url stringclasses 3
values | commit stringclasses 3
values | file_path stringlengths 20 79 | full_name stringlengths 3 115 | start list | end list | traced_tactics stringlengths 2 997k |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iSup_mul | [
652,
1
] | [
653,
56
] | [{"tactic": "rw [mul_comm, mul_iSup]", "annotated_tactic": ["rw [<a>mul_comm</a>, <a>mul_iSup</a>]", [{"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [302, 9], "def_end_pos": [302, 17]}, {"full_name": "ENNReal.mul_iSup", "def_path": "Mathlib/Topology/Instances/ENNReal.lean", "def_pos... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | iSup₂_le_iSup | [
891,
1
] | [
892,
34
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Buckets.exists_of_update | [
24,
1
] | [
27,
64
] | [{"tactic": "simp [Array.getElem_eq_data_get]", "annotated_tactic": ["simp [<a>Array.getElem_eq_data_get</a>]", [{"full_name": "Array.getElem_eq_data_get", "def_path": "lake-packages/std/Std/Data/Array/Init/Lemmas.lean", "def_pos": [28, 9], "def_end_pos": [28, 28]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.get_replicate | [
703,
9
] | [
704,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sups.lean | Finset.disjSups_comm | [
559,
1
] | [
567,
33
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\ninst\u271d\u2074 : DecidableEq \u03b1\ninst\u271d\u00b3 : DecidableEq \u03b2\ninst\u271d\u00b2 : SemilatticeSup \u03b1\ninst\u271d\u00b9 : OrderBot \u03b1\ninst\u271d : DecidableRel Disjoint\ns s\u20... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Tower.lean | Polynomial.aeval_algebraMap_eq_zero_iff | [
60,
1
] | [
63,
52
] | [{"tactic": "rw [aeval_algebraMap_apply, Algebra.algebraMap_eq_smul_one, smul_eq_zero,\n iff_false_intro (one_ne_zero' B), or_false_iff]", "annotated_tactic": ["rw [<a>aeval_algebraMap_apply</a>, <a>Algebra.algebraMap_eq_smul_one</a>, <a>smul_eq_zero</a>,\n <a>iff_false_intro</a> (<a>one_ne_zero'</a> B), <a>or_fals... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Coprod/Basic.lean | Monoid.Coprod.toProd_apply_inr | [
502,
1
] | [
502,
74
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_inf_principal_iff | [
1619,
1
] | [
1621,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Derivation/ToSquareZero.lean | derivationToSquareZeroOfLift_apply | [
75,
1
] | [
78,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Coset.lean | Subgroup.card_dvd_of_injective | [
816,
1
] | [
820,
45
] | [{"tactic": "classical calc\n card \u03b1 = card (f.range : Subgroup H) := card_congr (Equiv.ofInjective f hf)\n _ \u2223 card H := card_subgroup_dvd_card _", "annotated_tactic": ["classical calc\n <a>card</a> \u03b1 = <a>card</a> (f.range : <a>Subgroup</a> H) := <a>card_congr</a> (<a>Equiv.ofInjective</a> f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.mem_iff' | [
178,
1
] | [
179,
57
] | [{"tactic": "rw [\u2190 transpose_mem_iff, mem_iff, transpose_transpose]", "annotated_tactic": ["rw [\u2190 <a>transpose_mem_iff</a>, <a>mem_iff</a>, <a>transpose_transpose</a>]", [{"full_name": "SymplecticGroup.transpose_mem_iff", "def_path": "Mathlib/LinearAlgebra/SymplecticGroup.lean", "def_pos": [174, 9], "def_end_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Basic.lean | Nat.two_mul_ne_two_mul_add_one | [
353,
1
] | [
355,
84
] | [{"tactic": "rw [add_comm, add_mul_mod_self_left, mul_mod_right, mod_eq_of_lt] <;> simp", "annotated_tactic": ["rw [<a>add_comm</a>, <a>add_mul_mod_self_left</a>, <a>mul_mod_right</a>, <a>mod_eq_of_lt</a>] <;> simp", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/LocalExtr.lean | isLocalExtrOn_const | [
195,
1
] | [
196,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.submodule_iSup_eq_top | [
328,
1
] | [
330,
40
