in Waterproof.Libs.Analysis.Subsequences]
f:170 [in Waterproof.Libs.Analysis.Subsequences]
f:173 [in Waterproof.Libs.Functions]
f:175 [in Waterproof.Libs.Analysis.Subsequences]
f:181 [in Waterproof.Libs.Functions]
f:186 [in Waterproof.Libs.Analysis.Subsequences]
f:189 [in Waterproof.Libs.Functions]
f:19 [in Waterproof.Libs.Analysis.ContinuityDomainR]
f:193 [in Waterproof.Libs.Analysis.Subsequences]
f:197 [in Waterproof.Libs.Functions]
f:201 [in Waterproof.Libs.Functions]
f:205 [in Waterproof.Libs.Functions]
f:213 [in Waterproof.Libs.Functions]
f:221 [in Waterproof.Libs.Functions]
f:30 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
f:34 [in Waterproof.Libs.Analysis.ContinuityDomainR]
f:38 [in Waterproof.Libs.Analysis.Subsequences]
f:39 [in Waterproof.Libs.Functions]
f:45 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
f:48 [in Waterproof.Libs.Functions]
f:57 [in Waterproof.Libs.Functions]
f:66 [in Waterproof.Libs.Functions]
f:75 [in Waterproof.Libs.Functions]
f:80 [in Waterproof.Libs.Functions]
f:85 [in Waterproof.Libs.Functions]
f:9 [in Waterproof.Libs.Analysis.Subsequences]
f:96 [in Waterproof.Libs.Functions]
G
gcn:195 [in Waterproof.Chains.Inequalities]gcn:199 [in Waterproof.Chains.Inequalities]
gcn:235 [in Waterproof.Chains.Inequalities]
gcn:239 [in Waterproof.Chains.Inequalities]
gcx:197 [in Waterproof.Chains.Inequalities]
gcx:201 [in Waterproof.Chains.Inequalities]
gcx:237 [in Waterproof.Chains.Inequalities]
gcx:241 [in Waterproof.Chains.Inequalities]
g:115 [in Waterproof.Libs.Analysis.Subsequences]
g:12 [in Waterproof.Libs.Functions]
G:12 [in Waterproof.Util.Goals]
g:134 [in Waterproof.Libs.Functions]
g:139 [in Waterproof.Libs.Functions]
g:143 [in Waterproof.Libs.Functions]
g:144 [in Waterproof.Libs.Functions]
g:148 [in Waterproof.Libs.Functions]
G:15 [in Waterproof.Util.Goals]
g:152 [in Waterproof.Libs.Functions]
g:153 [in Waterproof.Libs.Functions]
g:157 [in Waterproof.Libs.Functions]
g:161 [in Waterproof.Libs.Functions]
g:162 [in Waterproof.Libs.Functions]
g:166 [in Waterproof.Libs.Functions]
g:174 [in Waterproof.Libs.Functions]
g:179 [in Waterproof.Libs.Analysis.Subsequences]
G:18 [in Waterproof.Util.Goals]
g:182 [in Waterproof.Libs.Functions]
g:184 [in Waterproof.Libs.Analysis.Subsequences]
g:190 [in Waterproof.Libs.Analysis.Subsequences]
g:190 [in Waterproof.Libs.Functions]
g:197 [in Waterproof.Libs.Analysis.Subsequences]
g:198 [in Waterproof.Libs.Functions]
G:2 [in Waterproof.Util.Goals]
g:202 [in Waterproof.Libs.Functions]
g:206 [in Waterproof.Libs.Functions]
g:21 [in Waterproof.Libs.Functions]
G:21 [in Waterproof.Util.Goals]
g:214 [in Waterproof.Libs.Functions]
g:222 [in Waterproof.Libs.Functions]
g:23 [in Waterproof.Libs.Analysis.Subsequences]
g:24 [in Waterproof.Libs.Analysis.Subsequences]
G:24 [in Waterproof.Util.Goals]
G:27 [in Waterproof.Util.Goals]
g:3 [in Waterproof.Libs.Functions]
g:30 [in Waterproof.Libs.Functions]
G:30 [in Waterproof.Util.Goals]
G:35 [in Waterproof.Util.Goals]
g:35 [in Waterproof.Libs.Analysis.SubsequencesMetric]
G:40 [in Waterproof.Util.Goals]
g:40 [in Waterproof.Libs.Analysis.SubsequencesMetric]
g:42 [in Waterproof.Libs.Analysis.Subsequences]
G:44 [in Waterproof.Util.Goals]
G:48 [in Waterproof.Util.Goals]
G:51 [in Waterproof.Util.Goals]
G:54 [in Waterproof.Util.Goals]
g:56 [in Waterproof.Libs.Analysis.Subsequences]
G:57 [in Waterproof.Util.Goals]
G:6 [in Waterproof.Util.Goals]
G:60 [in Waterproof.Util.Goals]
g:86 [in Waterproof.Libs.Analysis.Subsequences]
g:87 [in Waterproof.Libs.Analysis.Subsequences]
G:9 [in Waterproof.Util.Goals]
H
ha:35 [in Waterproof.Libs.Reals.Rational]ha:39 [in Waterproof.Libs.Reals.Rational]
ha:43 [in Waterproof.Libs.Reals.Rational]
ha:47 [in Waterproof.Libs.Reals.Rational]
ha:50 [in Waterproof.Libs.Reals.Rational]
hb:23 [in Waterproof.Libs.Reals.Rational]
hb:29 [in Waterproof.Libs.Reals.Rational]
hb:36 [in Waterproof.Libs.Reals.Rational]
hb:40 [in Waterproof.Libs.Reals.Rational]
hb:44 [in Waterproof.Libs.Reals.Rational]
hb:48 [in Waterproof.Libs.Reals.Rational]
hd:24 [in Waterproof.Libs.Reals.Rational]
hd:30 [in Waterproof.Libs.Reals.Rational]
hm:18 [in Waterproof.Libs.Reals.Rational]
hna:10 [in Waterproof.Libs.Reals.RealInequalities]
hnc:9 [in Waterproof.Libs.Reals.RealInequalities]
hnx:3 [in Waterproof.Libs.Reals.RealInequalities]
hny:4 [in Waterproof.Libs.Reals.RealInequalities]
hn:17 [in Waterproof.Libs.Reals.Rational]
hn:32 [in Waterproof.Libs.Reals.Rational]
hp:23 [in Waterproof.Libs.Integers.Even]
hp:26 [in Waterproof.Libs.Integers.Even]
hp:9 [in Waterproof.Libs.Integers.Square]
hq:15 [in Waterproof.Libs.Reals.Rational]
Hstep:101 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:160 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:189 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:23 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Hstep:57 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
HypP:17 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
HypP:49 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:154 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:174 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:19 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:51 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
H0:95 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
h:16 [in Waterproof.Libs.Reals.Rational]
h:24 [in Waterproof.Libs.Integers.Divisibility]
h:30 [in Waterproof.Libs.Analysis.Subsequences]
h:34 [in Waterproof.Util.Goals]
h:39 [in Waterproof.Util.Goals]
h:45 [in Waterproof.Libs.Analysis.ContinuityDomainR]
h:47 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
h:8 [in Waterproof.Libs.Reals.RealInequalities]
I
ii:11 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]ii:121 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
ii:20 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
ii:57 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:1 [in Waterproof.Notations.IndexedSets]
i:10 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:104 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
I:11 [in Waterproof.Libs.Sets.IndexedOperations]
i:12 [in Waterproof.Libs.Sets.IndexedOperations]
i:120 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:15 [in Waterproof.Libs.Sets.IndexedOperations]
i:16 [in Waterproof.Libs.Sets.IndexedOperations]
i:17 [in Waterproof.Libs.Sets.IndexedOperations]
i:18 [in Waterproof.Libs.Sets.IndexedOperations]
i:19 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:2 [in Waterproof.Notations.IndexedSets]
I:21 [in Waterproof.Libs.Sets.IndexedOperations]
i:22 [in Waterproof.Libs.Sets.IndexedOperations]
i:25 [in Waterproof.Libs.Sets.IndexedOperations]
i:26 [in Waterproof.Libs.Sets.IndexedOperations]
i:27 [in Waterproof.Libs.Sets.IndexedOperations]
i:28 [in Waterproof.Libs.Sets.IndexedOperations]
I:3 [in Waterproof.Libs.Sets.IndexedOperations]
i:30 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
I:31 [in Waterproof.Libs.Sets.IndexedOperations]
i:36 [in Waterproof.Libs.Sets.IndexedOperations]
I:39 [in Waterproof.Libs.Sets.IndexedOperations]
i:40 [in Waterproof.Libs.Sets.IndexedOperations]
i:43 [in Waterproof.Libs.Sets.IndexedOperations]
i:44 [in Waterproof.Libs.Sets.IndexedOperations]
i:45 [in Waterproof.Libs.Sets.IndexedOperations]
i:46 [in Waterproof.Libs.Sets.IndexedOperations]
I:49 [in Waterproof.Libs.Sets.IndexedOperations]
i:50 [in Waterproof.Libs.Sets.IndexedOperations]
i:53 [in Waterproof.Libs.Sets.IndexedOperations]
i:54 [in Waterproof.Libs.Sets.IndexedOperations]
i:55 [in Waterproof.Libs.Sets.IndexedOperations]
i:56 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
i:56 [in Waterproof.Libs.Sets.IndexedOperations]
i:8 [in Waterproof.Libs.Sets.IndexedOperations]
K
k0:138 [in Waterproof.Libs.Analysis.Subsequences]k0:139 [in Waterproof.Libs.Analysis.Subsequences]
k0:143 [in Waterproof.Libs.Analysis.Subsequences]
k0:144 [in Waterproof.Libs.Analysis.Subsequences]
k0:33 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k0:34 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k1:54 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:55 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:56 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:57 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:67 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k1:68 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:58 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:59 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:60 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:61 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:69 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k2:70 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:10 [in Waterproof.Tactics.Induction]
k:10 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:100 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:100 [in Waterproof.Libs.Analysis.Subsequences]
k:100 [in Waterproof.Libs.Analysis.Sequences]
k:101 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:101 [in Waterproof.Libs.Analysis.Subsequences]
k:102 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:102 [in Waterproof.Libs.Analysis.Subsequences]
k:103 [in Waterproof.Libs.Analysis.Subsequences]
k:103 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:105 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:105 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:106 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:107 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:107 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:108 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:109 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:11 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:110 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:110 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:111 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:111 [in Waterproof.Libs.Analysis.Subsequences]
k:111 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:112 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:112 [in Waterproof.Libs.Analysis.Subsequences]
k:112 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:113 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:113 [in Waterproof.Libs.Analysis.Subsequences]
K:114 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:114 [in Waterproof.Libs.Analysis.Subsequences]
K:115 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:116 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:116 [in Waterproof.Libs.Analysis.Subsequences]
k:117 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:117 [in Waterproof.Libs.Analysis.Subsequences]
k:118 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:12 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:12 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:120 [in Waterproof.Libs.Analysis.Subsequences]
k:121 [in Waterproof.Libs.Analysis.Subsequences]
k:121 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:122 [in Waterproof.Libs.Analysis.Subsequences]
k:122 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:123 [in Waterproof.Libs.Analysis.Subsequences]
k:123 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:124 [in Waterproof.Libs.Analysis.Subsequences]
k:124 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:125 [in Waterproof.Libs.Analysis.Subsequences]
K:125 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:126 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:127 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:128 [in Waterproof.Libs.Analysis.Subsequences]
K:128 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:129 [in Waterproof.Libs.Analysis.Subsequences]
k:129 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:130 [in Waterproof.Libs.Analysis.Subsequences]
k:130 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:131 [in Waterproof.Libs.Analysis.Subsequences]
k:131 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:132 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:133 [in Waterproof.Libs.Analysis.Subsequences]
k:133 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:134 [in Waterproof.Libs.Analysis.Subsequences]
k:134 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:135 [in Waterproof.Libs.Analysis.Subsequences]
k:136 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:136 [in Waterproof.Libs.Analysis.Subsequences]
k:137 [in Waterproof.Libs.Analysis.Subsequences]
k:139 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:14 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:141 [in Waterproof.Libs.Analysis.Subsequences]
k:142 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:142 [in Waterproof.Libs.Analysis.Subsequences]
k:146 [in Waterproof.Libs.Analysis.Subsequences]
k:147 [in Waterproof.Libs.Analysis.Subsequences]
k:149 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:15 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:150 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:150 [in Waterproof.Libs.Analysis.Subsequences]
k:151 [in Waterproof.Libs.Analysis.Subsequences]
k:152 [in Waterproof.Libs.Analysis.Subsequences]
k:155 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:156 [in Waterproof.Libs.Analysis.Subsequences]
k:162 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:163 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:164 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:165 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:166 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:166 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:167 [in Waterproof.Libs.Analysis.Subsequences]
k:168 [in Waterproof.Libs.Analysis.Subsequences]
k:168 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:17 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:171 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:172 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:173 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:173 [in Waterproof.Libs.Analysis.Subsequences]
k:174 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:175 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:18 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:18 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:180 [in Waterproof.Libs.Analysis.Subsequences]
k:181 [in Waterproof.Libs.Analysis.Subsequences]
k:182 [in Waterproof.Libs.Analysis.Subsequences]
k:183 [in Waterproof.Libs.Analysis.Subsequences]
k:19 [in Waterproof.Libs.Analysis.Subsequences]
k:19 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:19 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:192 [in Waterproof.Libs.Analysis.Subsequences]
k:194 [in Waterproof.Libs.Analysis.Subsequences]
k:194 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:195 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:196 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:197 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:198 [in Waterproof.Libs.Analysis.Subsequences]
k:199 [in Waterproof.Libs.Analysis.Subsequences]
k:199 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:2 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:2 [in Waterproof.Libs.Analysis.Series]
k:20 [in Waterproof.Libs.Analysis.Subsequences]
k:20 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:20 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:20 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:200 [in Waterproof.Libs.Analysis.Subsequences]
k:201 [in Waterproof.Libs.Analysis.Subsequences]
k:201 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:202 [in Waterproof.Libs.Analysis.Subsequences]
k:203 [in Waterproof.Libs.Analysis.Subsequences]
k:204 [in Waterproof.Libs.Analysis.Subsequences]
k:205 [in Waterproof.Libs.Analysis.Subsequences]
k:21 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:21 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:213 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:214 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:215 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:216 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:22 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:221 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:222 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:223 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:224 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:23 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:23 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:24 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:24 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:24 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:25 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:26 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:26 [in Waterproof.Libs.Analysis.Series]
k:27 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:27 [in Waterproof.Libs.Analysis.Subsequences]
k:27 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:273 [in Waterproof.Libs.Analysis.SupAndInf]
K:274 [in Waterproof.Libs.Analysis.SupAndInf]
K:275 [in Waterproof.Libs.Analysis.SupAndInf]
K:276 [in Waterproof.Libs.Analysis.SupAndInf]
