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/Data/Sigma/Order.lean | Sigma.lt_def | [
88,
1
] | [
95,
27
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 LT (\u03b1 i)\na b : (i : \u03b9) \u00d7 \u03b1 i\n\u22a2 a < b \u2194 \u2203 h, h \u25b8 a.snd < b.snd", "state_after": "case mp\n\u03b9 : Type u_1\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Basic.lean | Order.pred_eq_iSup | [
930,
1
] | [
935,
93
] | [{"tactic": "refine' le_antisymm _ (iSup_le fun b => iSup_le le_pred_of_lt)", "annotated_tactic": ["refine' <a>le_antisymm</a> _ (<a>iSup_le</a> fun b => <a>iSup_le</a> <a>le_pred_of_lt</a>)", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}, {"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/PartialSups.lean | bddAbove_range_partialSups | [
81,
1
] | [
89,
67
] | [{"tactic": "apply exists_congr fun a => _", "annotated_tactic": ["apply <a>exists_congr</a> fun a => _", [{"full_name": "exists_congr", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [379, 9], "def_end_pos": [379, 21]}]], "state_before": "\u03b1 : Type u_1\ninst\u271d : SemilatticeSup \u03b1\nf : \u2115 \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Sigma.lean | List.dlookup_kinsert_ne | [
591,
1
] | [
592,
61
] | [{"tactic": "simp [h]", "annotated_tactic": ["simp [h]", []], "state_before": "\u03b1 : Type u\n\u03b2 : \u03b1 \u2192 Type v\nl\u271d l\u2081 l\u2082 : List (Sigma \u03b2)\ninst\u271d : DecidableEq \u03b1\na a' : \u03b1\nb' : \u03b2 a'\nl : List (Sigma \u03b2)\nh : a \u2260 a'\n\u22a2 dlookup a (kinsert a' b' l) = dlo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToTypes_obj | [
57,
1
] | [
59,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.upperClosure | [
1416,
11
] | [
1417,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Basic.lean | Complex.re_surjective | [
66,
1
] | [
66,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.universally_eq | [
793,
1
] | [
795,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | AntitoneOn.map_isGreatest | [
1259,
1
] | [
1260,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.rat_add_iff | [
204,
1
] | [
204,
99
] | [{"tactic": "rw [add_comm, add_rat_iff]", "annotated_tactic": ["rw [<a>add_comm</a>, <a>add_rat_iff</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"full_name": "LiouvilleWith.add_rat_iff", "def_path": "Mathlib/NumberTheory/Liouville/Liou... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Constructions.lean | map_nhds_subtype_coe_eq_nhds | [
1069,
1
] | [
1071,
64
] | [{"tactic": "rw [Subtype.range_val]", "annotated_tactic": ["rw [<a>Subtype.range_val</a>]", [{"full_name": "Subtype.range_val", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [1417, 9], "def_end_pos": [1417, 18]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type u_1\n\u03b4 : Type u_2\n\u03b5 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_le_mul | [
232,
1
] | [
233,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Nodup.lean | List.not_nodup_cons_of_mem | [
72,
1
] | [
73,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo_left | [
435,
1
] | [
436,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.enum_zero_eq_bot | [
1213,
1
] | [
1217,
6
] | [{"tactic": "rwa [type_lt]", "annotated_tactic": ["rwa [<a>type_lt</a>]", [{"full_name": "Ordinal.type_lt", "def_path": "Mathlib/SetTheory/Ordinal/Basic.lean", "def_pos": [218, 9], "def_end_pos": [218, 16]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type u_1\n\u03b3 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sigma.lean | Set.sigma_subset_preimage_fst | [
234,
1
] | [
235,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Zlattice.lean | Zspan.floor_eq_self_of_mem | [
119,
1
] | [
125,
59
] | [{"tactic": "apply b.ext_elem", "annotated_tactic": ["apply b.ext_elem", []], "state_before": "E : Type u_1\n\u03b9 : Type u_2\nK : Type u_3\ninst\u271d\u2074 : NormedLinearOrderedField K\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace K E\nb : Basis \u03b9 K E\ninst\u271d\u00b9 : FloorRing K\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_reindex | [
2605,
1
] | [
2607,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_union | [
296,
1
] | [
299,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/StrongLaw.lean | ProbabilityTheory.truncation_eq_of_nonneg | [
116,
1
] | [
125,
81
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_1\nm : MeasurableSpace \u03b1\n\u03bc : Measure \u03b1\nf\u271d f : \u03b1 \u2192 \u211d\nA : \u211d\nh : \u2200 (x : \u03b1), 0 \u2264 f x\n\u22a2 truncation f A = indicator (Set.Ioc 0 A) id \u2218 f", "state_after": "case h\n\u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homeomorph.lean | Homeomorph.isSigmaCompact_preimage | [
282,
1
] | [
284,
55