] | [{"tactic": "rw [Submodule.iSup_eq_range_dfinsupp_lsum, LinearMap.range_eq_top]", "annotated_tactic": ["rw [<a>Submodule.iSup_eq_range_dfinsupp_lsum</a>, <a>LinearMap.range_eq_top</a>]", [{"full_name": "Submodule.iSup_eq_range_dfinsupp_lsum", "def_path": "Mathlib/LinearAlgebra/DFinsupp.lean", "def_pos": [307, 9], "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_injective_of_surjective | [
2543,
1
] | [
2548,
65
] | [{"tactic": "obtain \u27e8g, hg\u27e9 := hf.hasRightInverse", "annotated_tactic": ["obtain \u27e8g, hg\u27e9 := hf.hasRightInverse", []], "state_before": "R : Type u_1\nR\u2081 : Type u_2\nR\u2082 : Type u_3\nR\u2083 : Type u_4\nR\u2084 : Type u_5\nS : Type u_6\nK : Type u_7\nK\u2082 : Type u_8\nM : Type u_9\nM' : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ico' | [
1535,
1
] | [
1544,
43
] | [{"tactic": "ext1 x", "annotated_tactic": ["ext1 x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LinearOrder \u03b1\na a\u2081 a\u2082 b b\u2081 b\u2082 c d : \u03b1\nh\u2081 : c \u2264 b\nh\u2082 : a \u2264 d\n\u22a2 Ico a b \u222a Ico c d = Ico (min a c) (max b d)", "state_after": "case h... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq_zero_of_fst_eq_zero | [
218,
1
] | [
221,
69
] | [{"tactic": "rw [hx, (algebraMap R S).map_zero] at h", "annotated_tactic": ["rw [hx, (<a>algebraMap</a> R S).<a>map_zero</a>] at h", [{"full_name": "algebraMap", "def_path": "Mathlib/Algebra/Algebra/Basic.lean", "def_pos": [125, 5], "def_end_pos": [125, 15]}, {"full_name": "RingHom.map_zero", "def_path": "Mathlib/Algeb... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Regular.lean | MeasurableSet.measure_eq_iSup_isClosed_of_ne_top | [
600,
1
] | [
602,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Category/Semilat.lean | SemilatInfCat.coe_forget_to_partOrd | [
143,
1
] | [
145,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.unop_comp | [
83,
1
] | [
84,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Coprod/Basic.lean | Monoid.MulEquiv.coprodAssoc_symm_apply_inr_inr | [
690,
1
] | [
692,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAdjointPair.eq | [
1044,
1
] | [
1045,
5
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_left | [
120,
1
] | [
122,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Disjoint.lean | IsCompl.disjoint_left_iff | [
527,
1
] | [
529,
30
] | [{"tactic": "rw [disjoint_iff]", "annotated_tactic": ["rw [<a>disjoint_iff</a>]", [{"full_name": "disjoint_iff", "def_path": "Mathlib/Order/Disjoint.lean", "def_pos": [126, 9], "def_end_pos": [126, 21]}]], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : DistribLattice \u03b1\ninst\u271d : BoundedOrder \u03b1\na ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/DualQuaternion.lean | Quaternion.imI_snd_dualNumberEquiv | [
92,
1
] | [
94,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | MeasurableEquiv.symm_preimage_preimage | [
1409,
1
] | [
1410,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.exists_rat_pow_btwn_rat_aux | [
738,
1
] | [
750,
26
] | [{"tactic": "have hn' : 0 < (n : \u211d) := by exact_mod_cast hn.bot_lt", "annotated_tactic": ["have hn' : 0 < (n : \u211d) := by exact_mod_cast hn.bot_lt", []], "state_before": "z x\u271d y\u271d : \u211d\nn : \u2115\nhn : n \u2260 0\nx y : \u211d\nh : x < y\nhy : 0 < y\n\u22a2 \u2203 q, 0 < q \u2227 x < \u2191q ^ n \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Primrec.lean | Primrec.pair | [
362,
1
] | [
368,
55
] | [{"tactic": "cases @decode \u03b1 _ n <;> simp [encodek]", "annotated_tactic": ["cases @<a>decode</a> \u03b1 _ n <;> simp [<a>encodek</a>]", [{"full_name": "Encodable.decode", "def_path": "Mathlib/Logic/Encodable/Basic.lean", "def_pos": [51, 3], "def_end_pos": [51, 9]}, {"full_name": "Encodable.encodek", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/AddCircle.lean | continuousAt_toIocMod | [