k:28 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:28 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:29 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:29 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:299 [in Waterproof.Libs.Analysis.SupAndInf]
k:3 [in Waterproof.Tactics.Induction]
k:3 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:3 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:30 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:30 [in Waterproof.Libs.Analysis.SubsequencesMetric]
K:300 [in Waterproof.Libs.Analysis.SupAndInf]
K:301 [in Waterproof.Libs.Analysis.SupAndInf]
K:302 [in Waterproof.Libs.Analysis.SupAndInf]
k:31 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:31 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:32 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:32 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:32 [in Waterproof.Libs.Analysis.SequencesMetric]
K:325 [in Waterproof.Libs.Analysis.SupAndInf]
K:326 [in Waterproof.Libs.Analysis.SupAndInf]
K:327 [in Waterproof.Libs.Analysis.SupAndInf]
K:328 [in Waterproof.Libs.Analysis.SupAndInf]
k:33 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:33 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:34 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:34 [in Waterproof.Libs.Analysis.Subsequences]
k:34 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
K:349 [in Waterproof.Libs.Analysis.SupAndInf]
k:35 [in Waterproof.Libs.Analysis.Subsequences]
K:350 [in Waterproof.Libs.Analysis.SupAndInf]
K:351 [in Waterproof.Libs.Analysis.SupAndInf]
K:352 [in Waterproof.Libs.Analysis.SupAndInf]
k:36 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:36 [in Waterproof.Libs.Analysis.Subsequences]
k:36 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:37 [in Waterproof.Libs.Analysis.Subsequences]
k:37 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:38 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:38 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:39 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:39 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:4 [in Waterproof.Tactics.Induction]
k:4 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:41 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:42 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:42 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:43 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:43 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:44 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:44 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:46 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:46 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:47 [in Waterproof.Libs.Analysis.Sequences]
k:48 [in Waterproof.Libs.Analysis.Sequences]
k:49 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:49 [in Waterproof.Libs.Analysis.Sequences]
k:49 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:5 [in Waterproof.Tactics.Induction]
k:5 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
k:5 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:50 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:50 [in Waterproof.Libs.Analysis.Sequences]
k:50 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:51 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:51 [in Waterproof.Libs.Analysis.Subsequences]
k:51 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:52 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:52 [in Waterproof.Libs.Analysis.Subsequences]
k:52 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:52 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:523 [in Waterproof.Libs.Analysis.SupAndInf]
k:524 [in Waterproof.Libs.Analysis.SupAndInf]
k:529 [in Waterproof.Libs.Analysis.SupAndInf]
k:53 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:53 [in Waterproof.Libs.Analysis.Subsequences]
k:530 [in Waterproof.Libs.Analysis.SupAndInf]
k:536 [in Waterproof.Libs.Analysis.SupAndInf]
k:537 [in Waterproof.Libs.Analysis.SupAndInf]
k:54 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:54 [in Waterproof.Libs.Analysis.Subsequences]
k:549 [in Waterproof.Libs.Analysis.SupAndInf]
k:550 [in Waterproof.Libs.Analysis.SupAndInf]
k:561 [in Waterproof.Libs.Analysis.SupAndInf]
k:562 [in Waterproof.Libs.Analysis.SupAndInf]
k:563 [in Waterproof.Libs.Analysis.SupAndInf]
k:564 [in Waterproof.Libs.Analysis.SupAndInf]
k:573 [in Waterproof.Libs.Analysis.SupAndInf]
k:574 [in Waterproof.Libs.Analysis.SupAndInf]
k:575 [in Waterproof.Libs.Analysis.SupAndInf]
k:576 [in Waterproof.Libs.Analysis.SupAndInf]
k:577 [in Waterproof.Libs.Analysis.SupAndInf]
k:578 [in Waterproof.Libs.Analysis.SupAndInf]
k:59 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:6 [in Waterproof.Tactics.Induction]
k:60 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:61 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:62 [in Waterproof.Libs.Analysis.Subsequences]
k:62 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:63 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:63 [in Waterproof.Libs.Analysis.Subsequences]
k:63 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:64 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:64 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:64 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:65 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:67 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:67 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:68 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:69 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:7 [in Waterproof.Tactics.Induction]
k:7 [in Waterproof.Libs.Analysis.Subsequences]
k:7 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:70 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:71 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:72 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:73 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:73 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:74 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:74 [in Waterproof.Libs.Analysis.Subsequences]
k:75 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:75 [in Waterproof.Libs.Analysis.Subsequences]
k:76 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:76 [in Waterproof.Libs.Analysis.Sequences]
k:76 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:77 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
K:77 [in Waterproof.Libs.Analysis.Sequences]
k:77 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:78 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:78 [in Waterproof.Libs.Analysis.Subsequences]
K:78 [in Waterproof.Libs.Analysis.Sequences]
k:79 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:79 [in Waterproof.Libs.Analysis.Subsequences]
K:79 [in Waterproof.Libs.Analysis.Sequences]
k:79 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
k:8 [in Waterproof.Tactics.Induction]
k:8 [in Waterproof.Libs.Analysis.Subsequences]
k:8 [in Waterproof.Libs.Analysis.SubsequencesMetric]
k:80 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:81 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:82 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:83 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:84 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:84 [in Waterproof.Libs.Analysis.Subsequences]
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k:85 [in Waterproof.Libs.Analysis.Subsequences]
k:86 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:86 [in Waterproof.Libs.Analysis.SubsequencesMetric]
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k:89 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:89 [in Waterproof.Libs.Analysis.SubsequencesMetric]
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k:97 [in Waterproof.Libs.Analysis.SubsequencesMetric]
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k:99 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
k:99 [in Waterproof.Libs.Analysis.Sequences]
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lcn:179 [in Waterproof.Chains.Inequalities]lcn:183 [in Waterproof.Chains.Inequalities]
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lcn:223 [in Waterproof.Chains.Inequalities]
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lx:204 [in Waterproof.Chains.Inequalities]
lx:208 [in Waterproof.Chains.Inequalities]
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lx:224 [in Waterproof.Chains.Inequalities]
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m:3 [in Waterproof.Libs.Integers.Square]
m:3 [in Waterproof.Libs.Analysis.Subsequences]
m:3 [in Waterproof.Libs.Integers.Even]
m:3 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
M:300 [in Waterproof.Libs.Analysis.Sequences]
M:301 [in Waterproof.Libs.Analysis.Sequences]
M:302 [in Waterproof.Libs.Analysis.Sequences]
M:313 [in Waterproof.Libs.Analysis.SupAndInf]
M:314 [in Waterproof.Libs.Analysis.SupAndInf]
M:315 [in Waterproof.Libs.Analysis.SupAndInf]
M:316 [in Waterproof.Libs.Analysis.SupAndInf]
M:328 [in Waterproof.Libs.Analysis.Sequences]
M:329 [in Waterproof.Libs.Analysis.Sequences]
M:330 [in Waterproof.Libs.Analysis.Sequences]
M:331 [in Waterproof.Libs.Analysis.Sequences]
m:337 [in Waterproof.Libs.Analysis.SupAndInf]
m:338 [in Waterproof.Libs.Analysis.SupAndInf]
m:339 [in Waterproof.Libs.Analysis.SupAndInf]
m:340 [in Waterproof.Libs.Analysis.SupAndInf]
M:356 [in Waterproof.Libs.Analysis.Sequences]
M:357 [in Waterproof.Libs.Analysis.Sequences]
M:358 [in Waterproof.Libs.Analysis.Sequences]
M:359 [in Waterproof.Libs.Analysis.Sequences]
M:36 [in Waterproof.Libs.Analysis.SupAndInf]
M:361 [in Waterproof.Libs.Analysis.SupAndInf]
M:362 [in Waterproof.Libs.Analysis.SupAndInf]
M:363 [in Waterproof.Libs.Analysis.SupAndInf]
M:364 [in Waterproof.Libs.Analysis.Sequences]
M:364 [in Waterproof.Libs.Analysis.SupAndInf]
M:365 [in Waterproof.Libs.Analysis.Sequences]
M:366 [in Waterproof.Libs.Analysis.Sequences]
M:367 [in Waterproof.Libs.Analysis.Sequences]
M:37 [in Waterproof.Libs.Analysis.SupAndInf]
m:375 [in Waterproof.Libs.Analysis.SupAndInf]
m:376 [in Waterproof.Libs.Analysis.SupAndInf]
M:377 [in Waterproof.Libs.Analysis.Sequences]
m:377 [in Waterproof.Libs.Analysis.SupAndInf]
M:378 [in Waterproof.Libs.Analysis.Sequences]
m:378 [in Waterproof.Libs.Analysis.SupAndInf]
M:379 [in Waterproof.Libs.Analysis.Sequences]
M:38 [in Waterproof.Libs.Analysis.SupAndInf]
M:38 [in Waterproof.Libs.Analysis.Series]
M:380 [in Waterproof.Libs.Analysis.Sequences]
m:386 [in Waterproof.Libs.Analysis.Sequences]
m:387 [in Waterproof.Libs.Analysis.Sequences]
m:388 [in Waterproof.Libs.Analysis.Sequences]
M:388 [in Waterproof.Libs.Analysis.SupAndInf]
m:389 [in Waterproof.Libs.Analysis.Sequences]
M:39 [in Waterproof.Libs.Analysis.SupAndInf]
M:39 [in Waterproof.Libs.Analysis.Series]
M:395 [in Waterproof.Libs.Analysis.Sequences]
M:396 [in Waterproof.Libs.Analysis.Sequences]
M:397 [in Waterproof.Libs.Analysis.Sequences]
M:398 [in Waterproof.Libs.Analysis.Sequences]
m:398 [in Waterproof.Libs.Analysis.SupAndInf]
m:4 [in Waterproof.Libs.Integers.Square]
m:4 [in Waterproof.Libs.Analysis.Subsequences]
m:4 [in Waterproof.Libs.Reals.Integer]
m:4 [in Waterproof.Libs.Integers.Even]
M:4 [in Waterproof.Libs.Analysis.Series]
M:40 [in Waterproof.Libs.Analysis.SupAndInf]
M:40 [in Waterproof.Libs.Analysis.Series]
M:408 [in Waterproof.Libs.Analysis.Sequences]
M:408 [in Waterproof.Libs.Analysis.SupAndInf]
M:409 [in Waterproof.Libs.Analysis.Sequences]
M:41 [in Waterproof.Libs.Analysis.SupAndInf]
M:41 [in Waterproof.Libs.Analysis.Series]
M:410 [in Waterproof.Libs.Analysis.Sequences]
M:411 [in Waterproof.Libs.Analysis.Sequences]
M:42 [in Waterproof.Libs.Analysis.SupAndInf]
m:43 [in Waterproof.Libs.Analysis.Subsequences]
M:43 [in Waterproof.Libs.Analysis.SupAndInf]
m:44 [in Waterproof.Libs.Analysis.Subsequences]
m:450 [in Waterproof.Libs.Analysis.SupAndInf]
m:46 [in Waterproof.Libs.Analysis.SupAndInf]
m:47 [in Waterproof.Libs.Analysis.Subsequences]
m:47 [in Waterproof.Libs.Analysis.SupAndInf]
m:48 [in Waterproof.Libs.Analysis.Subsequences]
M:493 [in Waterproof.Libs.Analysis.SupAndInf]
M:494 [in Waterproof.Libs.Analysis.SupAndInf]
M:495 [in Waterproof.Libs.Analysis.SupAndInf]
M:496 [in Waterproof.Libs.Analysis.SupAndInf]
m:5 [in Waterproof.Libs.Integers.Square]
m:5 [in Waterproof.Libs.Integers.Even]
m:5 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
M:50 [in Waterproof.Libs.Analysis.SupAndInf]
M:510 [in Waterproof.Libs.Analysis.SupAndInf]
m:513 [in Waterproof.Libs.Analysis.SupAndInf]
m:547 [in Waterproof.Libs.Analysis.SupAndInf]
m:548 [in Waterproof.Libs.Analysis.SupAndInf]
m:553 [in Waterproof.Libs.Analysis.SupAndInf]
m:554 [in Waterproof.Libs.Analysis.SupAndInf]
m:555 [in Waterproof.Libs.Analysis.SupAndInf]
m:556 [in Waterproof.Libs.Analysis.SupAndInf]
m:565 [in Waterproof.Libs.Analysis.SupAndInf]
m:566 [in Waterproof.Libs.Analysis.SupAndInf]
m:567 [in Waterproof.Libs.Analysis.SupAndInf]
m:568 [in Waterproof.Libs.Analysis.SupAndInf]
m:58 [in Waterproof.Libs.Analysis.Subsequences]
m:59 [in Waterproof.Libs.Analysis.Subsequences]
m:6 [in Waterproof.Libs.Integers.Square]
m:6 [in Waterproof.Libs.Reals.Integer]
m:6 [in Waterproof.Libs.Reals.Rational]
M:60 [in Waterproof.Libs.Analysis.Series]
m:61 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:61 [in Waterproof.Libs.Analysis.Series]
m:62 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
M:62 [in Waterproof.Libs.Analysis.Series]
M:63 [in Waterproof.Libs.Analysis.Series]
m:64 [in Waterproof.Libs.Analysis.Subsequences]
m:65 [in Waterproof.Libs.Analysis.Subsequences]
M:65 [in Waterproof.Libs.Analysis.SupAndInf]
m:67 [in Waterproof.Libs.Analysis.SupAndInf]
m:7 [in Waterproof.Libs.Reals.Rational]
m:7 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:7 [in Waterproof.Libs.Integers.Even]
m:70 [in Waterproof.Libs.Analysis.Subsequences]
m:71 [in Waterproof.Libs.Analysis.Subsequences]
m:73 [in Waterproof.Libs.Analysis.SupAndInf]
m:74 [in Waterproof.Libs.Analysis.SupAndInf]
m:75 [in Waterproof.Libs.Analysis.SupAndInf]
m:76 [in Waterproof.Libs.Analysis.SupAndInf]
m:78 [in Waterproof.Libs.Analysis.SupAndInf]
m:8 [in Waterproof.Libs.Integers.Square]
m:8 [in Waterproof.Libs.Reals.Integer]
M:8 [in Waterproof.Libs.Analysis.SupAndInf]
m:8 [in Waterproof.Libs.Reals.Rational]
m:8 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:8 [in Waterproof.Libs.Integers.Even]
m:8 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
m:80 [in Waterproof.Libs.Analysis.Subsequences]
m:81 [in Waterproof.Libs.Analysis.Subsequences]
M:87 [in Waterproof.Libs.Analysis.SupAndInf]
m:88 [in Waterproof.Libs.Analysis.Subsequences]
M:88 [in Waterproof.Libs.Analysis.SupAndInf]
m:89 [in Waterproof.Libs.Analysis.Subsequences]
M:89 [in Waterproof.Libs.Analysis.SupAndInf]
M:9 [in Waterproof.Libs.Analysis.SupAndInf]
m:9 [in Waterproof.Libs.Reals.Rational]
m:9 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
m:9 [in Waterproof.Libs.Integers.Even]
M:90 [in Waterproof.Libs.Analysis.SupAndInf]
m:92 [in Waterproof.Libs.Analysis.Subsequences]
m:93 [in Waterproof.Libs.Analysis.Subsequences]
m:95 [in Waterproof.Libs.Analysis.SupAndInf]
m:96 [in Waterproof.Libs.Analysis.Subsequences]
m:96 [in Waterproof.Libs.Analysis.SupAndInf]
m:97 [in Waterproof.Libs.Analysis.Subsequences]
m:97 [in Waterproof.Libs.Analysis.SupAndInf]
M:98 [in Waterproof.Libs.Analysis.Subsequences]
m:98 [in Waterproof.Libs.Analysis.SupAndInf]
M:99 [in Waterproof.Libs.Analysis.Subsequences]
N
Na:192 [in Waterproof.Libs.Analysis.Sequences]Na:193 [in Waterproof.Libs.Analysis.Sequences]
Na:194 [in Waterproof.Libs.Analysis.Sequences]
Na:195 [in Waterproof.Libs.Analysis.Sequences]
Nc:198 [in Waterproof.Libs.Analysis.Sequences]
Nc:199 [in Waterproof.Libs.Analysis.Sequences]
Nc:200 [in Waterproof.Libs.Analysis.Sequences]
Nc:201 [in Waterproof.Libs.Analysis.Sequences]
Nn:227 [in Waterproof.Libs.Analysis.Sequences]
Nn:228 [in Waterproof.Libs.Analysis.Sequences]
Nn:229 [in Waterproof.Libs.Analysis.Sequences]
Nn:230 [in Waterproof.Libs.Analysis.Sequences]
Nn:29 [in Waterproof.Libs.Analysis.Series]
Nn:30 [in Waterproof.Libs.Analysis.Series]
Nn:31 [in Waterproof.Libs.Analysis.Series]
Nn:32 [in Waterproof.Libs.Analysis.Series]
Nn:33 [in Waterproof.Libs.Analysis.Series]
Nn:35 [in Waterproof.Libs.Analysis.Series]
Nn:36 [in Waterproof.Libs.Analysis.Series]
Nn:37 [in Waterproof.Libs.Analysis.Series]
Nn:48 [in Waterproof.Libs.Analysis.Series]
Nn:49 [in Waterproof.Libs.Analysis.Series]
Nn:50 [in Waterproof.Libs.Analysis.Series]
Nn:51 [in Waterproof.Libs.Analysis.Series]
Nn:52 [in Waterproof.Libs.Analysis.Series]
Nn:53 [in Waterproof.Libs.Analysis.Series]
Nn:54 [in Waterproof.Libs.Analysis.Series]
Nn:55 [in Waterproof.Libs.Analysis.Series]
Nn:569 [in Waterproof.Libs.Analysis.SupAndInf]
Nn:570 [in Waterproof.Libs.Analysis.SupAndInf]
Nn:571 [in Waterproof.Libs.Analysis.SupAndInf]
Nn:572 [in Waterproof.Libs.Analysis.SupAndInf]
Nn:58 [in Waterproof.Libs.Analysis.Series]
Nn:59 [in Waterproof.Libs.Analysis.Series]
n_kplus1:209 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:208 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:207 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:206 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:205 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:204 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:203 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:202 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:188 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:187 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:186 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:185 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:173 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:172 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:171 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:170 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:159 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:153 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:100 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_0:94 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:87 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_kplus1:83 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n_ge_k:34 [in Waterproof.Libs.Analysis.SequencesMetric]
n0:163 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n0:164 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n0:97 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n0:98 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N1:10 [in Waterproof.Notations.Reals]
N1:10 [in Waterproof.Libs.Analysis.SequencesMetric]
N1:11 [in Waterproof.Libs.Analysis.SequencesMetric]
N1:130 [in Waterproof.Libs.Analysis.Sequences]
N1:131 [in Waterproof.Libs.Analysis.Sequences]
N1:132 [in Waterproof.Libs.Analysis.Sequences]
N1:133 [in Waterproof.Libs.Analysis.Sequences]
N1:147 [in Waterproof.Libs.Analysis.Sequences]
N1:148 [in Waterproof.Libs.Analysis.Sequences]
N1:149 [in Waterproof.Libs.Analysis.Sequences]
N1:15 [in Waterproof.Libs.Analysis.Sequences]
N1:150 [in Waterproof.Libs.Analysis.Sequences]
n1:155 [in Waterproof.Libs.Analysis.Sequences]
n1:156 [in Waterproof.Libs.Analysis.Sequences]
n1:157 [in Waterproof.Libs.Analysis.Sequences]
n1:158 [in Waterproof.Libs.Analysis.Sequences]
N1:16 [in Waterproof.Libs.Analysis.Sequences]
N1:17 [in Waterproof.Libs.Analysis.Sequences]
N1:18 [in Waterproof.Libs.Analysis.Sequences]
N1:184 [in Waterproof.Libs.Analysis.Sequences]
N1:185 [in Waterproof.Libs.Analysis.Sequences]
N1:186 [in Waterproof.Libs.Analysis.Sequences]
N1:187 [in Waterproof.Libs.Analysis.Sequences]
N1:27 [in Waterproof.Libs.Analysis.Sequences]
N1:273 [in Waterproof.Libs.Analysis.Sequences]
N1:274 [in Waterproof.Libs.Analysis.Sequences]
N1:275 [in Waterproof.Libs.Analysis.Sequences]
N1:276 [in Waterproof.Libs.Analysis.Sequences]
N1:28 [in Waterproof.Libs.Analysis.Sequences]
N1:29 [in Waterproof.Libs.Analysis.Sequences]
N1:30 [in Waterproof.Libs.Analysis.Sequences]
N1:399 [in Waterproof.Libs.Analysis.Sequences]
N1:400 [in Waterproof.Libs.Analysis.Sequences]
N1:401 [in Waterproof.Libs.Analysis.Sequences]
N1:402 [in Waterproof.Libs.Analysis.Sequences]
N1:412 [in Waterproof.Libs.Analysis.Sequences]
N1:413 [in Waterproof.Libs.Analysis.Sequences]
N1:414 [in Waterproof.Libs.Analysis.Sequences]
N1:415 [in Waterproof.Libs.Analysis.Sequences]
N1:62 [in Waterproof.Libs.Analysis.Sequences]
N1:63 [in Waterproof.Libs.Analysis.Sequences]
N1:64 [in Waterproof.Libs.Analysis.Sequences]
N1:65 [in Waterproof.Libs.Analysis.Sequences]
N1:7 [in Waterproof.Notations.Reals]
N1:70 [in Waterproof.Libs.Analysis.Sequences]
N1:71 [in Waterproof.Libs.Analysis.Sequences]
N1:72 [in Waterproof.Libs.Analysis.Sequences]
N1:73 [in Waterproof.Libs.Analysis.Sequences]
N1:8 [in Waterproof.Notations.Reals]
N1:8 [in Waterproof.Libs.Analysis.SequencesMetric]
N1:82 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N1:83 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N1:84 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N1:85 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N1:9 [in Waterproof.Notations.Reals]
N1:9 [in Waterproof.Libs.Analysis.SequencesMetric]
N2:10 [in Waterproof.Libs.Analysis.Sequences]
N2:279 [in Waterproof.Libs.Analysis.Sequences]
N2:280 [in Waterproof.Libs.Analysis.Sequences]
N2:281 [in Waterproof.Libs.Analysis.Sequences]
N2:282 [in Waterproof.Libs.Analysis.Sequences]
N2:35 [in Waterproof.Libs.Analysis.Sequences]
N2:36 [in Waterproof.Libs.Analysis.Sequences]
N2:9 [in Waterproof.Libs.Analysis.Sequences]
N2:90 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N2:91 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N2:92 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N2:93 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N3:117 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N3:118 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N3:119 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N3:120 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:1 [in Waterproof.Libs.Integers.Square]
n:1 [in Waterproof.Tactics.Induction]
n:1 [in Waterproof.Libs.Analysis.Sequences]
n:1 [in Waterproof.Libs.Integers.Even]
n:1 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:1 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:10 [in Waterproof.Libs.Reals.Integer]
n:10 [in Waterproof.Libs.Analysis.Series]
n:101 [in Waterproof.Libs.Analysis.Sequences]
n:102 [in Waterproof.Libs.Analysis.Sequences]
n:102 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:103 [in Waterproof.Libs.Analysis.Sequences]
n:104 [in Waterproof.Libs.Analysis.Sequences]
n:104 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:105 [in Waterproof.Libs.Analysis.Sequences]
n:105 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:106 [in Waterproof.Libs.Analysis.Sequences]
n:106 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:106 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:107 [in Waterproof.Libs.Analysis.Sequences]
n:107 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:108 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:108 [in Waterproof.Libs.Analysis.Sequences]
n:108 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:109 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:109 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:11 [in Waterproof.Libs.Analysis.Sequences]
n:11 [in Waterproof.Notations.Reals]
n:11 [in Waterproof.Libs.Integers.Even]
n:11 [in Waterproof.Libs.Analysis.Series]
n:11 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:110 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:111 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:112 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:113 [in Waterproof.Libs.Analysis.Sequences]
n:114 [in Waterproof.Libs.Analysis.Sequences]
n:119 [in Waterproof.Libs.Analysis.Sequences]
n:12 [in Waterproof.Libs.Analysis.Sequences]
n:12 [in Waterproof.Notations.Reals]
n:12 [in Waterproof.Libs.Analysis.SequencesMetric]
n:12 [in Waterproof.Libs.Analysis.Series]
n:120 [in Waterproof.Libs.Analysis.Sequences]
n:124 [in Waterproof.Libs.Analysis.Sequences]
N:13 [in Waterproof.Libs.Analysis.Subsequences]
n:13 [in Waterproof.Libs.Analysis.Sequences]
n:13 [in Waterproof.Libs.Integers.Divisibility]
n:13 [in Waterproof.Libs.Reals.Rational]
n:13 [in Waterproof.Notations.Reals]
n:13 [in Waterproof.Libs.Analysis.SequencesMetric]
n:13 [in Waterproof.Libs.Analysis.Series]
n:132 [in Waterproof.Libs.Analysis.Subsequences]
n:134 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:134 [in Waterproof.Libs.Analysis.Sequences]
n:135 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:135 [in Waterproof.Libs.Analysis.Sequences]
n:136 [in Waterproof.Libs.Analysis.Sequences]
n:137 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:137 [in Waterproof.Libs.Analysis.Sequences]
n:138 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:138 [in Waterproof.Libs.Analysis.Sequences]
n:139 [in Waterproof.Libs.Analysis.Sequences]
N:14 [in Waterproof.Libs.Analysis.Subsequences]
n:14 [in Waterproof.Libs.Analysis.Sequences]
n:14 [in Waterproof.Notations.Reals]
n:14 [in Waterproof.Libs.Analysis.SequencesMetric]
n:14 [in Waterproof.Libs.Analysis.Series]
n:140 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:140 [in Waterproof.Libs.Analysis.Subsequences]
n:140 [in Waterproof.Libs.Analysis.Sequences]
n:141 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:141 [in Waterproof.Libs.Analysis.Sequences]
n:142 [in Waterproof.Libs.Analysis.Sequences]
N:145 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:145 [in Waterproof.Libs.Analysis.Subsequences]
N:146 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:147 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:148 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:15 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
n:15 [in Waterproof.Libs.Analysis.SequencesMetric]
n:15 [in Waterproof.Libs.Analysis.Series]
n:151 [in Waterproof.Libs.Analysis.Sequences]
n:152 [in Waterproof.Libs.Analysis.Sequences]
n:153 [in Waterproof.Libs.Analysis.Sequences]
n:154 [in Waterproof.Libs.Analysis.Sequences]
n:155 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:156 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:156 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:157 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:157 [in Waterproof.Libs.Analysis.Subsequences]
n:158 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:159 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:159 [in Waterproof.Libs.Analysis.Sequences]
n:16 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:16 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
n:16 [in Waterproof.Libs.Integers.Even]
N:160 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:160 [in Waterproof.Libs.Analysis.Sequences]
N:161 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:161 [in Waterproof.Libs.Analysis.Sequences]
n:161 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:162 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:162 [in Waterproof.Libs.Analysis.Subsequences]
n:162 [in Waterproof.Libs.Analysis.Sequences]
n:163 [in Waterproof.Libs.Analysis.Sequences]
n:163 [in Waterproof.Chains.Inequalities]
n:164 [in Waterproof.Libs.Analysis.Sequences]
N:165 [in Waterproof.Libs.Analysis.Subsequences]
n:165 [in Waterproof.Libs.Analysis.Sequences]
n:165 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:166 [in Waterproof.Libs.Analysis.Subsequences]
n:166 [in Waterproof.Libs.Analysis.Sequences]
N:167 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:167 [in Waterproof.Libs.Analysis.Sequences]
n:167 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:168 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:169 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:17 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:17 [in Waterproof.Libs.Analysis.Subsequences]
N:170 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:171 [in Waterproof.Chains.Inequalities]
n:172 [in Waterproof.Libs.Analysis.Sequences]
n:173 [in Waterproof.Libs.Analysis.Sequences]
n:174 [in Waterproof.Libs.Analysis.Sequences]
n:175 [in Waterproof.Libs.Analysis.Sequences]
n:176 [in Waterproof.Libs.Analysis.Sequences]
n:176 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:177 [in Waterproof.Libs.Analysis.Sequences]
n:178 [in Waterproof.Libs.Analysis.Sequences]
n:179 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:179 [in Waterproof.Libs.Analysis.Sequences]
N:18 [in Waterproof.Libs.Analysis.Subsequences]
n:180 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:181 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:182 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:185 [in Waterproof.Libs.Analysis.Subsequences]
n:187 [in Waterproof.Chains.Inequalities]
n:188 [in Waterproof.Libs.Analysis.Sequences]
n:189 [in Waterproof.Libs.Analysis.Sequences]
n:19 [in Waterproof.Libs.Analysis.Sequences]
n:19 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:190 [in Waterproof.Libs.Analysis.Sequences]
n:190 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:191 [in Waterproof.Libs.Analysis.Subsequences]
n:191 [in Waterproof.Libs.Analysis.Sequences]
n:191 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:192 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:193 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:196 [in Waterproof.Libs.Analysis.Sequences]
n:197 [in Waterproof.Libs.Analysis.Sequences]
n:198 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:2 [in Waterproof.Libs.Integers.Square]
n:2 [in Waterproof.Libs.Reals.ArchimedN]
n:2 [in Waterproof.Libs.Analysis.Sequences]
n:2 [in Waterproof.Libs.Reals.Rational]
n:20 [in Waterproof.Libs.Analysis.Sequences]
n:20 [in Waterproof.Libs.Integers.Divisibility]
n:20 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:200 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:202 [in Waterproof.Libs.Analysis.Sequences]
n:203 [in Waterproof.Libs.Analysis.Sequences]
n:203 [in Waterproof.Chains.Inequalities]
n:204 [in Waterproof.Libs.Analysis.Sequences]
n:205 [in Waterproof.Libs.Analysis.Sequences]
n:206 [in Waterproof.Libs.Analysis.Sequences]
n:207 [in Waterproof.Libs.Analysis.Sequences]
n:21 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:21 [in Waterproof.Libs.Analysis.Sequences]
n:21 [in Waterproof.Libs.Integers.Even]
n:21 [in Waterproof.Libs.Analysis.Series]
n:211 [in Waterproof.Libs.Analysis.Sequences]
n:211 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:211 [in Waterproof.Chains.Inequalities]
n:212 [in Waterproof.Libs.Analysis.Sequences]
n:212 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:213 [in Waterproof.Libs.Analysis.Sequences]
n:214 [in Waterproof.Libs.Analysis.Sequences]
n:215 [in Waterproof.Libs.Analysis.Sequences]
n:216 [in Waterproof.Libs.Analysis.Sequences]
n:217 [in Waterproof.Libs.Analysis.Sequences]
n:217 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:218 [in Waterproof.Libs.Analysis.Sequences]
n:218 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:219 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:22 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:22 [in Waterproof.Libs.Analysis.Sequences]
n:220 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:221 [in Waterproof.Libs.Analysis.Sequences]
N:222 [in Waterproof.Libs.Analysis.Sequences]
N:223 [in Waterproof.Libs.Analysis.Sequences]
N:224 [in Waterproof.Libs.Analysis.Sequences]
n:225 [in Waterproof.Libs.Analysis.Sequences]
n:226 [in Waterproof.Libs.Analysis.Sequences]
n:227 [in Waterproof.Chains.Inequalities]
n:231 [in Waterproof.Libs.Analysis.Sequences]
n:232 [in Waterproof.Libs.Analysis.Sequences]
n:236 [in Waterproof.Libs.Analysis.Sequences]
n:237 [in Waterproof.Libs.Analysis.Sequences]
n:238 [in Waterproof.Libs.Analysis.Sequences]
n:239 [in Waterproof.Libs.Analysis.Sequences]
n:24 [in Waterproof.Libs.Integers.Even]
n:24 [in Waterproof.Libs.Analysis.Series]
n:240 [in Waterproof.Libs.Analysis.Sequences]
n:241 [in Waterproof.Libs.Analysis.Sequences]
n:242 [in Waterproof.Libs.Analysis.Sequences]
n:243 [in Waterproof.Libs.Analysis.Sequences]
n:244 [in Waterproof.Libs.Analysis.Sequences]
n:249 [in Waterproof.Libs.Analysis.Sequences]
N:25 [in Waterproof.Libs.Analysis.Subsequences]
n:250 [in Waterproof.Libs.Analysis.Sequences]
n:251 [in Waterproof.Libs.Analysis.Sequences]
n:252 [in Waterproof.Libs.Analysis.Sequences]
n:253 [in Waterproof.Libs.Analysis.Sequences]
n:254 [in Waterproof.Libs.Analysis.Sequences]
n:255 [in Waterproof.Libs.Analysis.Sequences]
n:256 [in Waterproof.Libs.Analysis.Sequences]
N:259 [in Waterproof.Libs.Analysis.Sequences]
N:26 [in Waterproof.Libs.Analysis.Subsequences]
n:26 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:26 [in Waterproof.Libs.Analysis.SequencesMetric]
n:26 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:260 [in Waterproof.Libs.Analysis.Sequences]
N:261 [in Waterproof.Libs.Analysis.Sequences]
N:262 [in Waterproof.Libs.Analysis.Sequences]
n:263 [in Waterproof.Libs.Analysis.Sequences]
n:264 [in Waterproof.Libs.Analysis.Sequences]
N:267 [in Waterproof.Libs.Analysis.Sequences]
N:268 [in Waterproof.Libs.Analysis.Sequences]
N:269 [in Waterproof.Libs.Analysis.Sequences]
n:27 [in Waterproof.Libs.Integers.Even]
n:27 [in Waterproof.Libs.Analysis.SequencesMetric]
n:27 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:270 [in Waterproof.Libs.Analysis.Sequences]
n:271 [in Waterproof.Libs.Analysis.Sequences]
n:272 [in Waterproof.Libs.Analysis.Sequences]
n:277 [in Waterproof.Libs.Analysis.Sequences]
n:278 [in Waterproof.Libs.Analysis.Sequences]
n:28 [in Waterproof.Libs.Integers.Even]
n:28 [in Waterproof.Libs.Analysis.SequencesMetric]
n:28 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:283 [in Waterproof.Libs.Analysis.Sequences]
n:284 [in Waterproof.Libs.Analysis.Sequences]
n:29 [in Waterproof.Libs.Analysis.SequencesMetric]
n:29 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:294 [in Waterproof.Libs.Analysis.Sequences]
n:295 [in Waterproof.Libs.Analysis.Sequences]
n:296 [in Waterproof.Libs.Analysis.Sequences]
n:297 [in Waterproof.Libs.Analysis.Sequences]
n:3 [in Waterproof.Libs.Reals.Integer]
n:3 [in Waterproof.Libs.Reals.Rational]
n:3 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
n:303 [in Waterproof.Libs.Analysis.Sequences]
n:304 [in Waterproof.Libs.Analysis.Sequences]
n:305 [in Waterproof.Libs.Analysis.Sequences]
n:306 [in Waterproof.Libs.Analysis.Sequences]