112,
1
] | [
117,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.parallelPairHom_app_zero | [
267,
1
] | [
270,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.natDegree_restriction | [
312,
1
] | [
313,
19
] | [{"tactic": "simp [natDegree]", "annotated_tactic": ["simp [<a>natDegree</a>]", [{"full_name": "Polynomial.natDegree", "def_path": "Mathlib/Data/Polynomial/Degree/Definitions.lean", "def_pos": [65, 5], "def_end_pos": [65, 14]}]], "state_before": "R : Type u\nS : Type u_1\ninst\u271d : Ring R\np : R[X]\n\u22a2 natDegree... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.finset_sup_comp | [
917,
1
] | [
921,
6
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\ud835\udd5c : Type u_1\n\ud835\udd5c\u2082 : Type u_2\n\ud835\udd5d : Type u_3\n\ud835\udd5d\u2082 : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\n\u03b9 : Type u_8\n\u03b9' : Type u_9\ninst\u271d\u2076 : NormedField \ud835\udd5c\ninst\u271... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.coeToFun_mul | [
294,
1
] | [
295,
6
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Classes/Order.lean | Std.OrientedCmp.cmp_refl | [
37,
1
] | [
41,
48
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/Alter.lean | Std.RBNode.WF.alter | [
394,
1
] | [
398,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Cofinite.lean | Filter.cofinite_eq_bot | [
64,
1
] | [
64,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_lt_aleph0_iff_of_ne_zero | [
1597,
1
] | [
1598,
72
] | [{"tactic": "simp [mul_lt_aleph0_iff, ha, hb]", "annotated_tactic": ["simp [<a>mul_lt_aleph0_iff</a>, ha, hb]", [{"full_name": "Cardinal.mul_lt_aleph0_iff", "def_path": "Mathlib/SetTheory/Cardinal/Basic.lean", "def_pos": [1567, 9], "def_end_pos": [1567, 26]}]], "state_before": "\u03b1 \u03b2 : Type u\na b : Cardinal.{u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.continuous_of_finiteDimensional | [
246,
1
] | [
261,
49
] | [{"tactic": "let b := Basis.ofVectorSpace \ud835\udd5c E", "annotated_tactic": ["let b := <a>Basis.ofVectorSpace</a> \ud835\udd5c E", [{"full_name": "Basis.ofVectorSpace", "def_path": "Mathlib/LinearAlgebra/Basis/VectorSpace.lean", "def_pos": [110, 19], "def_end_pos": [110, 32]}]], "state_before": "\ud835\udd5c : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.target_inter_preimage_symm_source_eq | [
201,
1
] | [
203,
72
] | [{"tactic": "rw [inter_comm, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]", "annotated_tactic": ["rw [<a>inter_comm</a>, f.target_eq, e.source_eq, f.preimage_symm_proj_inter]", [{"full_name": "Set.inter_comm", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [940, 9], "def_end_pos": [940, 19]}]], "state_b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_formula | [
105,
1
] | [
107,
97
] | [{"tactic": "rw [Formula.Realize, Formula.Realize, \u2190 f.map_boundedFormula, Unique.eq_default (f \u2218 default)]", "annotated_tactic": ["rw [<a>Formula.Realize</a>, <a>Formula.Realize</a>, \u2190 f.map_boundedFormula, <a>Unique.eq_default</a> (f \u2218 <a>default</a>)]", [{"full_name": "FirstOrder.Language.Formula... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sigma.lean | Set.sigma_empty | [
90,
1
] | [
91,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/NAry.lean | Set.image2_singleton_right | [
200,
1
] | [
201,
23
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b1' : Type u_2\n\u03b2 : Type u_3\n\u03b2' : Type u_4\n\u03b3 : Type u_5\n\u03b3' : Type u_6\n\u03b4 : Type u_7\n\u03b4' : Type u_8\n\u03b5 : Type u_9\n\u03b5' : Type u_10\n\u03b6 : Type u_11\n\u03b6' : Type u_12\n\u03bd : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Units.lean | Units.divp_add_divp | [
113,
1
] | [
118,
13