N:31 [in Waterproof.Libs.Analysis.Subsequences]
n:31 [in Waterproof.Libs.Analysis.Sequences]
n:31 [in Waterproof.Libs.Reals.Rational]
n:31 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:316 [in Waterproof.Libs.Analysis.Sequences]
n:317 [in Waterproof.Libs.Analysis.Sequences]
n:318 [in Waterproof.Libs.Analysis.Sequences]
n:319 [in Waterproof.Libs.Analysis.Sequences]
n:32 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:32 [in Waterproof.Libs.Analysis.Subsequences]
n:32 [in Waterproof.Libs.Analysis.Sequences]
n:322 [in Waterproof.Libs.Analysis.Sequences]
n:323 [in Waterproof.Libs.Analysis.Sequences]
n:324 [in Waterproof.Libs.Analysis.Sequences]
n:325 [in Waterproof.Libs.Analysis.Sequences]
n:326 [in Waterproof.Libs.Analysis.Sequences]
n:327 [in Waterproof.Libs.Analysis.Sequences]
n:33 [in Waterproof.Libs.Analysis.Subsequences]
n:33 [in Waterproof.Libs.Analysis.Sequences]
n:33 [in Waterproof.Libs.Analysis.SequencesMetric]
n:332 [in Waterproof.Libs.Analysis.Sequences]
n:333 [in Waterproof.Libs.Analysis.Sequences]
n:334 [in Waterproof.Libs.Analysis.Sequences]
n:335 [in Waterproof.Libs.Analysis.Sequences]
n:336 [in Waterproof.Libs.Analysis.Sequences]
n:337 [in Waterproof.Libs.Analysis.Sequences]
n:338 [in Waterproof.Libs.Analysis.Sequences]
n:339 [in Waterproof.Libs.Analysis.Sequences]
n:34 [in Waterproof.Libs.Analysis.Sequences]
n:34 [in Waterproof.Libs.Analysis.SubsequencesMetric]
N:34 [in Waterproof.Libs.Analysis.Series]
n:344 [in Waterproof.Libs.Analysis.Sequences]
n:345 [in Waterproof.Libs.Analysis.Sequences]
n:346 [in Waterproof.Libs.Analysis.Sequences]
n:347 [in Waterproof.Libs.Analysis.Sequences]
n:348 [in Waterproof.Libs.Analysis.Sequences]
n:349 [in Waterproof.Libs.Analysis.Sequences]
n:350 [in Waterproof.Libs.Analysis.Sequences]
n:351 [in Waterproof.Libs.Analysis.Sequences]
n:360 [in Waterproof.Libs.Analysis.Sequences]
n:361 [in Waterproof.Libs.Analysis.Sequences]
n:362 [in Waterproof.Libs.Analysis.Sequences]
n:363 [in Waterproof.Libs.Analysis.Sequences]
n:368 [in Waterproof.Libs.Analysis.Sequences]
n:369 [in Waterproof.Libs.Analysis.Sequences]
n:37 [in Waterproof.Libs.Analysis.Sequences]
n:370 [in Waterproof.Libs.Analysis.Sequences]
n:371 [in Waterproof.Libs.Analysis.Sequences]
n:372 [in Waterproof.Libs.Analysis.Sequences]
n:373 [in Waterproof.Libs.Analysis.Sequences]
n:374 [in Waterproof.Libs.Analysis.Sequences]
n:375 [in Waterproof.Libs.Analysis.Sequences]
n:38 [in Waterproof.Libs.Analysis.Sequences]
n:381 [in Waterproof.Libs.Analysis.Sequences]
n:382 [in Waterproof.Libs.Analysis.Sequences]
n:383 [in Waterproof.Libs.Analysis.Sequences]
n:384 [in Waterproof.Libs.Analysis.Sequences]
n:39 [in Waterproof.Libs.Analysis.Sequences]
n:390 [in Waterproof.Libs.Analysis.Sequences]
n:391 [in Waterproof.Libs.Analysis.Sequences]
n:392 [in Waterproof.Libs.Analysis.Sequences]
n:393 [in Waterproof.Libs.Analysis.Sequences]
n:4 [in Waterproof.Libs.Reals.Rational]
n:4 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
n:4 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:40 [in Waterproof.Libs.Analysis.Sequences]
n:403 [in Waterproof.Libs.Analysis.Sequences]
n:404 [in Waterproof.Libs.Analysis.Sequences]
n:405 [in Waterproof.Libs.Analysis.Sequences]
n:406 [in Waterproof.Libs.Analysis.Sequences]
n:41 [in Waterproof.Libs.Analysis.Sequences]
n:41 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:416 [in Waterproof.Libs.Analysis.Sequences]
n:417 [in Waterproof.Libs.Analysis.Sequences]
n:418 [in Waterproof.Libs.Analysis.Sequences]
n:419 [in Waterproof.Libs.Analysis.Sequences]
n:42 [in Waterproof.Libs.Analysis.Sequences]
n:42 [in Waterproof.Libs.Analysis.Series]
n:42 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:43 [in Waterproof.Libs.Analysis.Sequences]
n:43 [in Waterproof.Libs.Analysis.Series]
n:43 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:44 [in Waterproof.Libs.Analysis.Sequences]
n:44 [in Waterproof.Libs.Analysis.Series]
n:44 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:45 [in Waterproof.Libs.Analysis.Subsequences]
n:45 [in Waterproof.Libs.Analysis.Series]
N:46 [in Waterproof.Libs.Analysis.Subsequences]
n:46 [in Waterproof.Libs.Analysis.Series]
n:47 [in Waterproof.Libs.Analysis.Series]
N:49 [in Waterproof.Libs.Analysis.Subsequences]
N:5 [in Waterproof.Libs.Analysis.Subsequences]
n:5 [in Waterproof.Libs.Reals.Integer]
n:5 [in Waterproof.Libs.Reals.Rational]
N:50 [in Waterproof.Libs.Analysis.Subsequences]
n:51 [in Waterproof.Libs.Analysis.Sequences]
n:52 [in Waterproof.Libs.Analysis.Sequences]
n:53 [in Waterproof.Libs.Analysis.Sequences]
n:53 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:54 [in Waterproof.Libs.Analysis.Sequences]
n:541 [in Waterproof.Libs.Analysis.SupAndInf]
n:542 [in Waterproof.Libs.Analysis.SupAndInf]
N:557 [in Waterproof.Libs.Analysis.SupAndInf]
N:558 [in Waterproof.Libs.Analysis.SupAndInf]
N:559 [in Waterproof.Libs.Analysis.SupAndInf]
N:56 [in Waterproof.Libs.Analysis.Series]
N:560 [in Waterproof.Libs.Analysis.SupAndInf]
N:57 [in Waterproof.Libs.Analysis.Series]
n:58 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:59 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:6 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N:6 [in Waterproof.Libs.Analysis.Subsequences]
n:6 [in Waterproof.Libs.Reals.ArchimedN]
n:6 [in Waterproof.Libs.Integers.Even]
n:6 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:6 [in Waterproof.Libs.Analysis.Series]
n:6 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:60 [in Waterproof.Libs.Analysis.Subsequences]
N:61 [in Waterproof.Libs.Analysis.Subsequences]
n:64 [in Waterproof.Libs.Analysis.Series]
n:65 [in Waterproof.Libs.Analysis.Series]
N:66 [in Waterproof.Libs.Analysis.Subsequences]
n:66 [in Waterproof.Libs.Analysis.Sequences]
n:66 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:66 [in Waterproof.Libs.Analysis.Series]
N:67 [in Waterproof.Libs.Analysis.Subsequences]
n:67 [in Waterproof.Libs.Analysis.Sequences]
n:67 [in Waterproof.Libs.Analysis.Series]
n:68 [in Waterproof.Libs.Analysis.Sequences]
n:68 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:68 [in Waterproof.Libs.Analysis.Series]
n:69 [in Waterproof.Libs.Analysis.Sequences]
n:69 [in Waterproof.Libs.Analysis.Series]
n:7 [in Waterproof.Libs.Integers.Square]
n:7 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:7 [in Waterproof.Libs.Reals.ArchimedN]
n:7 [in Waterproof.Libs.Reals.Integer]
n:7 [in Waterproof.Libs.Analysis.Series]
n:7 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
n:70 [in Waterproof.Libs.Analysis.Series]
n:71 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:71 [in Waterproof.Libs.Analysis.Series]
n:72 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N:72 [in Waterproof.Libs.Analysis.Series]
N:73 [in Waterproof.Libs.Analysis.Series]
n:74 [in Waterproof.Libs.Analysis.Sequences]
n:74 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:75 [in Waterproof.Libs.Analysis.Sequences]
n:75 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:75 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:76 [in Waterproof.Libs.Analysis.Subsequences]
n:76 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:77 [in Waterproof.Libs.Analysis.Subsequences]
n:77 [in Waterproof.Libs.Analysis.SubsequencesMetric]
n:8 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:8 [in Waterproof.Libs.Reals.ArchimedN]
n:8 [in Waterproof.Libs.Analysis.Series]
n:80 [in Waterproof.Libs.Analysis.Sequences]
n:80 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:81 [in Waterproof.Libs.Analysis.Sequences]
N:82 [in Waterproof.Libs.Analysis.Subsequences]
n:82 [in Waterproof.Libs.Analysis.Sequences]
N:83 [in Waterproof.Libs.Analysis.Subsequences]
n:83 [in Waterproof.Libs.Analysis.Sequences]
n:84 [in Waterproof.Libs.Analysis.Sequences]
n:85 [in Waterproof.Libs.Analysis.Sequences]
n:85 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
n:89 [in Waterproof.Libs.Analysis.Sequences]
n:9 [in Waterproof.Libs.Reals.ArchimedN]
n:9 [in Waterproof.Libs.Reals.Integer]
n:9 [in Waterproof.Libs.Analysis.Series]
n:9 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
N:90 [in Waterproof.Libs.Analysis.Subsequences]
n:90 [in Waterproof.Libs.Analysis.Sequences]
N:91 [in Waterproof.Libs.Analysis.Subsequences]
n:91 [in Waterproof.Libs.Analysis.Sequences]
n:92 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:92 [in Waterproof.Libs.Analysis.Sequences]
n:93 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
n:93 [in Waterproof.Libs.Analysis.Sequences]
N:94 [in Waterproof.Libs.Analysis.Subsequences]
n:94 [in Waterproof.Libs.Analysis.Sequences]
N:95 [in Waterproof.Libs.Analysis.Subsequences]
n:95 [in Waterproof.Libs.Analysis.Sequences]
n:96 [in Waterproof.Libs.Analysis.Sequences]
n:97 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
N₀:13 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N₀:31 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N₀:72 [in Waterproof.Libs.Analysis.Subsequences]
N₀:73 [in Waterproof.Libs.Analysis.Subsequences]
O
OrderInterpretation0:102 [in Waterproof.Chains.Inequalities]OrderInterpretation0:105 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:110 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:112 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:115 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:118 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:123 [in Waterproof.Chains.Inequalities]
OrderInterpretation0:99 [in Waterproof.Chains.Inequalities]
P
pat:1 [in Waterproof.Tactics.Help]pat:1 [in Waterproof.Waterprove]
pat:10 [in Waterproof.Tactics.Help]
pat:11 [in Waterproof.Tactics.Induction]
pat:11 [in Waterproof.Tactics.Help]
pat:12 [in Waterproof.Tactics.Induction]
pat:12 [in Waterproof.Tactics.Help]
pat:13 [in Waterproof.Tactics.Help]
pat:14 [in Waterproof.Tactics.Help]
pat:15 [in Waterproof.Tactics.Help]
pat:16 [in Waterproof.Tactics.Help]
pat:17 [in Waterproof.Tactics.Help]
pat:18 [in Waterproof.Tactics.Help]
pat:19 [in Waterproof.Tactics.Help]
pat:2 [in Waterproof.Tactics.Help]
pat:2 [in Waterproof.Waterprove]
pat:20 [in Waterproof.Tactics.Help]
pat:21 [in Waterproof.Tactics.Help]
pat:22 [in Waterproof.Tactics.Help]
pat:23 [in Waterproof.Tactics.Help]
pat:24 [in Waterproof.Tactics.Help]
pat:25 [in Waterproof.Tactics.Help]
pat:26 [in Waterproof.Tactics.Help]
pat:27 [in Waterproof.Tactics.Help]
pat:28 [in Waterproof.Tactics.Help]
pat:29 [in Waterproof.Tactics.Help]
pat:3 [in Waterproof.Tactics.Help]
pat:3 [in Waterproof.Waterprove]
pat:30 [in Waterproof.Tactics.Help]
pat:33 [in Waterproof.Tactics.Help]
pat:34 [in Waterproof.Tactics.Help]
pat:35 [in Waterproof.Tactics.Help]
pat:36 [in Waterproof.Tactics.Help]
pat:37 [in Waterproof.Tactics.Help]
pat:38 [in Waterproof.Tactics.Help]
pat:39 [in Waterproof.Tactics.Help]
pat:4 [in Waterproof.Tactics.Help]
pat:4 [in Waterproof.Waterprove]
pat:40 [in Waterproof.Tactics.Help]
pat:41 [in Waterproof.Tactics.Help]
pat:42 [in Waterproof.Tactics.Help]
pat:43 [in Waterproof.Tactics.Help]
pat:44 [in Waterproof.Tactics.Help]
pat:45 [in Waterproof.Tactics.Help]
pat:46 [in Waterproof.Tactics.Help]
pat:47 [in Waterproof.Tactics.Help]
pat:48 [in Waterproof.Tactics.Help]
pat:49 [in Waterproof.Tactics.Help]
pat:5 [in Waterproof.Tactics.Help]
pat:50 [in Waterproof.Tactics.Help]
pat:51 [in Waterproof.Tactics.Help]
pat:52 [in Waterproof.Tactics.Help]
pat:53 [in Waterproof.Tactics.Help]
pat:54 [in Waterproof.Tactics.Help]
pat:55 [in Waterproof.Tactics.Help]
pat:56 [in Waterproof.Tactics.Help]
pat:57 [in Waterproof.Tactics.Help]
pat:58 [in Waterproof.Tactics.Help]
pat:59 [in Waterproof.Tactics.Help]
pat:6 [in Waterproof.Tactics.Help]
pat:60 [in Waterproof.Tactics.Help]
pat:61 [in Waterproof.Tactics.Help]
pat:62 [in Waterproof.Tactics.Help]
pat:63 [in Waterproof.Tactics.Help]
pat:64 [in Waterproof.Tactics.Help]
pat:65 [in Waterproof.Tactics.Help]
pat:66 [in Waterproof.Tactics.Help]
pat:67 [in Waterproof.Tactics.Help]
pat:68 [in Waterproof.Tactics.Help]
pat:69 [in Waterproof.Tactics.Help]
pat:7 [in Waterproof.Tactics.Help]
pat:70 [in Waterproof.Tactics.Help]
pat:71 [in Waterproof.Tactics.Help]
pat:72 [in Waterproof.Tactics.Help]
pat:8 [in Waterproof.Tactics.Help]
pat:9 [in Waterproof.Tactics.Help]
prev:21 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
prev:53 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
pr1:2 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
pr2:3 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
pr:517 [in Waterproof.Libs.Analysis.SupAndInf]
pr:518 [in Waterproof.Libs.Analysis.SupAndInf]
pr:545 [in Waterproof.Libs.Analysis.SupAndInf]
pr:546 [in Waterproof.Libs.Analysis.SupAndInf]
pr:552 [in Waterproof.Libs.Analysis.SupAndInf]
P:1 [in Waterproof.Libs.Logic.InformativeEpsilon]
P:1 [in Waterproof.Libs.Logic.ConstructiveLogic]
p:1 [in Waterproof.Libs.Analysis.OpenAndClosed]
p:102 [in Waterproof.Libs.Analysis.SubsequencesMetric]
P:11 [in Waterproof.Libs.Logic.ConstructiveLogic]
P:113 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:14 [in Waterproof.Libs.Negation]
P:14 [in Waterproof.Libs.Logic.ConstructiveLogic]
P:16 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:164 [in Waterproof.Libs.Analysis.Subsequences]
P:17 [in Waterproof.Libs.Logic.ConstructiveLogic]
P:2 [in Waterproof.Tactics.Induction]
P:2 [in Waterproof.Libs.Analysis.Subsequences]
P:2 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:20 [in Waterproof.Libs.Negation]
P:20 [in Waterproof.Libs.Logic.ConstructiveLogic]
p:22 [in Waterproof.Libs.Analysis.SubsequencesMetric]
P:3 [in Waterproof.Libs.Logic.Quantification]
P:3 [in Waterproof.Libs.Logic.ConstructiveLogic]
P:33 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:38 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:42 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:48 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
P:5 [in Waterproof.Libs.Logic.ConstructiveLogic]
P:54 [in Waterproof.Libs.Negation]
P:57 [in Waterproof.Libs.Analysis.Subsequences]
P:60 [in Waterproof.Libs.Negation]
P:66 [in Waterproof.Libs.Negation]
P:69 [in Waterproof.Libs.Analysis.Subsequences]
P:72 [in Waterproof.Libs.Negation]
P:72 [in Waterproof.Notations.Sets]
p:73 [in Waterproof.Libs.Analysis.SubsequencesMetric]
P:8 [in Waterproof.Libs.Logic.ConstructiveLogic]
Q
q:1 [in Waterproof.Libs.Reals.Rational]q:12 [in Waterproof.Libs.Reals.Rational]
Q:12 [in Waterproof.Libs.Logic.ConstructiveLogic]
q:14 [in Waterproof.Libs.Integers.Divisibility]
Q:15 [in Waterproof.Libs.Negation]
Q:15 [in Waterproof.Libs.Logic.ConstructiveLogic]
Q:152 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:169 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:17 [in Waterproof.Notations.Sets]
Q:18 [in Waterproof.Libs.Logic.ConstructiveLogic]
q:18 [in Waterproof.Libs.Analysis.SequencesMetric]
q:19 [in Waterproof.Libs.Analysis.SequencesMetric]
Q:2 [in Waterproof.Libs.Logic.InformativeEpsilon]
Q:2 [in Waterproof.Notations.Sets]
Q:2 [in Waterproof.Libs.Logic.ConstructiveLogic]
q:20 [in Waterproof.Libs.Analysis.SequencesMetric]
Q:21 [in Waterproof.Libs.Negation]
q:21 [in Waterproof.Libs.Integers.Divisibility]
q:21 [in Waterproof.Libs.Analysis.ContinuityDomainR]
Q:21 [in Waterproof.Libs.Logic.ConstructiveLogic]
q:21 [in Waterproof.Libs.Analysis.SequencesMetric]
q:286 [in Waterproof.Libs.Analysis.Sequences]
q:287 [in Waterproof.Libs.Analysis.Sequences]
q:288 [in Waterproof.Libs.Analysis.Sequences]
q:289 [in Waterproof.Libs.Analysis.Sequences]
q:308 [in Waterproof.Libs.Analysis.Sequences]
q:309 [in Waterproof.Libs.Analysis.Sequences]
q:310 [in Waterproof.Libs.Analysis.Sequences]
q:311 [in Waterproof.Libs.Analysis.Sequences]
q:352 [in Waterproof.Libs.Analysis.Sequences]
q:353 [in Waterproof.Libs.Analysis.Sequences]
q:354 [in Waterproof.Libs.Analysis.Sequences]
q:355 [in Waterproof.Libs.Analysis.Sequences]
q:4 [in Waterproof.Libs.Analysis.Sequences]
Q:4 [in Waterproof.Libs.Logic.ConstructiveLogic]
Q:55 [in Waterproof.Libs.Negation]
Q:6 [in Waterproof.Libs.Logic.ConstructiveLogic]
Q:61 [in Waterproof.Libs.Negation]
Q:66 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:67 [in Waterproof.Libs.Negation]
Q:70 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:71 [in Waterproof.Notations.Sets]
Q:71 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:73 [in Waterproof.Libs.Negation]
Q:74 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:78 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:87 [in Waterproof.Notations.Sets]
Q:9 [in Waterproof.Libs.Logic.ConstructiveLogic]
Q:93 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Q:95 [in Waterproof.Notations.Sets]
R
rel1:80 [in Waterproof.Chains.Inequalities]rel1:83 [in Waterproof.Chains.Inequalities]
rel2:81 [in Waterproof.Chains.Inequalities]
rel2:84 [in Waterproof.Chains.Inequalities]
rel:124 [in Waterproof.Chains.Inequalities]
rel:128 [in Waterproof.Chains.Inequalities]
rel:132 [in Waterproof.Chains.Inequalities]
rel:136 [in Waterproof.Chains.Inequalities]
rel:155 [in Waterproof.Libs.Analysis.Subsequences]
rel:160 [in Waterproof.Libs.Analysis.Subsequences]
rel:67 [in Waterproof.Chains.Inequalities]
r1:11 [in Waterproof.Libs.Reals]
r1:17 [in Waterproof.Libs.Reals]
r1:25 [in Waterproof.Libs.Reals]
r1:27 [in Waterproof.Libs.Reals]
r1:29 [in Waterproof.Libs.Reals]
r1:31 [in Waterproof.Libs.Reals]
r1:9 [in Waterproof.Libs.Reals]
r2:10 [in Waterproof.Libs.Reals]
r2:12 [in Waterproof.Libs.Reals]
r2:18 [in Waterproof.Libs.Reals]
r2:26 [in Waterproof.Libs.Reals]
r2:28 [in Waterproof.Libs.Reals]
r2:30 [in Waterproof.Libs.Reals]
r2:32 [in Waterproof.Libs.Reals]
r:1 [in Waterproof.Libs.Reals.ArchimedN]
r:1 [in Waterproof.Libs.Reals.Integer]
R:10 [in Waterproof.Libs.Logic.ConstructiveLogic]
R:13 [in Waterproof.Libs.Logic.ConstructiveLogic]
r:15 [in Waterproof.Libs.Integers.Divisibility]
R:16 [in Waterproof.Libs.Logic.ConstructiveLogic]
r:16 [in Waterproof.Libs.Reals]
R:19 [in Waterproof.Libs.Logic.ConstructiveLogic]
r:2 [in Waterproof.Libs.Analysis.OpenAndClosed]
r:22 [in Waterproof.Libs.Integers.Divisibility]
R:22 [in Waterproof.Libs.Logic.ConstructiveLogic]
r:37 [in Waterproof.Libs.Analysis.ContinuityDomainR]
r:38 [in Waterproof.Libs.Analysis.ContinuityDomainR]
r:39 [in Waterproof.Libs.Analysis.ContinuityDomainR]
r:40 [in Waterproof.Libs.Analysis.ContinuityDomainR]
r:5 [in Waterproof.Libs.Reals.ArchimedN]
r:6 [in Waterproof.Libs.Analysis.OpenAndClosed]
R:7 [in Waterproof.Libs.Logic.ConstructiveLogic]
r:7 [in Waterproof.Libs.Analysis.OpenAndClosed]
r:8 [in Waterproof.Libs.Analysis.OpenAndClosed]
r:9 [in Waterproof.Libs.Analysis.OpenAndClosed]
S
seq:13 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]seq:25 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:28 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:35 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:39 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:43 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:58 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:60 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
seq:63 [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
T
T:1 [in Waterproof.Libs.Logic.Quantification]T:1 [in Waterproof.Util.Assertions]
T:1 [in Waterproof.Util.Init]
T:10 [in Waterproof.Chains.Inequalities]
T:101 [in Waterproof.Chains.Inequalities]
T:104 [in Waterproof.Chains.Inequalities]
T:109 [in Waterproof.Chains.Inequalities]
T:11 [in Waterproof.Notations.Common]
T:111 [in Waterproof.Chains.Inequalities]
T:114 [in Waterproof.Chains.Inequalities]
T:117 [in Waterproof.Chains.Inequalities]
T:122 [in Waterproof.Chains.Inequalities]
T:13 [in Waterproof.Chains.Inequalities]
T:14 [in Waterproof.Notations.Sets]
T:16 [in Waterproof.Notations.Sets]
T:21 [in Waterproof.Chains.Inequalities]
T:22 [in Waterproof.Chains.Inequalities]
T:23 [in Waterproof.Chains.Inequalities]
T:24 [in Waterproof.Chains.Inequalities]
T:25 [in Waterproof.Chains.Inequalities]
T:26 [in Waterproof.Chains.Inequalities]
T:27 [in Waterproof.Chains.Inequalities]
T:33 [in Waterproof.Chains.Inequalities]
T:34 [in Waterproof.Chains.Inequalities]
T:35 [in Waterproof.Chains.Inequalities]
T:36 [in Waterproof.Chains.Inequalities]
T:40 [in Waterproof.Chains.Inequalities]
T:44 [in Waterproof.Chains.Inequalities]
T:48 [in Waterproof.Chains.Inequalities]
T:51 [in Waterproof.Chains.Inequalities]
T:54 [in Waterproof.Chains.Inequalities]
T:57 [in Waterproof.Chains.Inequalities]
T:63 [in Waterproof.Chains.Inequalities]
T:66 [in Waterproof.Notations.Sets]
T:66 [in Waterproof.Chains.Inequalities]
T:7 [in Waterproof.Chains.Inequalities]
T:70 [in Waterproof.Notations.Sets]
T:70 [in Waterproof.Chains.Inequalities]
T:73 [in Waterproof.Chains.Inequalities]
T:78 [in Waterproof.Chains.Inequalities]
T:86 [in Waterproof.Notations.Sets]
T:86 [in Waterproof.Chains.Inequalities]
T:90 [in Waterproof.Chains.Inequalities]
T:94 [in Waterproof.Notations.Sets]
T:94 [in Waterproof.Chains.Inequalities]
T:98 [in Waterproof.Chains.Inequalities]
U
U:1 [in Waterproof.Libs.Sets.Operations]U:1 [in Waterproof.Libs.Sets.IndexedOperations]
U:1 [in Waterproof.Libs.Sets]
U:10 [in Waterproof.Libs.Sets]
U:13 [in Waterproof.Libs.Sets.Operations]
U:13 [in Waterproof.Libs.Functions]
U:14 [in Waterproof.Libs.Sets]
U:19 [in Waterproof.Libs.Sets.IndexedOperations]
U:2 [in Waterproof.Libs.Logic.Quantification]
U:22 [in Waterproof.Libs.Functions]
U:29 [in Waterproof.Libs.Sets.IndexedOperations]
U:31 [in Waterproof.Libs.Functions]
U:37 [in Waterproof.Libs.Sets.IndexedOperations]
U:4 [in Waterproof.Libs.Functions]
U:4 [in Waterproof.Libs.Sets]
U:47 [in Waterproof.Libs.Sets.IndexedOperations]
U:5 [in Waterproof.Libs.Sets.Operations]
U:7 [in Waterproof.Libs.Sets]
U:8 [in Waterproof.Notations.Sets]
U:9 [in Waterproof.Libs.Sets.Operations]
U:9 [in Waterproof.Libs.Sets.IndexedOperations]
U:9 [in Waterproof.Notations.Sets]
V
V:10 [in Waterproof.Libs.Sets.IndexedOperations]V:2 [in Waterproof.Libs.Sets.IndexedOperations]
V:20 [in Waterproof.Libs.Sets.IndexedOperations]
V:30 [in Waterproof.Libs.Sets.IndexedOperations]
v:31 [in Waterproof.Tactics.Help]
v:32 [in Waterproof.Tactics.Help]
V:38 [in Waterproof.Libs.Sets.IndexedOperations]
V:40 [in Waterproof.Libs.Functions]
V:48 [in Waterproof.Libs.Sets.IndexedOperations]
V:49 [in Waterproof.Libs.Functions]
V:58 [in Waterproof.Libs.Functions]
V:67 [in Waterproof.Libs.Functions]
V:76 [in Waterproof.Libs.Functions]
V:81 [in Waterproof.Libs.Functions]
X
x0:27 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]x0:28 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x0:29 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x0:30 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x:1 [in Waterproof.Util.Constr]
x:1 [in Waterproof.Libs.Integers.Divisibility]
X:1 [in Waterproof.Libs.Functions]
x:1 [in Waterproof.Libs.Reals.RealInequalities]
x:1 [in Waterproof.Notations.Common]
X:1 [in Waterproof.Notations.Sets]
x:1 [in Waterproof.Libs.Reals]
X:1 [in Waterproof.Libs.Analysis.MetricSpaces]
X:10 [in Waterproof.Libs.Functions]
x:10 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:10 [in Waterproof.Libs.Analysis.MetricSpaces]
x:100 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:100 [in Waterproof.Notations.Sets]
x:100 [in Waterproof.Libs.Analysis.SubsequencesMetric]
x:100 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:101 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:101 [in Waterproof.Notations.Sets]
x:102 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:102 [in Waterproof.Notations.Sets]
x:103 [in Waterproof.Notations.Sets]
x:105 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:106 [in Waterproof.Libs.Functions]
x:107 [in Waterproof.Libs.Functions]
x:108 [in Waterproof.Libs.Functions]
x:109 [in Waterproof.Libs.Functions]
x:11 [in Waterproof.Libs.Reals.Rational]
x:11 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
X:11 [in Waterproof.Libs.Sets]
x:11 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:11 [in Waterproof.Libs.Analysis.MetricSpaces]
X:110 [in Waterproof.Libs.Functions]
x:111 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:112 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:113 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:114 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:114 [in Waterproof.Libs.Functions]
x:115 [in Waterproof.Libs.Functions]
x:116 [in Waterproof.Libs.Functions]
x:117 [in Waterproof.Libs.Functions]
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x:12 [in Waterproof.Notations.Common]
x:12 [in Waterproof.Notations.Sets]
x:12 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
x:12 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:12 [in Waterproof.Libs.Analysis.MetricSpaces]
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x:124 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
X:124 [in Waterproof.Libs.Functions]
x:125 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:125 [in Waterproof.Chains.Inequalities]
X:127 [in Waterproof.Libs.Functions]
x:129 [in Waterproof.Chains.Inequalities]
X:13 [in Waterproof.Libs.Sets.IndexedOperations]
x:13 [in Waterproof.Util.Goals]
x:13 [in Waterproof.Notations.Sets]
x:13 [in Waterproof.Libs.Sets]
x:13 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:13 [in Waterproof.Libs.Analysis.MetricSpaces]
x:130 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
X:130 [in Waterproof.Libs.Functions]
x:131 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:132 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:133 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:133 [in Waterproof.Chains.Inequalities]
x:135 [in Waterproof.Libs.Functions]
X:136 [in Waterproof.Libs.Functions]
x:137 [in Waterproof.Chains.Inequalities]
x:14 [in Waterproof.Libs.Sets.IndexedOperations]
X:140 [in Waterproof.Libs.Functions]
x:145 [in Waterproof.Libs.Analysis.SupAndInf]
X:145 [in Waterproof.Libs.Functions]
x:146 [in Waterproof.Libs.Analysis.SupAndInf]
X:149 [in Waterproof.Libs.Functions]
x:15 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:15 [in Waterproof.Libs.Functions]
x:15 [in Waterproof.Notations.Reals]
x:15 [in Waterproof.Notations.Sets]
x:15 [in Waterproof.Libs.Sets]
x:15 [in Waterproof.Libs.Reals]
X:154 [in Waterproof.Libs.Functions]
x:157 [in Waterproof.Libs.Analysis.SupAndInf]
x:158 [in Waterproof.Libs.Analysis.SupAndInf]
X:158 [in Waterproof.Libs.Functions]
x:159 [in Waterproof.Libs.Analysis.SupAndInf]
x:16 [in Waterproof.Libs.Sets.Operations]
x:16 [in Waterproof.Libs.Negation]
x:16 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:16 [in Waterproof.Libs.Functions]
x:16 [in Waterproof.Notations.Reals]
X:16 [in Waterproof.Libs.Analysis.SequencesMetric]
x:160 [in Waterproof.Libs.Analysis.SupAndInf]
X:163 [in Waterproof.Libs.Functions]
x:165 [in Waterproof.Chains.Inequalities]
x:167 [in Waterproof.Libs.Functions]
x:168 [in Waterproof.Libs.Functions]
x:169 [in Waterproof.Libs.Functions]
x:17 [in Waterproof.Libs.Negation]
x:17 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:17 [in Waterproof.Libs.Functions]
x:17 [in Waterproof.Notations.Reals]
x:170 [in Waterproof.Libs.Functions]
X:171 [in Waterproof.Libs.Functions]
x:173 [in Waterproof.Chains.Inequalities]
x:175 [in Waterproof.Libs.Functions]
x:176 [in Waterproof.Libs.Functions]
x:177 [in Waterproof.Libs.Functions]
x:178 [in Waterproof.Libs.Functions]
X:179 [in Waterproof.Libs.Functions]
x:18 [in Waterproof.Libs.Negation]
x:18 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:18 [in Waterproof.Libs.Functions]
x:18 [in Waterproof.Notations.Reals]
x:18 [in Waterproof.Libs.Analysis.MetricSpaces]
x:180 [in Waterproof.Chains.Inequalities]
X:187 [in Waterproof.Libs.Functions]
x:189 [in Waterproof.Chains.Inequalities]
X:19 [in Waterproof.Libs.Functions]
x:19 [in Waterproof.Util.Goals]
x:19 [in Waterproof.Notations.Reals]
x:19 [in Waterproof.Libs.Reals]
x:19 [in Waterproof.Libs.Analysis.MetricSpaces]
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x:196 [in Waterproof.Chains.Inequalities]
X:199 [in Waterproof.Libs.Functions]
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x:2 [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
X:2 [in Waterproof.Libs.Sets]
x:2 [in Waterproof.Util.Init]
x:2 [in Waterproof.Libs.Analysis.MetricSpaces]
x:20 [in Waterproof.Notations.Reals]
x:20 [in Waterproof.Libs.Reals]
x:20 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:20 [in Waterproof.Libs.Analysis.MetricSpaces]
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x:207 [in Waterproof.Libs.Functions]
x:208 [in Waterproof.Libs.Functions]
x:209 [in Waterproof.Libs.Functions]
x:21 [in Waterproof.Libs.Analysis.MetricSpaces]
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X:211 [in Waterproof.Libs.Functions]
x:213 [in Waterproof.Chains.Inequalities]
X:219 [in Waterproof.Libs.Functions]
x:22 [in Waterproof.Libs.Negation]
x:220 [in Waterproof.Chains.Inequalities]
x:223 [in Waterproof.Libs.Functions]
x:224 [in Waterproof.Libs.Functions]
x:225 [in Waterproof.Libs.Functions]
x:226 [in Waterproof.Libs.Functions]
x:229 [in Waterproof.Chains.Inequalities]
x:23 [in Waterproof.Libs.Negation]
X:23 [in Waterproof.Libs.Sets.IndexedOperations]
x:23 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:236 [in Waterproof.Chains.Inequalities]
x:24 [in Waterproof.Libs.Negation]
x:24 [in Waterproof.Libs.Sets.IndexedOperations]
x:24 [in Waterproof.Libs.Functions]
x:241 [in Waterproof.Libs.Analysis.SupAndInf]
x:242 [in Waterproof.Libs.Analysis.SupAndInf]
x:25 [in Waterproof.Libs.Functions]
x:25 [in Waterproof.Util.Goals]
x:25 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:259 [in Waterproof.Libs.Analysis.SupAndInf]
x:26 [in Waterproof.Libs.Functions]
x:26 [in Waterproof.Libs.Analysis.MetricSpaces]
x:260 [in Waterproof.Libs.Analysis.SupAndInf]
x:27 [in Waterproof.Libs.Functions]
x:27 [in Waterproof.Libs.Analysis.MetricSpaces]
X:28 [in Waterproof.Libs.Functions]
x:28 [in Waterproof.Libs.Analysis.MetricSpaces]
x:29 [in Waterproof.Libs.Analysis.MetricSpaces]
x:3 [in Waterproof.Notations.Common]
X:3 [in Waterproof.Notations.Sets]
x:3 [in Waterproof.Libs.Reals]
x:3 [in Waterproof.Libs.Analysis.OpenAndClosed]
x:3 [in Waterproof.Libs.Analysis.MetricSpaces]
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x:30 [in Waterproof.Libs.Analysis.SupAndInf]
X:30 [in Waterproof.Libs.Analysis.SequencesMetric]
x:31 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:31 [in Waterproof.Util.Goals]
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x:32 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:33 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:33 [in Waterproof.Libs.Functions]
x:34 [in Waterproof.Libs.Functions]
x:35 [in Waterproof.Libs.Sets.IndexedOperations]
x:35 [in Waterproof.Libs.Functions]
x:36 [in Waterproof.Libs.Functions]
X:37 [in Waterproof.Libs.Functions]
x:38 [in Waterproof.Libs.Analysis.MetricSpaces]
x:39 [in Waterproof.Libs.Analysis.MetricSpaces]
x:4 [in Waterproof.Libs.Sets.Operations]
X:4 [in Waterproof.Libs.Sets.IndexedOperations]
x:4 [in Waterproof.Libs.Logic.Quantification]
x:4 [in Waterproof.Libs.Analysis.MetricSpaces]
x:40 [in Waterproof.Libs.Analysis.MetricSpaces]
X:41 [in Waterproof.Libs.Sets.IndexedOperations]
x:41 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:41 [in Waterproof.Libs.Functions]
x:41 [in Waterproof.Util.Goals]
x:41 [in Waterproof.Libs.Analysis.MetricSpaces]
x:42 [in Waterproof.Libs.Sets.IndexedOperations]
x:42 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:42 [in Waterproof.Libs.Analysis.MetricSpaces]
x:43 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:44 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:44 [in Waterproof.Libs.Analysis.SupAndInf]
x:44 [in Waterproof.Libs.Analysis.MetricSpaces]
x:45 [in Waterproof.Libs.Analysis.SupAndInf]
X:46 [in Waterproof.Libs.Functions]
x:46 [in Waterproof.Libs.Analysis.MetricSpaces]
x:47 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:48 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:48 [in Waterproof.Libs.Analysis.SupAndInf]
x:49 [in Waterproof.Libs.Analysis.SupAndInf]
x:49 [in Waterproof.Util.Goals]
x:5 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
x:5 [in Waterproof.Notations.Common]
x:5 [in Waterproof.Libs.Logic.Quantification]
X:5 [in Waterproof.Notations.Sets]
X:5 [in Waterproof.Libs.Sets]
x:5 [in Waterproof.Libs.Reals]
x:5 [in Waterproof.Libs.Analysis.MetricSpaces]
x:50 [in Waterproof.Libs.Functions]
X:51 [in Waterproof.Libs.Sets.IndexedOperations]
x:52 [in Waterproof.Libs.Sets.IndexedOperations]
x:54 [in Waterproof.Notations.Sets]
x:55 [in Waterproof.Libs.Analysis.ContinuityDomainR]
X:55 [in Waterproof.Libs.Functions]
x:55 [in Waterproof.Util.Goals]
x:55 [in Waterproof.Notations.Sets]
x:56 [in Waterproof.Libs.Negation]
x:56 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:56 [in Waterproof.Notations.Sets]
x:57 [in Waterproof.Libs.Negation]
x:57 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:57 [in Waterproof.Notations.Sets]
x:57 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:58 [in Waterproof.Libs.Negation]
x:58 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:58 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:59 [in Waterproof.Libs.Functions]
x:59 [in Waterproof.Notations.Sets]
x:59 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:6 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:6 [in Waterproof.Libs.Functions]
x:6 [in Waterproof.Libs.Logic.Quantification]
x:60 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:61 [in Waterproof.Util.Goals]
x:61 [in Waterproof.Notations.Sets]
x:62 [in Waterproof.Libs.Negation]
x:63 [in Waterproof.Libs.Negation]
x:63 [in Waterproof.Notations.Sets]
x:64 [in Waterproof.Libs.Negation]
X:64 [in Waterproof.Libs.Functions]
x:65 [in Waterproof.Notations.Sets]
x:67 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:67 [in Waterproof.Notations.Sets]
x:68 [in Waterproof.Libs.Negation]
x:68 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:68 [in Waterproof.Libs.Functions]
x:68 [in Waterproof.Notations.Sets]
x:68 [in Waterproof.Chains.Inequalities]
x:69 [in Waterproof.Libs.Negation]
x:69 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:69 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:7 [in Waterproof.Libs.Sets.IndexedOperations]
x:7 [in Waterproof.Libs.Integers.Divisibility]
x:7 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:7 [in Waterproof.Libs.Functions]
x:7 [in Waterproof.Notations.Common]
x:7 [in Waterproof.Libs.Logic.Quantification]
x:7 [in Waterproof.Util.Goals]
x:7 [in Waterproof.Notations.Sets]
x:7 [in Waterproof.Libs.Reals]
x:70 [in Waterproof.Libs.Negation]