] | [{"tactic": "simp only [divp, add_mul, mul_inv_rev, val_mul]", "annotated_tactic": ["simp only [<a>divp</a>, <a>add_mul</a>, <a>mul_inv_rev</a>, <a>val_mul</a>]", [{"full_name": "divp", "def_path": "Mathlib/Algebra/Group/Units.lean", "def_pos": [434, 5], "def_end_pos": [434, 9]}, {"full_name": "add_mul", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edge_other_incident_set | [
1080,
1
] | [
1083,
48
] | [{"tactic": "use h.1", "annotated_tactic": ["use h.1", []], "state_before": "\u03b9 : Sort u_1\n\ud835\udd5c : Type u_2\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v\u271d w : V\ne\u271d : Sym2 V\ninst\u271d : DecidableEq V\nv : V\ne : Sym2 V\nh : e \u2208 incidenceSet G v\n\u22a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.monotone_distinctConstantsTheory | [
1148,
1
] | [
1150,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_exp_pos | [
611,
1
] | [
612,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_empty_right | [
156,
1
] | [
157,
73
] | [{"tactic": "rw [edgeDensity, Finset.card_empty, Nat.cast_zero, mul_zero, div_zero]", "annotated_tactic": ["rw [<a>edgeDensity</a>, <a>Finset.card_empty</a>, <a>Nat.cast_zero</a>, <a>mul_zero</a>, <a>div_zero</a>]", [{"full_name": "Rel.edgeDensity", "def_path": "Mathlib/Combinatorics/SimpleGraph/Density.lean", "def_pos... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_mul_apply_aux | [
565,
1
] | [
575,
64
] | [{"tactic": "classical exact\n have : (f.sum fun a b => ite (x * a = y) (0 * b) 0) = 0 := by simp\n calc\n (HMul.hMul (\u03b1 := MonoidAlgebra k G) (single x r) f) y =\n sum f fun a b => ite (x * a = y) (r * b) 0 :=\n (mul_apply _ _ _).trans <| sum_single_index this\n _ = f.sum fun a b =... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | uniformCauchySeqOnFilter_of_deriv | [
479,
1
] | [
483,
68
] | [{"tactic": "simp_rw [hasDerivAt_iff_hasFDerivAt] at hf", "annotated_tactic": ["simp_rw [<a>hasDerivAt_iff_hasFDerivAt</a>] at hf", [{"full_name": "hasDerivAt_iff_hasFDerivAt", "def_path": "Mathlib/Analysis/Calculus/Deriv/Basic.lean", "def_pos": [222, 9], "def_end_pos": [222, 35]}]], "state_before": "\u03b9 : Type u_1\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Prod/Basic.lean | Prod.mk.eta | [
32,
1
] | [
33,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Between.lean | wbtw_const_vsub_iff | [
198,
1
] | [
200,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.card | [
174,
1
] | [
176,
7
] | [{"tactic": "rw [\u2190 Fintype.card_eq.mpr \u27e8fintypeHelper\u27e9, Fintype.card_sum, ZMod.card, two_mul]", "annotated_tactic": ["rw [\u2190 Fintype.card_eq.mpr \u27e8<a>fintypeHelper</a>\u27e9, <a>Fintype.card_sum</a>, <a>ZMod.card</a>, <a>two_mul</a>]", [{"full_name": "_private.Mathlib.GroupTheory.SpecificGroups.Q... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Order/LinearOrder.lean | min_eq_right_of_lt | [
146,
1
] | [
147,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_liminf | [
1519,
1
] | [
1521,
70
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.ext_iff | [
146,
1
] | [
147,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/DiffContOnCl.lean | diffContOnCl_const | [
52,
1
] | [
53,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Diffeomorph.lean | Diffeomorph.symm_refl | [
238,
1
] | [
239,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Int.le_floor_add_floor | [
763,
1
] | [
767,
19
] | [{"tactic": "rw [\u2190 sub_le_iff_le_add, le_floor, Int.cast_sub, sub_le_comm, Int.cast_sub, Int.cast_one]", "annotated_tactic": ["rw [\u2190 <a>sub_le_iff_le_add</a>, <a>le_floor</a>, <a>Int.cast_sub</a>, <a>sub_le_comm</a>, <a>Int.cast_sub</a>, <a>Int.cast_one</a>]", [{"full_name": "sub_le_iff_le_add", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | RingHom.not_one_mem_ker | [
2090,
1
] | [
2092,
20