x:70 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:70 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:71 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:72 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
X:73 [in Waterproof.Libs.Functions]
x:73 [in Waterproof.Notations.Sets]
x:73 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:74 [in Waterproof.Libs.Negation]
x:74 [in Waterproof.Notations.Sets]
x:74 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:75 [in Waterproof.Libs.Negation]
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x:75 [in Waterproof.Notations.Sets]
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x:78 [in Waterproof.Notations.Sets]
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x:79 [in Waterproof.Notations.Sets]
x:8 [in Waterproof.Libs.Sets.Operations]
x:8 [in Waterproof.Libs.Analysis.ContinuityDomainR]
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x:8 [in Waterproof.Libs.Logic.Quantification]
X:8 [in Waterproof.Libs.Sets]
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x:80 [in Waterproof.Notations.Sets]
x:81 [in Waterproof.Libs.Negation]
x:81 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:82 [in Waterproof.Libs.Negation]
x:82 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:82 [in Waterproof.Libs.Functions]
x:83 [in Waterproof.Libs.Negation]
X:83 [in Waterproof.Libs.Functions]
x:84 [in Waterproof.Libs.Negation]
x:84 [in Waterproof.Libs.Analysis.SupAndInf]
x:85 [in Waterproof.Libs.Negation]
x:85 [in Waterproof.Notations.Sets]
x:85 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:86 [in Waterproof.Libs.Negation]
x:86 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:87 [in Waterproof.Libs.Negation]
x:87 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:87 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:88 [in Waterproof.Libs.Negation]
x:88 [in Waterproof.Libs.Analysis.ContinuityDomainR]
x:88 [in Waterproof.Notations.Sets]
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x:89 [in Waterproof.Libs.Analysis.ContinuityDomainR]
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x:91 [in Waterproof.Notations.Sets]
x:92 [in Waterproof.Libs.Negation]
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x:97 [in Waterproof.Notations.Sets]
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x:98 [in Waterproof.Notations.Sets]
x:98 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
x:99 [in Waterproof.Libs.Analysis.ContinuityDomainR]
X:99 [in Waterproof.Libs.Functions]
x:99 [in Waterproof.Notations.Sets]
x:99 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
Y
y:10 [in Waterproof.Notations.Common]y:10 [in Waterproof.Libs.Logic.Quantification]
y:10 [in Waterproof.Libs.Reals.Rational]
Y:100 [in Waterproof.Libs.Functions]
y:101 [in Waterproof.Libs.Analysis.SubsequencesMetric]
y:102 [in Waterproof.Libs.Functions]
y:103 [in Waterproof.Libs.Functions]
y:104 [in Waterproof.Libs.Functions]
y:105 [in Waterproof.Libs.Functions]
Y:11 [in Waterproof.Libs.Functions]
y:11 [in Waterproof.Libs.Logic.Quantification]
Y:111 [in Waterproof.Libs.Functions]
y:113 [in Waterproof.Libs.Functions]
Y:119 [in Waterproof.Libs.Functions]
y:12 [in Waterproof.Libs.Logic.Quantification]
Y:12 [in Waterproof.Libs.Sets]
Y:122 [in Waterproof.Libs.Functions]
Y:125 [in Waterproof.Libs.Functions]
y:126 [in Waterproof.Chains.Inequalities]
Y:128 [in Waterproof.Libs.Functions]
y:13 [in Waterproof.Libs.Logic.Quantification]
y:130 [in Waterproof.Chains.Inequalities]
Y:131 [in Waterproof.Libs.Functions]
y:134 [in Waterproof.Chains.Inequalities]
Y:137 [in Waterproof.Libs.Functions]
y:138 [in Waterproof.Chains.Inequalities]
y:14 [in Waterproof.Libs.Functions]
y:14 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:141 [in Waterproof.Libs.Functions]
Y:146 [in Waterproof.Libs.Functions]
y:15 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:150 [in Waterproof.Libs.Functions]
Y:155 [in Waterproof.Libs.Functions]
Y:159 [in Waterproof.Libs.Functions]
y:16 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:164 [in Waterproof.Libs.Functions]
y:17 [in Waterproof.Libs.Analysis.MetricSpaces]
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y:18 [in Waterproof.Notations.Sets]
Y:180 [in Waterproof.Libs.Functions]
y:183 [in Waterproof.Libs.Functions]
y:184 [in Waterproof.Libs.Functions]
y:185 [in Waterproof.Libs.Functions]
y:186 [in Waterproof.Libs.Functions]
Y:188 [in Waterproof.Libs.Functions]
y:191 [in Waterproof.Libs.Functions]
y:192 [in Waterproof.Libs.Functions]
y:193 [in Waterproof.Libs.Functions]
y:194 [in Waterproof.Libs.Functions]
Y:196 [in Waterproof.Libs.Functions]
y:2 [in Waterproof.Libs.Integers.Divisibility]
Y:2 [in Waterproof.Libs.Functions]
y:2 [in Waterproof.Libs.Reals.RealInequalities]
y:2 [in Waterproof.Notations.Common]
y:2 [in Waterproof.Libs.Reals]
Y:20 [in Waterproof.Libs.Functions]
Y:200 [in Waterproof.Libs.Functions]
Y:204 [in Waterproof.Libs.Functions]
Y:212 [in Waterproof.Libs.Functions]
y:215 [in Waterproof.Libs.Functions]
y:216 [in Waterproof.Libs.Functions]
y:217 [in Waterproof.Libs.Functions]
y:218 [in Waterproof.Libs.Functions]
y:22 [in Waterproof.Notations.Sets]
y:22 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:220 [in Waterproof.Libs.Functions]
y:227 [in Waterproof.Libs.Functions]
y:228 [in Waterproof.Libs.Functions]
y:229 [in Waterproof.Libs.Functions]
y:23 [in Waterproof.Libs.Functions]
y:23 [in Waterproof.Libs.Analysis.MetricSpaces]
y:230 [in Waterproof.Libs.Functions]
y:24 [in Waterproof.Notations.Sets]
y:24 [in Waterproof.Libs.Analysis.MetricSpaces]
y:25 [in Waterproof.Libs.Analysis.MetricSpaces]
y:26 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
Y:29 [in Waterproof.Libs.Functions]
y:29 [in Waterproof.Notations.Sets]
Y:3 [in Waterproof.Libs.Sets]
y:30 [in Waterproof.Libs.Analysis.MetricSpaces]
y:31 [in Waterproof.Notations.Sets]
y:31 [in Waterproof.Libs.Analysis.MetricSpaces]
y:32 [in Waterproof.Libs.Functions]
y:32 [in Waterproof.Libs.Analysis.MetricSpaces]
y:33 [in Waterproof.Libs.Analysis.MetricSpaces]
y:36 [in Waterproof.Notations.Sets]
Y:38 [in Waterproof.Libs.Functions]
y:38 [in Waterproof.Notations.Sets]
y:4 [in Waterproof.Notations.Common]
y:4 [in Waterproof.Libs.Reals]
y:42 [in Waterproof.Libs.Functions]
y:43 [in Waterproof.Libs.Functions]
y:43 [in Waterproof.Notations.Sets]
y:43 [in Waterproof.Libs.Analysis.MetricSpaces]
y:44 [in Waterproof.Libs.Functions]
y:45 [in Waterproof.Libs.Functions]
y:45 [in Waterproof.Notations.Sets]
y:45 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:47 [in Waterproof.Libs.Functions]
y:47 [in Waterproof.Libs.Analysis.MetricSpaces]
y:5 [in Waterproof.Libs.Functions]
y:50 [in Waterproof.Notations.Sets]
y:51 [in Waterproof.Libs.Functions]
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y:52 [in Waterproof.Notations.Sets]
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y:540 [in Waterproof.Libs.Analysis.SupAndInf]
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Y:6 [in Waterproof.Libs.Sets]
y:6 [in Waterproof.Libs.Reals]
y:6 [in Waterproof.Libs.Analysis.MetricSpaces]
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y:61 [in Waterproof.Libs.Functions]
y:62 [in Waterproof.Libs.Functions]
y:63 [in Waterproof.Libs.Functions]
Y:65 [in Waterproof.Libs.Functions]
y:69 [in Waterproof.Libs.Functions]
y:69 [in Waterproof.Chains.Inequalities]
y:7 [in Waterproof.Libs.Analysis.MetricSpaces]
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y:71 [in Waterproof.Libs.Functions]
y:72 [in Waterproof.Libs.Functions]
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y:8 [in Waterproof.Libs.Integers.Divisibility]
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y:8 [in Waterproof.Libs.Analysis.MetricSpaces]
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y:82 [in Waterproof.Notations.Sets]
y:83 [in Waterproof.Notations.Sets]
Y:84 [in Waterproof.Libs.Functions]
y:84 [in Waterproof.Notations.Sets]
y:9 [in Waterproof.Libs.Analysis.MetricSpaces]
Y:95 [in Waterproof.Libs.Functions]
Z
z:10 [in Waterproof.Libs.Integers.Divisibility]z:11 [in Waterproof.Libs.Integers.Divisibility]
z:12 [in Waterproof.Libs.Integers.Divisibility]
Z:132 [in Waterproof.Libs.Functions]
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z:166 [in Waterproof.Libs.Analysis.SupAndInf]
z:2 [in Waterproof.Libs.Reals.Integer]
z:23 [in Waterproof.Notations.Sets]
z:25 [in Waterproof.Notations.Sets]
z:3 [in Waterproof.Libs.Reals.ArchimedN]
z:3 [in Waterproof.Libs.Integers.Divisibility]
z:30 [in Waterproof.Notations.Sets]
z:32 [in Waterproof.Notations.Sets]
z:34 [in Waterproof.Libs.Analysis.MetricSpaces]
z:35 [in Waterproof.Libs.Analysis.MetricSpaces]
z:36 [in Waterproof.Libs.Analysis.MetricSpaces]
z:37 [in Waterproof.Notations.Sets]
z:37 [in Waterproof.Libs.Analysis.MetricSpaces]
z:39 [in Waterproof.Notations.Sets]
z:4 [in Waterproof.Libs.Reals.ArchimedN]
z:4 [in Waterproof.Libs.Integers.Divisibility]
z:44 [in Waterproof.Notations.Sets]
z:46 [in Waterproof.Notations.Sets]
z:5 [in Waterproof.Libs.Integers.Divisibility]
z:51 [in Waterproof.Notations.Sets]
z:53 [in Waterproof.Notations.Sets]
z:58 [in Waterproof.Notations.Sets]
z:6 [in Waterproof.Libs.Integers.Divisibility]
z:60 [in Waterproof.Notations.Sets]
z:62 [in Waterproof.Notations.Sets]
z:64 [in Waterproof.Notations.Sets]
z:9 [in Waterproof.Libs.Integers.Divisibility]
other
δ1:71 [in Waterproof.Libs.Analysis.ContinuityDomainR]δ1:72 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ1:73 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ1:74 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:107 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:108 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:109 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:110 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:26 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:27 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:28 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:29 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:37 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:38 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:39 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:40 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:51 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:52 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:53 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:53 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:54 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:54 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:55 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:56 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:63 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:64 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:65 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:65 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:66 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:66 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:67 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:68 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:81 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:82 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:83 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:84 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:93 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:94 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:95 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:95 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:96 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:96 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
δ:97 [in Waterproof.Libs.Analysis.ContinuityDomainR]
δ:98 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε1:5 [in Waterproof.Libs.Analysis.Sequences]
ε1:6 [in Waterproof.Libs.Analysis.Sequences]
ε1:7 [in Waterproof.Libs.Analysis.Sequences]
ε1:8 [in Waterproof.Libs.Analysis.Sequences]
ε:101 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:102 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:103 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:103 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:104 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:104 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:105 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:106 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:11 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:113 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:114 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:115 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:116 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:12 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:126 [in Waterproof.Libs.Analysis.Sequences]
ε:127 [in Waterproof.Libs.Analysis.Sequences]
ε:128 [in Waterproof.Libs.Analysis.Sequences]
ε:129 [in Waterproof.Libs.Analysis.Sequences]
ε:13 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:14 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:143 [in Waterproof.Libs.Analysis.Sequences]
ε:144 [in Waterproof.Libs.Analysis.Sequences]
ε:145 [in Waterproof.Libs.Analysis.Sequences]
ε:146 [in Waterproof.Libs.Analysis.Sequences]
ε:15 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:16 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:17 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:18 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:180 [in Waterproof.Libs.Analysis.Sequences]
ε:181 [in Waterproof.Libs.Analysis.Sequences]
ε:182 [in Waterproof.Libs.Analysis.Sequences]
ε:183 [in Waterproof.Libs.Analysis.Sequences]
ε:2 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:22 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:22 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:23 [in Waterproof.Libs.Analysis.Sequences]
ε:23 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:23 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:24 [in Waterproof.Libs.Analysis.Sequences]
ε:24 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:24 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:25 [in Waterproof.Libs.Analysis.Sequences]
ε:25 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:25 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:26 [in Waterproof.Libs.Analysis.Sequences]
ε:3 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:3 [in Waterproof.Notations.Reals]
ε:317 [in Waterproof.Libs.Analysis.SupAndInf]
ε:318 [in Waterproof.Libs.Analysis.SupAndInf]
ε:319 [in Waterproof.Libs.Analysis.SupAndInf]
ε:320 [in Waterproof.Libs.Analysis.SupAndInf]
ε:329 [in Waterproof.Libs.Analysis.SupAndInf]
ε:33 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:330 [in Waterproof.Libs.Analysis.SupAndInf]
ε:34 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:341 [in Waterproof.Libs.Analysis.SupAndInf]
ε:342 [in Waterproof.Libs.Analysis.SupAndInf]
ε:343 [in Waterproof.Libs.Analysis.SupAndInf]
ε:344 [in Waterproof.Libs.Analysis.SupAndInf]
ε:35 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:353 [in Waterproof.Libs.Analysis.SupAndInf]
ε:354 [in Waterproof.Libs.Analysis.SupAndInf]
ε:36 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:365 [in Waterproof.Libs.Analysis.SupAndInf]
ε:366 [in Waterproof.Libs.Analysis.SupAndInf]
ε:367 [in Waterproof.Libs.Analysis.SupAndInf]
ε:368 [in Waterproof.Libs.Analysis.SupAndInf]
ε:379 [in Waterproof.Libs.Analysis.SupAndInf]
ε:380 [in Waterproof.Libs.Analysis.SupAndInf]
ε:381 [in Waterproof.Libs.Analysis.SupAndInf]
ε:382 [in Waterproof.Libs.Analysis.SupAndInf]
ε:389 [in Waterproof.Libs.Analysis.SupAndInf]
ε:390 [in Waterproof.Libs.Analysis.SupAndInf]
ε:391 [in Waterproof.Libs.Analysis.SupAndInf]
ε:392 [in Waterproof.Libs.Analysis.SupAndInf]
ε:399 [in Waterproof.Libs.Analysis.SupAndInf]
ε:4 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:4 [in Waterproof.Notations.Reals]
ε:4 [in Waterproof.Libs.Analysis.SequencesMetric]
ε:400 [in Waterproof.Libs.Analysis.SupAndInf]
ε:401 [in Waterproof.Libs.Analysis.SupAndInf]
ε:402 [in Waterproof.Libs.Analysis.SupAndInf]
ε:409 [in Waterproof.Libs.Analysis.SupAndInf]
ε:410 [in Waterproof.Libs.Analysis.SupAndInf]
ε:421 [in Waterproof.Libs.Analysis.SupAndInf]
ε:422 [in Waterproof.Libs.Analysis.SupAndInf]
ε:425 [in Waterproof.Libs.Analysis.SupAndInf]
ε:426 [in Waterproof.Libs.Analysis.SupAndInf]
ε:429 [in Waterproof.Libs.Analysis.SupAndInf]
ε:430 [in Waterproof.Libs.Analysis.SupAndInf]
ε:441 [in Waterproof.Libs.Analysis.SupAndInf]
ε:442 [in Waterproof.Libs.Analysis.SupAndInf]
ε:443 [in Waterproof.Libs.Analysis.SupAndInf]
ε:444 [in Waterproof.Libs.Analysis.SupAndInf]
ε:451 [in Waterproof.Libs.Analysis.SupAndInf]
ε:452 [in Waterproof.Libs.Analysis.SupAndInf]
ε:463 [in Waterproof.Libs.Analysis.SupAndInf]
ε:464 [in Waterproof.Libs.Analysis.SupAndInf]
ε:467 [in Waterproof.Libs.Analysis.SupAndInf]
ε:468 [in Waterproof.Libs.Analysis.SupAndInf]
ε:47 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:471 [in Waterproof.Libs.Analysis.SupAndInf]
ε:472 [in Waterproof.Libs.Analysis.SupAndInf]
ε:475 [in Waterproof.Libs.Analysis.SupAndInf]
ε:476 [in Waterproof.Libs.Analysis.SupAndInf]
ε:48 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:49 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:49 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:5 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:5 [in Waterproof.Notations.Reals]
ε:5 [in Waterproof.Libs.Analysis.SequencesMetric]
ε:50 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:50 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:51 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:519 [in Waterproof.Libs.Analysis.SupAndInf]
ε:52 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:520 [in Waterproof.Libs.Analysis.SupAndInf]
ε:521 [in Waterproof.Libs.Analysis.SupAndInf]
ε:522 [in Waterproof.Libs.Analysis.SupAndInf]
ε:525 [in Waterproof.Libs.Analysis.SupAndInf]
ε:526 [in Waterproof.Libs.Analysis.SupAndInf]
ε:527 [in Waterproof.Libs.Analysis.SupAndInf]
ε:528 [in Waterproof.Libs.Analysis.SupAndInf]
ε:532 [in Waterproof.Libs.Analysis.SupAndInf]
ε:533 [in Waterproof.Libs.Analysis.SupAndInf]
ε:534 [in Waterproof.Libs.Analysis.SupAndInf]
ε:535 [in Waterproof.Libs.Analysis.SupAndInf]
ε:58 [in Waterproof.Libs.Analysis.Sequences]
ε:59 [in Waterproof.Libs.Analysis.Sequences]
ε:59 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:6 [in Waterproof.Notations.Reals]
ε:6 [in Waterproof.Libs.Analysis.SequencesMetric]
ε:60 [in Waterproof.Libs.Analysis.Sequences]
ε:60 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:61 [in Waterproof.Libs.Analysis.Sequences]
ε:61 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:61 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:62 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:62 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:63 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:64 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:7 [in Waterproof.Libs.Analysis.SequencesMetric]
ε:77 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:78 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:78 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:79 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:79 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:80 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:80 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:81 [in Waterproof.Libs.Analysis.SubsequencesMetric]
ε:83 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:84 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:85 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:86 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:89 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:90 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:91 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:91 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:92 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:92 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
ε:93 [in Waterproof.Libs.Analysis.ContinuityDomainR]
ε:94 [in Waterproof.Libs.Analysis.ContinuityDomainR]
Module Index
B
ByContradiction [in Waterproof.Util.Goals]C
Case [in Waterproof.Util.Goals]H
HelpNewHyp [in Waterproof.Tactics.Help]N
NaturalInduction [in Waterproof.Util.Goals]NaturalInduction.Base [in Waterproof.Util.Goals]
NaturalInduction.Step [in Waterproof.Util.Goals]
Q
Quantifiers [in Waterproof.Notations.Common]S
StateGoal [in Waterproof.Util.Goals]StateHyp [in Waterproof.Util.Goals]
StrongIndIndxSeq [in Waterproof.Util.Goals]
StrongIndIndxSeq.Base [in Waterproof.Util.Goals]
StrongIndIndxSeq.Step [in Waterproof.Util.Goals]
V
VerifyGoal [in Waterproof.Util.Goals]Variable Index
M
metricspace.X [in Waterproof.Libs.Analysis.ContinuityDomainNat]my_section.X [in Waterproof.Libs.Analysis.SubsequencesMetric]
Library Index
A
AnalysisArchimedN
Assertions
Assume
Automation
B
BecauseBinders
BothDirections
BothStatements
BySince
C
ChainsChoose
Claims
Common
Conclusion
Constr
ConstructiveLogic
ContinuityDomainNat
ContinuityDomainR
Contradiction
D
DefineDivisibility
E
EitherEvars
Even
F
FunctionsFunctions
G
GoalsH
HelpHints
Hypothesis
I
IndexedOperationsIndexedSets
Induction
Inequalities
InformativeEpsilon
Init
Integer
Integers
Integers
Intervals
ItHolds
ItSuffices
L
LimsupLiminfBolzanoLogic
M
ManipulationMessagesToUser
MetricSpaces
N
NegationNotations
O
ObtainOpenAndClosed
Operations
Q
QuantificationR
RationalRealInequalities
Reals
Reals
RealsWithSubsets
S
SequencesSequencesMetric
SequentialAccumulationPoints
Series
Sets
Sets
Specialize
Square
StrongInductionIndexSequence
Subsequences
SubsequencesMetric
SupAndInf
T
TacticsTake
ToShow
TypeCorrector
U
UnfoldV
VersionW
WaterproofWaterprove
Lemma Index
A
acc_pt_bds_seq_ub [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]all_not_ex_func [in Waterproof.Libs.Negation]
all_func [in Waterproof.Libs.Negation]
alternative_char_unique_exists [in Waterproof.Libs.Logic.Quantification]
alt_char_continuity [in Waterproof.Libs.Analysis.ContinuityDomainR]
alt_char_inf [in Waterproof.Libs.Analysis.SupAndInf]
alt_char_sup [in Waterproof.Libs.Analysis.SupAndInf]
alt_char_continuity [in Waterproof.Libs.Analysis.ContinuityDomainNat]
and_not_impl_func [in Waterproof.Libs.Negation]
and_not_or_func [in Waterproof.Libs.Negation]
and_func [in Waterproof.Libs.Negation]
any_low_bd_le_inf [in Waterproof.Libs.Analysis.SupAndInf]
any_upp_bd_ge_sup [in Waterproof.Libs.Analysis.SupAndInf]
archimedN [in Waterproof.Libs.Reals.ArchimedN]
archimedN_exists [in Waterproof.Libs.Reals.ArchimedN]
aux1 [in Waterproof.Libs.Analysis.ContinuityDomainNat]
B
bdd_below_to_bdd_above_set_opp [in Waterproof.Libs.Analysis.SupAndInf]bdd_above_bound_iff [in Waterproof.Libs.Analysis.SupAndInf]
bijective_iff [in Waterproof.Libs.Functions]
bijective_is_surjective [in Waterproof.Libs.Functions]
bijective_is_injective [in Waterproof.Libs.Functions]
Bolzano_Weierstrass [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
Bolzano_Weierstrass_gen [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
bounded_by_lower_bound_propform [in Waterproof.Libs.Analysis.SupAndInf]
bounded_by_upper_bound_propform [in Waterproof.Libs.Analysis.SupAndInf]
built_seq_is_index_seq [in Waterproof.Libs.Analysis.Subsequences]
C
classic_strong_ind_index_seq_with_prop_with_element_notation [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]classic_strong_ind_index_seq_with_prop [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
convergence_opp [in Waterproof.Libs.Analysis.Sequences]
convergence_minus [in Waterproof.Libs.Analysis.Sequences]
convergence_plus [in Waterproof.Libs.Analysis.Sequences]
convergence_equivalence [in Waterproof.Libs.Analysis.Sequences]
conv_evt_eq_seq [in Waterproof.Libs.Analysis.Sequences]
created_seq_is_index_seq [in Waterproof.Libs.Analysis.Subsequences]
D
dep_only_on_start_index_seq_prop_family [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]diff_is_rational [in Waterproof.Libs.Reals.Rational]
divide_char_inv [in Waterproof.Libs.Integers.Divisibility]
divide_char [in Waterproof.Libs.Integers.Divisibility]
div_is_rational [in Waterproof.Libs.Reals.Rational]
div_one_neq_zero [in Waterproof.Libs.Reals]
div_non_zero [in Waterproof.Libs.Reals]
div_pos [in Waterproof.Libs.Reals]
div_sign_flip [in Waterproof.Libs.Reals]
double_sumbool_sumtriad_cba [in Waterproof.Tactics.Either]
double_sumbool_sumtriad_cab [in Waterproof.Tactics.Either]
double_sumbool_sumtriad_bca [in Waterproof.Tactics.Either]
double_sumbool_sumtriad_bac [in Waterproof.Tactics.Either]
double_sumbool_sumtriad_acb [in Waterproof.Tactics.Either]
double_sumbool_sumtriad_abc [in Waterproof.Tactics.Either]
double_is_even [in Waterproof.Libs.Analysis.SubsequencesMetric]
d'_eq_3 [in Waterproof.Libs.Analysis.MetricSpaces]
d'_eq_0 [in Waterproof.Libs.Analysis.MetricSpaces]
E
elements_le_seq_of_max [in Waterproof.Libs.Analysis.Subsequences]elements_le_seq_of_max_pre [in Waterproof.Libs.Analysis.Subsequences]
empty_set_characterization [in Waterproof.Libs.Sets]
equivalent_subsequence_convergence [in Waterproof.Libs.Analysis.SubsequencesMetric]
eq_seq_conv_to_same_lim [in Waterproof.Libs.Analysis.Sequences]
even_or_odd [in Waterproof.Libs.Integers.Even]
even_of [in Waterproof.Libs.Integers.Even]
every_point_in_R_acc_point_R [in Waterproof.Libs.Analysis.ContinuityDomainR]
existence_next_el_to_fun [in Waterproof.Libs.Analysis.Subsequences]
exists_subseq_to_limsup_bdd [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
exists_almost_lim_sup [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
exists_good_subseq [in Waterproof.Libs.Analysis.Subsequences]
exists_almost_lim_sup_aux [in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_minimizer_ε [in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_maximizer_ε [in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_minimizer [in Waterproof.Libs.Analysis.SupAndInf]
exists_almost_maximizer [in Waterproof.Libs.Analysis.SupAndInf]
exists_inf [in Waterproof.Libs.Analysis.SupAndInf]
exists_exists_in_iff [in Waterproof.Notations.Sets]
ex_not_all_func [in Waterproof.Libs.Negation]
ex_func [in Waterproof.Libs.Negation]
F
false_Req [in Waterproof.Libs.Reals]finite_or_find_one [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
forall_forall_in_iff [in Waterproof.Notations.Sets]
G
ge_zero_gt_one [in Waterproof.Libs.Reals.Integer]H
help_with_choice [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]I
if_almost_minimizer_ε_then_every_low_bd_smaller [in Waterproof.Libs.Analysis.SupAndInf]if_almost_maximizer_ε_then_every_upp_bd_larger [in Waterproof.Libs.Analysis.SupAndInf]
if_almost_minimizer_then_every_low_bd_smaller [in Waterproof.Libs.Analysis.SupAndInf]
if_almost_maximizer_then_every_upp_bd_larger [in Waterproof.Libs.Analysis.SupAndInf]
impl_not_and_func [in Waterproof.Libs.Negation]
impl_func [in Waterproof.Libs.Negation]
incr_loc_to_glob [in Waterproof.Libs.Analysis.Subsequences]
incr_loc_to_glob [in Waterproof.Libs.Analysis.SubsequencesMetric]
index_seq_grows [in Waterproof.Libs.Analysis.Subsequences]
index_seq_grows_0 [in Waterproof.Libs.Analysis.Subsequences]
index_seq_strictly_incr [in Waterproof.Libs.Analysis.Subsequences]
index_union_elim_left [in Waterproof.Libs.Sets.IndexedOperations]
index_union_elim [in Waterproof.Libs.Sets.IndexedOperations]
index_intersection_elim_left [in Waterproof.Libs.Sets.IndexedOperations]
index_intersection_elim [in Waterproof.Libs.Sets.IndexedOperations]
index_sequence_property2_automation [in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property2 [in Waterproof.Libs.Analysis.SubsequencesMetric]
index_seq_equiv [in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property_automation [in Waterproof.Libs.Analysis.SubsequencesMetric]
index_sequence_property [in Waterproof.Libs.Analysis.SubsequencesMetric]
induction_principle_elements [in Waterproof.Tactics.Induction]
informative_or_lift [in Waterproof.Libs.Logic.InformativeEpsilon]
inf_el_to_fun [in Waterproof.Libs.Analysis.Subsequences]
inf_is_low_bd [in Waterproof.Libs.Analysis.SupAndInf]
injective_elim [in Waterproof.Libs.Functions]
INR_0 [in Waterproof.Libs.Reals.Integer]
INR_1 [in Waterproof.Libs.Reals.Integer]
intersection_characterization_left [in Waterproof.Libs.Sets.Operations]
intersection_characterization [in Waterproof.Libs.Sets.Operations]
int_is_rational [in Waterproof.Libs.Reals.Rational]
inverse_intro [in Waterproof.Libs.Functions]
inverse_elim_right [in Waterproof.Libs.Functions]
inverse_elim_left [in Waterproof.Libs.Functions]
inverse_is_right_inverse [in Waterproof.Libs.Functions]
inverse_is_left_inverse [in Waterproof.Libs.Functions]
inv_remove [in Waterproof.Libs.Reals]
in_preimage_iff [in Waterproof.Libs.Functions]
in_preimage_elim [in Waterproof.Libs.Functions]
in_preimage_intro [in Waterproof.Libs.Functions]
in_image_iff [in Waterproof.Libs.Functions]
in_image_elim [in Waterproof.Libs.Functions]
in_image_intro [in Waterproof.Libs.Functions]
in_implies_not_in_compl [in Waterproof.Libs.Analysis.OpenAndClosed]
is_bounded_equivalence [in Waterproof.Libs.Analysis.Sequences]
is_sup_is_lub_iff [in Waterproof.Libs.Analysis.SupAndInf]
is_upper_bound_Raxioms_is_upper_bound_iff [in Waterproof.Libs.Analysis.SupAndInf]
L
left_inverse_intro [in Waterproof.Libs.Functions]left_inverse_elim [in Waterproof.Libs.Functions]
left_in_closed_open [in Waterproof.Libs.Reals]
lim_sup_bdd_is_lub_seq_acc_pts [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
lim_const_min_1_over_n_plus_1 [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
lim_d_0 [in Waterproof.Libs.Analysis.Sequences]
lim_const_seq [in Waterproof.Libs.Analysis.Sequences]
low_bd_seq_is_low_bd_lim [in Waterproof.Libs.Analysis.Sequences]
low_bd_set_opp_to_upp_bd_set [in Waterproof.Libs.Analysis.SupAndInf]
low_bd_set_to_upp_bd_set_opp [in Waterproof.Libs.Analysis.SupAndInf]
M
make_sumtriad_uninformative_6 [in Waterproof.Libs.Logic.ConstructiveLogic]make_sumtriad_uninformative_5 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_4 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_3 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_2 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumtriad_uninformative_1 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumbool_uninformative_2 [in Waterproof.Libs.Logic.ConstructiveLogic]
make_sumbool_uninformative_1 [in Waterproof.Libs.Logic.ConstructiveLogic]
max_or_strict [in Waterproof.Libs.Analysis.SupAndInf]
mem_of_preimage [in Waterproof.Libs.Functions]
mem_subset_full_set [in Waterproof.Notations.Sets]
minus_Z_in_R [in Waterproof.Libs.Reals.Integer]
min_1_over_n_plus_1_to_0 [in Waterproof.Libs.Analysis.Sequences]
min_frac [in Waterproof.Libs.Reals.Rational]
mouse_tail [in Waterproof.Libs.Analysis.Series]
mult_Z_in_R [in Waterproof.Libs.Reals.Integer]
mult_neq_zero [in Waterproof.Libs.Reals.RealInequalities]
mult_is_rational [in Waterproof.Libs.Reals.Rational]
N
nat_dist_less_than_one_iff_equal [in Waterproof.Libs.Analysis.ContinuityDomainNat]nat_dist_larger_zero_not_equal [in Waterproof.Libs.Analysis.ContinuityDomainNat]
nat_not_equal_dist_larger_one [in Waterproof.Libs.Analysis.ContinuityDomainNat]
neg_Z_in_R [in Waterproof.Libs.Reals.Integer]
neg_is_rational [in Waterproof.Libs.Reals.Rational]
not_neg_pos_func [in Waterproof.Libs.Negation]
not_ex_all_func [in Waterproof.Libs.Negation]
not_all_ex_func [in Waterproof.Libs.Negation]
not_impl_and_func [in Waterproof.Libs.Negation]
not_and_impl_func [in Waterproof.Libs.Negation]
not_and_or_func [in Waterproof.Libs.Negation]
not_or_and_func [in Waterproof.Libs.Negation]
not_even_and_odd [in Waterproof.Libs.Integers.Even]
not_in_empty [in Waterproof.Libs.Sets]
not_in_compl_implies_in [in Waterproof.Libs.Analysis.OpenAndClosed]
O
odd_of [in Waterproof.Libs.Integers.Even]one_Z_in_R [in Waterproof.Libs.Reals.Integer]
one_in_complement_interval_closed_zero_open_one [in Waterproof.Libs.Analysis.OpenAndClosed]
or_not_and_func [in Waterproof.Libs.Negation]
or_func [in Waterproof.Libs.Negation]
P
partial_sums_pos_incr [in Waterproof.Libs.Analysis.Series]perfect_square_of [in Waterproof.Libs.Integers.Square]
plus_Z_in_R [in Waterproof.Libs.Reals.Integer]
plus_frac [in Waterproof.Libs.Reals.Rational]
pos_not_neg_func [in Waterproof.Libs.Negation]
power_set_characterization_alt [in Waterproof.Libs.Sets]
power_set_characterization [in Waterproof.Libs.Sets]
preimage_of_mem [in Waterproof.Libs.Functions]
Q
quant_over_start_dep_only_on_start [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]R
Rabs_left1_with_minus [in Waterproof.Libs.Reals]Rabs_zero [in Waterproof.Libs.Reals]
Rabs_m_lt_n [in Waterproof.Libs.Analysis.ContinuityDomainNat]
Rabs_n_min_m [in Waterproof.Libs.Analysis.ContinuityDomainNat]
rational_of [in Waterproof.Libs.Reals.Rational]
Rdivid_ineq_interchange [in Waterproof.Libs.Reals.RealInequalities]
reformulate_step_prop_index [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_final_prop_index [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_base_prop_index [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_final_prop_strong [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
reformulate_base_prop_strong [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
relation_shift [in Waterproof.Libs.Analysis.SequencesMetric]
remainder_of [in Waterproof.Libs.Integers.Divisibility]
Req_false [in Waterproof.Libs.Reals]
Req_true [in Waterproof.Libs.Reals]
Rge_lt_or_eq_dec [in Waterproof.Libs.Reals]
Rge_le_dec [in Waterproof.Libs.Reals]
Rge_min_abs [in Waterproof.Libs.Reals]
right_inverse_intro [in Waterproof.Libs.Functions]
right_inverse_elim [in Waterproof.Libs.Functions]
right_in_open_closed [in Waterproof.Libs.Reals]
Rle_ge_dec [in Waterproof.Libs.Reals]
Rle_abs_min [in Waterproof.Libs.Reals]
Rlt_ge_dec [in Waterproof.Libs.Reals]
Rmax_abs [in Waterproof.Libs.Reals]
R_complete_unsealed [in Waterproof.Libs.Analysis.SupAndInf]
R_complete [in Waterproof.Libs.Analysis.SupAndInf]
S
sequence_ub_bds [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]seq_of_max_is_increasing [in Waterproof.Libs.Analysis.Subsequences]
seq_ordered_lim_ordered [in Waterproof.Libs.Analysis.Sequences]
seq_ex_almost_maximizer_m [in Waterproof.Libs.Analysis.SupAndInf]
seq_ex_almost_maximizer_ε [in Waterproof.Libs.Analysis.SupAndInf]
seq_bdd_seq_acc_pts_bdd [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
set_difference_elim [in Waterproof.Libs.Sets]
sigma_split_v2 [in Waterproof.Libs.Analysis.Series]