] | [{"tactic": "rw [mem_ker, map_one]", "annotated_tactic": ["rw [<a>mem_ker</a>, <a>map_one</a>]", [{"full_name": "RingHom.mem_ker", "def_path": "Mathlib/RingTheory/Ideal/Operations.lean", "def_pos": [2074, 9], "def_end_pos": [2074, 16]}, {"full_name": "map_one", "def_path": "Mathlib/Algebra/Hom/Group/Defs.lean", "def_po... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Pi/Algebra.lean | Pi.mul_apply | [
83,
1
] | [
84,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IsAdjoinRoot.lean | IsAdjoinRoot.map_repr | [
169,
1
] | [
170,
35
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/Lemmas.lean | Std.RBSet.toStream_eq | [
647,
1
] | [
647,
78
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Dual.lean | LinearEquiv.dualMap_apply | [
246,
1
] | [
248,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Bitwise.lean | Int.bitwise_or | [
221,
1
] | [
235,
32
] | [{"tactic": "funext m n", "annotated_tactic": ["funext m n", []], "state_before": "\u22a2 bitwise or = lor", "state_after": "case h.h\nm n : \u2124\n\u22a2 bitwise or m n = lor m n"}, {"tactic": "cases' m with m m <;> cases' n with n n <;> try {rfl}\n <;> simp only [bitwise, natBitwise, Bool.not_false, Bool.or_true, c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoundedVariation.lean | LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn | [
788,
1
] | [
795,
33
] | [{"tactic": "rcases eq_empty_or_nonempty s with (rfl | \u27e8c, cs\u27e9)", "annotated_tactic": ["rcases <a>eq_empty_or_nonempty</a> s with (rfl | \u27e8c, cs\u27e9)", [{"full_name": "Set.eq_empty_or_nonempty", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [635, 9], "def_end_pos": [635, 29]}]], "state_before": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bases.lean | Set.Finite.isSeparable | [
492,
1
] | [
493,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TuringMachine.lean | Turing.eval_maximal₁ | [
851,
1
] | [
855,
27
] | [{"tactic": "let \u27e8_, b0\u27e9 := mem_eval.1 h", "annotated_tactic": ["let \u27e8_, b0\u27e9 := <a>mem_eval</a>.1 h", [{"full_name": "Turing.mem_eval", "def_path": "Mathlib/Computability/TuringMachine.lean", "def_pos": [830, 9], "def_end_pos": [830, 17]}]], "state_before": "\u03c3 : Type u_1\nf : \u03c3 \u2192 Opti... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.subset_zeroLocus_vanishingIdeal | [
172,
1
] | [
174,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.mem_top | [
140,
1
] | [
141,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Hausdorff.lean | MeasureTheory.OuterMeasure.mkMetric'.mono_pre_nat | [
284,
1
] | [
285,
66
] | [{"tactic": "simpa", "annotated_tactic": ["simpa", []], "state_before": "\u03b9 : Type u_1\nX : Type u_2\nY : Type u_3\ninst\u271d\u00b9 : EMetricSpace X\ninst\u271d : EMetricSpace Y\nm\u271d : Set X \u2192 \u211d\u22650\u221e\nr : \u211d\u22650\u221e\n\u03bc : OuterMeasure X\ns\u271d : Set X\nm : Set X \u2192 \u211d\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Basic.lean | exists_of_bex | [
1077,
1
] | [
1078,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiffDef.lean | tsupport_iteratedFDeriv_subset | [
1569,
1
] | [
1576,
61
] | [{"tactic": "induction' n with n IH", "annotated_tactic": ["induction' n with n IH", []], "state_before": "\ud835\udd5c : Type u\ninst\u271d\u2078 : NontriviallyNormedField \ud835\udd5c\nE : Type uE\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\nF : Type uF\ninst\u271d\u2075 : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_smul | [
443,
1
] | [
445,
51
] | [{"tactic": "simp only [SMul.smul, HSMul.hSMul, RatFunc.smul]", "annotated_tactic": ["simp only [<a>SMul.smul</a>, <a>HSMul.hSMul</a>, <a>RatFunc.smul</a>]", [{"full_name": "SMul.smul", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [82, 3], "def_end_pos": [82, 7]}, {"full_name": "HSMul.hSMul", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₈_nat_mod_eight | [