Sn_eq_nplus1 [in Waterproof.Tactics.Induction]
squeeze_theorem [in Waterproof.Libs.Analysis.Sequences]
strong_ind_index_seq_with_prop [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
strong_ind_seq_with_prop [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
subsequence_of_convergent_sequence [in Waterproof.Libs.Analysis.SubsequencesMetric]
subseq_sat_rel [in Waterproof.Libs.Analysis.Subsequences]
sumbool_comm [in Waterproof.Tactics.Either]
sum_is_rational [in Waterproof.Libs.Reals.Rational]
sup_is_upp_bd [in Waterproof.Libs.Analysis.SupAndInf]
sup_set_opp_is_inf_set [in Waterproof.Libs.Analysis.SupAndInf]
surjective_elim [in Waterproof.Libs.Functions]
T
true_Req [in Waterproof.Libs.Reals]two_Z_in_R [in Waterproof.Libs.Reals.Integer]
U
union_characterization_left [in Waterproof.Libs.Sets.Operations]union_characterization [in Waterproof.Libs.Sets.Operations]
upp_bd_seq_is_upp_bd_lim [in Waterproof.Libs.Analysis.Sequences]
upp_bd_set_opp_to_low_bd_set [in Waterproof.Libs.Analysis.SupAndInf]
upp_bd_set_to_low_bd_set_opp [in Waterproof.Libs.Analysis.SupAndInf]
Z
zero_Z_in_R [in Waterproof.Libs.Reals.Integer]zero_in_interval_closed_zero_open_one [in Waterproof.Libs.Analysis.OpenAndClosed]
Zeven_char_inv [in Waterproof.Libs.Integers.Even]
Zeven_char [in Waterproof.Libs.Integers.Even]
Zodd_char_inv [in Waterproof.Libs.Integers.Even]
Zodd_char [in Waterproof.Libs.Integers.Even]
_
_and_assoc1 [in Waterproof.Waterprove]Constructor Index
B
base_gc [in Waterproof.Chains.Inequalities]base_lc [in Waterproof.Chains.Inequalities]
base_ec [in Waterproof.Chains.Inequalities]
ByContradiction.wrap [in Waterproof.Util.Goals]
C
Case.wrap [in Waterproof.Util.Goals]chain_base [in Waterproof.Chains.Inequalities]
chain_link [in Waterproof.Chains.Inequalities]
chain_ge [in Waterproof.Chains.Inequalities]
chain_gt [in Waterproof.Chains.Inequalities]
chain_le [in Waterproof.Chains.Inequalities]
chain_lt [in Waterproof.Chains.Inequalities]
chain_eq [in Waterproof.Chains.Inequalities]
Closed [in Waterproof.Libs.Reals.Intervals]
Closed_Open [in Waterproof.Libs.Reals.Intervals]
I
index_union_intro [in Waterproof.Libs.Sets.IndexedOperations]index_intersection_intro [in Waterproof.Libs.Sets.IndexedOperations]
L
left [in Waterproof.Tactics.Either]link_gc_grtr [in Waterproof.Chains.Inequalities]
link_gc_eq [in Waterproof.Chains.Inequalities]
link_ec_grtr [in Waterproof.Chains.Inequalities]
link_lc_less [in Waterproof.Chains.Inequalities]
link_lc_eq [in Waterproof.Chains.Inequalities]
link_ec_less [in Waterproof.Chains.Inequalities]
link_ec_eq [in Waterproof.Chains.Inequalities]
M
middle [in Waterproof.Tactics.Either]N
NaturalInduction.Base.wrap [in Waterproof.Util.Goals]NaturalInduction.Step.wrap [in Waterproof.Util.Goals]
O
Open [in Waterproof.Libs.Reals.Intervals]Open_Closed [in Waterproof.Libs.Reals.Intervals]
R
right [in Waterproof.Tactics.Either]S
StateGoal.wrap [in Waterproof.Util.Goals]StateHyp.wrap [in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.wrap [in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.wrap [in Waterproof.Util.Goals]
V
VerifyGoal.wrap [in Waterproof.Util.Goals]Inductive Index
B
ByContradiction.Wrapper [in Waterproof.Util.Goals]C
Case.Wrapper [in Waterproof.Util.Goals]ChainBase [in Waterproof.Chains.Inequalities]
ChainLink [in Waterproof.Chains.Inequalities]
E
EqualChain [in Waterproof.Chains.Inequalities]EqualRel [in Waterproof.Chains.Inequalities]
F
fix_earlier_warning [in Waterproof.Util.Goals]G
GreaterChain [in Waterproof.Chains.Inequalities]GreaterRel [in Waterproof.Chains.Inequalities]
I
indexed_union [in Waterproof.Libs.Sets.IndexedOperations]indexed_intersection [in Waterproof.Libs.Sets.IndexedOperations]
is_interval [in Waterproof.Libs.Reals.Intervals]
L
LessChain [in Waterproof.Chains.Inequalities]LessRel [in Waterproof.Chains.Inequalities]
N
NaturalInduction.Base.Wrapper [in Waterproof.Util.Goals]NaturalInduction.Step.Wrapper [in Waterproof.Util.Goals]
S
StateGoal.Wrapper [in Waterproof.Util.Goals]StateHyp.Wrapper [in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.Wrapper [in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.Wrapper [in Waterproof.Util.Goals]
sumtriad [in Waterproof.Tactics.Either]
V
VerifyGoal.Wrapper [in Waterproof.Util.Goals]Projection Index
C
chain_base [in Waterproof.Chains.Inequalities]chain_link [in Waterproof.Chains.Inequalities]
E
eq_rel_to_pred [in Waterproof.Chains.Inequalities]G
ge_op [in Waterproof.Notations.Sets]global_statement [in Waterproof.Chains.Inequalities]
grtr_rel_to_pred [in Waterproof.Chains.Inequalities]
gt_op [in Waterproof.Notations.Sets]
L
less_rel_to_pred [in Waterproof.Chains.Inequalities]le_op [in Waterproof.Notations.Sets]
lt_op [in Waterproof.Notations.Sets]
N
ne_op [in Waterproof.Notations.Sets]T
total_statement [in Waterproof.Chains.Inequalities]W
weak_global_statement [in Waterproof.Chains.Inequalities]Instance Index
B
base_gc_R_Z [in Waterproof.Chains.Inequalities]base_gc_Z_R [in Waterproof.Chains.Inequalities]
base_lc_R_Z [in Waterproof.Chains.Inequalities]
base_lc_Z_R [in Waterproof.Chains.Inequalities]
base_ec_R_Z [in Waterproof.Chains.Inequalities]
base_ec_Z_R [in Waterproof.Chains.Inequalities]
base_gc_R_nat [in Waterproof.Chains.Inequalities]
base_gc_nat_R [in Waterproof.Chains.Inequalities]
base_lc_R_nat [in Waterproof.Chains.Inequalities]
base_lc_nat_R [in Waterproof.Chains.Inequalities]
base_ec_R_nat [in Waterproof.Chains.Inequalities]
base_ec_nat_R [in Waterproof.Chains.Inequalities]
base_gc_inst [in Waterproof.Chains.Inequalities]
base_lc_inst [in Waterproof.Chains.Inequalities]
base_ec_inst [in Waterproof.Chains.Inequalities]
E
ec_interpretable [in Waterproof.Chains.Inequalities]equal_interpretation [in Waterproof.Chains.Inequalities]
G
gc_interpretable [in Waterproof.Chains.Inequalities]L
lc_interpretable [in Waterproof.Chains.Inequalities]link_gc_grtr_R_Z [in Waterproof.Chains.Inequalities]
link_gc_grtr_Z_R [in Waterproof.Chains.Inequalities]
link_gc_eq_R_Z [in Waterproof.Chains.Inequalities]
link_gc_eq_Z_R [in Waterproof.Chains.Inequalities]
link_ec_grtr_R_Z [in Waterproof.Chains.Inequalities]
link_ec_grtr_Z_R [in Waterproof.Chains.Inequalities]
link_lc_less_R_Z [in Waterproof.Chains.Inequalities]
link_lc_less_Z_R [in Waterproof.Chains.Inequalities]
link_lc_eq_R_Z [in Waterproof.Chains.Inequalities]
link_lc_eq_Z_R [in Waterproof.Chains.Inequalities]
link_ec_less_R_Z [in Waterproof.Chains.Inequalities]
link_ec_less_Z_R [in Waterproof.Chains.Inequalities]
link_ec_eq_R_Z [in Waterproof.Chains.Inequalities]
link_ec_eq_Z_R [in Waterproof.Chains.Inequalities]
link_gc_grtr_R_nat [in Waterproof.Chains.Inequalities]
link_gc_grtr_nat_R [in Waterproof.Chains.Inequalities]
link_gc_eq_R_nat [in Waterproof.Chains.Inequalities]
link_gc_eq_nat_R [in Waterproof.Chains.Inequalities]
link_ec_grtr_R_nat [in Waterproof.Chains.Inequalities]
link_ec_grtr_nat_R [in Waterproof.Chains.Inequalities]
link_lc_less_R_nat [in Waterproof.Chains.Inequalities]
link_lc_less_nat_R [in Waterproof.Chains.Inequalities]
link_lc_eq_R_nat [in Waterproof.Chains.Inequalities]
link_lc_eq_nat_R [in Waterproof.Chains.Inequalities]
link_ec_less_R_nat [in Waterproof.Chains.Inequalities]
link_ec_less_nat_R [in Waterproof.Chains.Inequalities]
link_ec_eq_R_nat [in Waterproof.Chains.Inequalities]
link_ec_eq_nat_R [in Waterproof.Chains.Inequalities]
link_gc_grtr_inst [in Waterproof.Chains.Inequalities]
link_gc_eq_inst [in Waterproof.Chains.Inequalities]
link_ec_grtr_inst [in Waterproof.Chains.Inequalities]
link_lc_less_inst [in Waterproof.Chains.Inequalities]
link_lc_eq_inst [in Waterproof.Chains.Inequalities]
link_ec_less_inst [in Waterproof.Chains.Inequalities]
link_ec_eq_inst [in Waterproof.Chains.Inequalities]
N
nat_ne_type [in Waterproof.Notations.Sets]nat_lt_type [in Waterproof.Notations.Sets]
nat_le_type [in Waterproof.Notations.Sets]
nat_gt_type [in Waterproof.Notations.Sets]
nat_ge_type [in Waterproof.Notations.Sets]
O
order_interpretation_R [in Waterproof.Chains.Inequalities]order_interpretation_nat [in Waterproof.Chains.Inequalities]
R
R_ne_type [in Waterproof.Notations.Sets]R_lt_type [in Waterproof.Notations.Sets]
R_le_type [in Waterproof.Notations.Sets]
R_gt_type [in Waterproof.Notations.Sets]
R_ge_type [in Waterproof.Notations.Sets]
Section Index
C
Construction [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]D
Definitions [in Waterproof.Libs.Analysis.MetricSpaces]M
metricspace [in Waterproof.Libs.Analysis.ContinuityDomainNat]my_section [in Waterproof.Libs.Analysis.SubsequencesMetric]
S
StrongInduction [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]StrongInductionIndexSequence [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
Abbreviation Index
P
partial_sums [in Waterproof.Libs.Analysis.Series]Definition Index
A
as_subset [in Waterproof.Notations.Sets]a_seq [in Waterproof.Libs.Analysis.Sequences]
B
bijective [in Waterproof.Libs.Functions]bounded [in Waterproof.Libs.Analysis.SequencesMetric]
build_seq [in Waterproof.Libs.Analysis.Subsequences]
ByContradiction.unwrap [in Waterproof.Util.Goals]
C
Case.unwrap [in Waterproof.Util.Goals]complement [in Waterproof.Libs.Analysis.OpenAndClosed]
composition [in Waterproof.Libs.Functions]
constant_sequence [in Waterproof.Libs.Analysis.Sequences]
const_seq_from [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
const_seq [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
conv [in Waterproof.Notations.Sets]
convergence [in Waterproof.Libs.Analysis.SequencesMetric]
converges_to [in Waterproof.Notations.Reals]
create_seq [in Waterproof.Libs.Analysis.Subsequences]
cv_implies_cv_abs_to_l_abs [in Waterproof.Notations.Reals]
D
d [in Waterproof.Libs.Analysis.Sequences]dep_choice [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
dep_only_on_start [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
dist_reflexive [in Waterproof.Libs.Analysis.MetricSpaces]
dist_triangle_inequality [in Waterproof.Libs.Analysis.MetricSpaces]
dist_symmetric [in Waterproof.Libs.Analysis.MetricSpaces]
dist_non_degenerate [in Waterproof.Libs.Analysis.MetricSpaces]
dist_positive [in Waterproof.Libs.Analysis.MetricSpaces]
diverges_to_minus_infinity [in Waterproof.Libs.Analysis.Sequences]
diverges_to_plus_infinity [in Waterproof.Libs.Analysis.Sequences]
d_discrete_R [in Waterproof.Libs.Analysis.MetricSpaces]
E
ec_map [in Waterproof.Chains.Inequalities]ec_total_statement [in Waterproof.Chains.Inequalities]
ec_global_statement [in Waterproof.Chains.Inequalities]
ec_tail [in Waterproof.Chains.Inequalities]
ec_head [in Waterproof.Chains.Inequalities]
empty [in Waterproof.Notations.Sets]
evt_eq_sequences [in Waterproof.Libs.Analysis.Sequences]
F
finite_triangle_inequalty [in Waterproof.Notations.Reals]first_satisfying_element [in Waterproof.Libs.Analysis.Subsequences]
first_satisfying_element_helper [in Waterproof.Libs.Analysis.Subsequences]
full [in Waterproof.Notations.Sets]
G
gc_map [in Waterproof.Chains.Inequalities]gc_total_statement [in Waterproof.Chains.Inequalities]
gc_weak_global_statement [in Waterproof.Chains.Inequalities]
gc_global_statement [in Waterproof.Chains.Inequalities]
gc_tail [in Waterproof.Chains.Inequalities]
gc_head [in Waterproof.Chains.Inequalities]
global_grtr_rel [in Waterproof.Chains.Inequalities]
global_less_rel [in Waterproof.Chains.Inequalities]
grtr_relation_flow [in Waterproof.Chains.Inequalities]
H
has_inverse [in Waterproof.Libs.Functions]has_right_inverse [in Waterproof.Libs.Functions]
has_left_inverse [in Waterproof.Libs.Functions]
I
identity_seal [in Waterproof.Notations.Common]image [in Waterproof.Libs.Functions]
index_seq_prop_family [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
ind_seq_with_prop [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
ind_seq_of_seq_and_prop [in Waterproof.Libs.Analysis.StrongInductionIndexSequence]
injective [in Waterproof.Libs.Functions]
inverse [in Waterproof.Libs.Functions]
is_square [in Waterproof.Libs.Integers.Square]
is_increasing [in Waterproof.Libs.Analysis.Subsequences]
is_index_seq [in Waterproof.Libs.Analysis.Subsequences]
is_bounded_below [in Waterproof.Libs.Analysis.Sequences]
is_bounded_above [in Waterproof.Libs.Analysis.Sequences]
is_bounded_equivalent [in Waterproof.Libs.Analysis.Sequences]
is_bounded [in Waterproof.Libs.Analysis.Sequences]
is_continuous_in [in Waterproof.Libs.Analysis.ContinuityDomainR]
is_isolated_point [in Waterproof.Libs.Analysis.ContinuityDomainR]
is_accumulation_point [in Waterproof.Libs.Analysis.ContinuityDomainR]
is_inf_alt_char [in Waterproof.Libs.Analysis.SupAndInf]
is_sup_alt_char [in Waterproof.Libs.Analysis.SupAndInf]
is_inf [in Waterproof.Libs.Analysis.SupAndInf]
is_bounded_below [in Waterproof.Libs.Analysis.SupAndInf]
is_lower_bound [in Waterproof.Libs.Analysis.SupAndInf]
is_max [in Waterproof.Libs.Analysis.SupAndInf]
is_sup [in Waterproof.Libs.Analysis.SupAndInf]
is_bounded_above [in Waterproof.Libs.Analysis.SupAndInf]
is_upper_bound [in Waterproof.Libs.Analysis.SupAndInf]
is_rational [in Waterproof.Libs.Reals.Rational]
is_seq_acc_pt [in Waterproof.Libs.Analysis.SequentialAccumulationPoints]
is_increasing [in Waterproof.Libs.Analysis.SubsequencesMetric]
is_accumulation_point [in Waterproof.Libs.Analysis.SubsequencesMetric]
is_subsequence [in Waterproof.Libs.Analysis.SubsequencesMetric]
is_index_seq [in Waterproof.Libs.Analysis.SubsequencesMetric]
is_index_sequence [in Waterproof.Libs.Analysis.SubsequencesMetric]
is_closed [in Waterproof.Libs.Analysis.OpenAndClosed]
is_open [in Waterproof.Libs.Analysis.OpenAndClosed]
is_interior_point [in Waterproof.Libs.Analysis.OpenAndClosed]
is_continuous_in [in Waterproof.Libs.Analysis.ContinuityDomainNat]
is_isolated_point [in Waterproof.Libs.Analysis.ContinuityDomainNat]
is_accumulation_point [in Waterproof.Libs.Analysis.ContinuityDomainNat]
L
lc_map [in Waterproof.Chains.Inequalities]lc_total_statement [in Waterproof.Chains.Inequalities]
lc_weak_global_statement [in Waterproof.Chains.Inequalities]
lc_global_statement [in Waterproof.Chains.Inequalities]
lc_tail [in Waterproof.Chains.Inequalities]
lc_head [in Waterproof.Chains.Inequalities]
left_inverse [in Waterproof.Libs.Functions]
less_relation_flow [in Waterproof.Chains.Inequalities]
limit_in_point [in Waterproof.Libs.Analysis.ContinuityDomainR]
limit_in_point [in Waterproof.Libs.Analysis.ContinuityDomainNat]
lim_sup_bdd [in Waterproof.Libs.Analysis.LimsupLiminfBolzano]
N
NaturalInduction.Base.unwrap [in Waterproof.Util.Goals]NaturalInduction.Step.unwrap [in Waterproof.Util.Goals]
O
open_ball [in Waterproof.Libs.Analysis.OpenAndClosed]P
preimage [in Waterproof.Libs.Functions]Q
Q_in_R [in Waterproof.Libs.Reals.Rational]R
remainder [in Waterproof.Libs.Integers.Divisibility]right_inverse [in Waterproof.Libs.Functions]
S
seal [in Waterproof.Notations.Sets]seq_of_max [in Waterproof.Libs.Analysis.Subsequences]
series_cv_abs_to [in Waterproof.Libs.Analysis.Series]
series_cv_abs [in Waterproof.Libs.Analysis.Series]
series_cv [in Waterproof.Libs.Analysis.Series]
series_cv_to [in Waterproof.Libs.Analysis.Series]
set_opp [in Waterproof.Libs.Analysis.SupAndInf]
snd_map [in Waterproof.Chains.Inequalities]
square [in Waterproof.Libs.Integers.Square]
StateGoal.unwrap [in Waterproof.Util.Goals]
StateHyp.unwrap [in Waterproof.Util.Goals]
StrongIndIndxSeq.Base.unwrap [in Waterproof.Util.Goals]
StrongIndIndxSeq.Step.unwrap [in Waterproof.Util.Goals]
subset_in [in Waterproof.Notations.Sets]
subset_type [in Waterproof.Notations.Sets]
surjective [in Waterproof.Libs.Functions]
T
type_of_test_aux [in Waterproof.Util.Assertions]type_of [in Waterproof.Util.Init]
U
unique_exists [in Waterproof.Notations.Sets]V
VerifyGoal.unwrap [in Waterproof.Util.Goals]Y
y_seq [in Waterproof.Libs.Analysis.Sequences]Z
Z_in_R [in Waterproof.Libs.Reals.Integer]Record Index
C
ChainBase [in Waterproof.Chains.Inequalities]ChainLink [in Waterproof.Chains.Inequalities]
E
EqualInterpretation [in Waterproof.Chains.Inequalities]G
ge_type [in Waterproof.Notations.Sets]gt_type [in Waterproof.Notations.Sets]
I
InterpretableChain [in Waterproof.Chains.Inequalities]L
le_type [in Waterproof.Notations.Sets]lt_type [in Waterproof.Notations.Sets]
N
ne_type [in Waterproof.Notations.Sets]O
OrderInterpretation [in Waterproof.Chains.Inequalities]| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (4073 entries) |
| Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (195 entries) |
| Binder Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (3260 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Variable Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (2 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (79 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (241 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (35 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (22 entries) |
| Projection Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Instance Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (66 entries) |
| Section Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (6 entries) |
| Abbreviation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (1 entry) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (130 entries) |
| Record Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (10 entries) |
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