150,
1
] | [
150,
92
] | [{"tactic": "rw [\u2190 ZMod.nat_cast_mod n 8]", "annotated_tactic": ["rw [\u2190 <a>ZMod.nat_cast_mod</a> n 8]", [{"full_name": "ZMod.nat_cast_mod", "def_path": "Mathlib/Data/ZMod/Basic.lean", "def_pos": [712, 9], "def_end_pos": [712, 21]}]], "state_before": "n : \u2115\n\u22a2 \u2191\u03c7\u2088 \u2191n = \u2191\u03c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.exists_right_complement'_of_coprime | [
291,
1
] | [
308,
34
] | [{"tactic": "by_cases hN1 : Nat.card N = 0", "annotated_tactic": ["by_cases hN1 : <a>Nat.card</a> N = 0", [{"full_name": "Nat.card", "def_path": "Mathlib/SetTheory/Cardinal/Finite.lean", "def_pos": [37, 15], "def_end_pos": [37, 19]}]], "state_before": "n : \u2115\nG : Type u\ninst\u271d\u00b9 : Group G\nN : Subgroup G\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_obj_X_dTo | [
163,
1
] | [
165,
7
] | [{"tactic": "rw [dTo_eq ((single\u2080 V).obj X) rfl]", "annotated_tactic": ["rw [<a>dTo_eq</a> ((<a>single\u2080</a> V).<a>obj</a> X) <a>rfl</a>]", [{"full_name": "HomologicalComplex.dTo_eq", "def_path": "Mathlib/Algebra/Homology/HomologicalComplex.lean", "def_pos": [467, 9], "def_end_pos": [467, 15]}, {"full_name": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Function.lean | Set.BijOn.union | [
963,
1
] | [
965,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.mem_nhds_one | [
130,
1
] | [
131,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | isOpen_Ioi | [
332,
1
] | [
333,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Analytic/Basic.lean | AnalyticOn.mono | [
706,
1
] | [
707,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Heyting/Basic.lean | sdiff_le_iff' | [
504,
1
] | [
504,
80
] | [{"tactic": "rw [sdiff_le_iff, sup_comm]", "annotated_tactic": ["rw [<a>sdiff_le_iff</a>, <a>sup_comm</a>]", [{"full_name": "sdiff_le_iff", "def_path": "Mathlib/Order/Heyting/Basic.lean", "def_pos": [500, 9], "def_end_pos": [500, 21]}, {"full_name": "sup_comm", "def_path": "Mathlib/Order/Lattice.lean", "def_pos": [250,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/CharP/Basic.lean | Commute.add_pow_prime_eq | [
45,
11
] | [
48,
45
] | [{"tactic": "simpa using h.add_pow_prime_pow_eq hp 1", "annotated_tactic": ["simpa using h.add_pow_prime_pow_eq hp 1", []], "state_before": "R : Type u_1\ninst\u271d : Semiring R\np : \u2115\nx y : R\nhp : Nat.Prime p\nh : Commute x y\n\u22a2 (x + y) ^ p = x ^ p + y ^ p + \u2191p * \u2211 k in Ioo 0 p, x ^ k * y ^ (p -... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Notation.lean | Matrix.vec2_dotProduct | [
513,
1
] | [
514,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nndist_eq_iSup | [
501,
1
] | [
506,
27
] | [{"tactic": "push_cast", "annotated_tactic": ["push_cast", []], "state_before": "p : \u211d\u22650\u221e\n\ud835\udd5c : Type u_1\n\ud835\udd5c' : Type u_2\n\u03b9 : Type u_3\n\u03b1 : \u03b9 \u2192 Type u_4\n\u03b2\u271d : \u03b9 \u2192 Type u_5\ninst\u271d\u00b2 : Fintype \u03b9\ninst\u271d\u00b9 : Fact (1 \u2264 p)\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Intervals.lean | List.Ico.filter_le_of_le_bot | [
184,
1
] | [
188,
36
] | [{"tactic": "rw [decide_eq_true_eq]", "annotated_tactic": ["rw [<a>decide_eq_true_eq</a>]", [{"full_name": "decide_eq_true_eq", "def_path": "lake-packages/lean4/src/lean/Init/SimpLemmas.lean", "def_pos": [139, 17], "def_end_pos": [139, 34]}]], "state_before": "n m l : \u2115\nhln : l \u2264 n\nk : \u2115\nhk : k \u2208... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | sInf_eq_bot | [
664,
1
] | [
665,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prime_X_sub_C | [
406,
1
] | [
409,
14
] | [{"tactic": "simp_rw [dvd_iff_isRoot, IsRoot.def, eval_mul, mul_eq_zero]", "annotated_tactic": ["simp_rw [<a>dvd_iff_isRoot</a>, <a>IsRoot.def</a>, <a>eval_mul</a>, <a>mul_eq_zero</a>]", [{"full_name": "Polynomial.dvd_iff_isRoot", "def_path": "Mathlib/Data/Polynomial/Div.lean", "def_pos": [472, 9], "def_end_pos": [472,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.is_left_invariant_index | [
286,
1
] | [
290,
80
] | [{"tactic": "refine' le_antisymm (mul_left_index_le hK hV g) _", "annotated_tactic": ["refine' <a>le_antisymm</a> (<a>mul_left_index_le</a> hK hV g) _", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}, {"full_name": "MeasureTheory.Measure.haar.mul... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/NonUnitalSubring/Basic.lean | NonUnitalSubring.coe_set_mk | [
169,
1
] | [
171,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Int.ceil_sub_ofNat | [
1249,
1
] | [
1250,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.attach_map_coe' | [
3029,
1
] | [
3031,
51
] | [{"tactic": "rw [attach, map_pmap]", "annotated_tactic": ["rw [<a>attach</a>, <a>map_pmap</a>]", [{"full_name": "List.attach", "def_path": "lake-packages/std/Std/Data/List/Basic.lean", "def_pos": [767, 34], "def_end_pos": [767, 40]}, {"full_name": "List.map_pmap", "def_path": "Mathlib/Data/List/Basic.lean", "def_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mem_toSubalgebra | [
113,
1
] | [
114,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/List.lean | List.mem_of_formPerm_ne_self | [
399,
1
] | [
403,
16
] | [{"tactic": "suffices x \u2208 { y | formPerm l y \u2260 y } by\n rw [\u2190 mem_toFinset]\n exact support_formPerm_le' _ this", "annotated_tactic": ["suffices x \u2208 { y | <a>formPerm</a> l y \u2260 y } by\n rw [\u2190 <a>mem_toFinset</a>]\n exact <a>support_formPerm_le'</a> _ this", [{"full_name": "List.for... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.functor_unit_comp | [
153,
1
] | [
155,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Category/GroupCat/Basic.lean | GroupCat.coe_of | [
102,
1
] | [
103,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.map_id | [
588,
1
] | [
589,
72
] | [{"tactic": "rw [map_apply v measurable_id hi, Set.preimage_id]", "annotated_tactic": ["rw [<a>map_apply</a> v <a>measurable_id</a> hi, <a>Set.preimage_id</a>]", [{"full_name": "MeasureTheory.VectorMeasure.map_apply", "def_path": "Mathlib/MeasureTheory/Measure/VectorMeasure.lean", "def_pos": [581, 9], "def_end_pos": [5... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/AddCircle.lean | AddCircle.closedBall_ae_eq_ball | [
34,
1
] | [
48,
53
] | [{"tactic": "cases' le_or_lt \u03b5 0 with h\u03b5 h\u03b5", "annotated_tactic": ["cases' <a>le_or_lt</a> \u03b5 0 with h\u03b5 h\u03b5", [{"full_name": "le_or_lt", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [340, 9], "def_end_pos": [340, 17]}]], "state_before": "T : \u211d\nhT : Fact (0 < T)\nx : AddCircle... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/NonUnitalSubring/Basic.lean | NonUnitalSubring.map_id | [
435,
1
] | [
436,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.closure_def | [
107,
1
] | [
108,
21
] | [{"tactic": "simp [closure, hf]", "annotated_tactic": ["simp [<a>closure</a>, hf]", [{"full_name": "LinearPMap.closure", "def_path": "Mathlib/Topology/Algebra/Module/LinearPMap.lean", "def_pos": [103, 19], "def_end_pos": [103, 26]}]], "state_before": "R : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u00b9\u00b9 : C... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Basic.lean | xor_true | [
285,
9
] | [
285,
61
] | [{"tactic": "simp [Xor']", "annotated_tactic": ["simp [<a>Xor'</a>]", [{"full_name": "Xor'", "def_path": "Mathlib/Init/Logic.lean", "def_pos": [103, 5], "def_end_pos": [103, 9]}]], "state_before": "\u22a2 Xor' True = Not", "state_after": "no goals"}] |
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