] | [{"tactic": "rw [\u2190 image_symm]", "annotated_tactic": ["rw [\u2190 <a>image_symm</a>]", [{"full_name": "Homeomorph.image_symm", "def_path": "Mathlib/Topology/Homeomorph.lean", "def_pos": [210, 9], "def_end_pos": [210, 19]}]], "state_before": "X : Type u_1\nY : Type u_2\nZ : Type u_3\ninst\u271d\u2074 : TopologicalS... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.continuous_extend | [
152,
1
] | [
153,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_fp | [
119,
1
] | [
125,
43
] | [{"tactic": "unfold nfpFamily", "annotated_tactic": ["unfold <a>nfpFamily</a>", [{"full_name": "Ordinal.nfpFamily", "def_path": "Mathlib/SetTheory/Ordinal/FixedPoint.lean", "def_pos": [53, 5], "def_end_pos": [53, 14]}]], "state_before": "\u03b9 : Type u\nf : \u03b9 \u2192 Ordinal.{max u v} \u2192 Ordinal.{max u v}\ni :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.dist_single_same | [
290,
1
] | [
292,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/LineDeriv/Basic.lean | hasLineDerivAt_iff_isLittleO_nhds_zero | [
147,
1
] | [
150,
96
] | [{"tactic": "simp only [HasLineDerivAt, hasDerivAt_iff_isLittleO_nhds_zero, zero_add, zero_smul, add_zero]", "annotated_tactic": ["simp only [<a>HasLineDerivAt</a>, <a>hasDerivAt_iff_isLittleO_nhds_zero</a>, <a>zero_add</a>, <a>zero_smul</a>, <a>add_zero</a>]", [{"full_name": "HasLineDerivAt", "def_path": "Mathlib/Anal... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.map_comp | [
224,
1
] | [
229,
6
] | [{"tactic": "ext \u27e8v\u27e9", "annotated_tactic": ["ext \u27e8v\u27e9", []], "state_before": "K : Type u_1\nV : Type u_2\ninst\u271d\u2079 : DivisionRing K\ninst\u271d\u2078 : AddCommGroup V\ninst\u271d\u2077 : Module K V\nL : Type u_3\nW : Type u_4\ninst\u271d\u2076 : DivisionRing L\ninst\u271d\u2075 : AddCommGroup... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.neg_apply | [
258,
1
] | [
259,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Basic.lean | RingHom.map_list_sum | [
236,
11
] | [
238,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_sSup_of_mem | [
1059,
1
] | [
1061,
50
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_updateColumn_equiv | [
2942,
1
] | [
2945,
95
] | [{"tactic": "simp_rw [Equiv.apply_symm_apply]", "annotated_tactic": ["simp_rw [<a>Equiv.apply_symm_apply</a>]", [{"full_name": "Equiv.apply_symm_apply", "def_path": "Mathlib/Logic/Equiv/Defs.lean", "def_pos": [280, 17], "def_end_pos": [280, 33]}]], "state_before": "l : Type u_1\nm : Type u_2\nn : Type u_3\no : Type u_4... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Inseparable.lean | ker_nhds_eq_specializes | [
111,
1
] | [
112,
43
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "X : Type u_1\nY : Type u_2\nZ : Type u_3\n\u03b1 : Type u_4\n\u03b9 : Type u_5\n\u03c0 : \u03b9 \u2192 Type u_6\ninst\u271d\u00b3 : TopologicalSpace X\ninst\u271d\u00b2 : TopologicalSpace Y\ninst\u271d\u00b9 : TopologicalSpace Z\ninst\u271d : (i : \u0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Aut.lean | MulAut.conj_apply | [
153,
1
] | [
154,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_comap | [
251,
1
] | [
253,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Adjoin.lean | IntermediateField.algebra_adjoin_le_adjoin | [
421,
1
] | [
422,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Closure.lean | ClosureOperator.monotone | [
149,
1
] | [
150,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.coe_restrict_apply | [
1172,
1
] | [
1174,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | t1Space_antitone | [
571,
1
] | [
572,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Sublists.lean | List.sublists_singleton | [
108,
1
] | [
109,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.closure_cycle_coprime_swap | [
1674,
1
] | [
1686,
101
] | [{"tactic": "rw [\u2190 Finset.card_univ, \u2190 h2, \u2190 h1.orderOf] at h0", "annotated_tactic": ["rw [\u2190 <a>Finset.card_univ</a>, \u2190 h2, \u2190 h1.orderOf] at h0", [{"full_name": "Finset.card_univ", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [247, 9], "def_end_pos": [247, 25]}]], "state_before... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.fromCoset_ne_of_nin_range | [
157,
1
] | [
167,
46
] | [{"tactic": "intro r", "annotated_tactic": ["intro r", []], "state_before": "A B : GroupCat\nf : A \u27f6 B\nb : \u2191B\nhb : \u00acb \u2208 MonoidHom.range f\n\u22a2 fromCoset\n { val := b *l (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier,\n property :=\n (_ :\n \u2203 y,\n ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.coeff_restriction' | [
289,
1
] | [
290,
20
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Classes/LawfulMonad.lean | SatisfiesM.seqRight | [
163,
11
] | [
166,
55
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.lt_div_add_one_mul_self | [
548,
1
] | [
550,
72
] | [{"tactic": "rw [Int.add_mul, Int.one_mul, Int.mul_comm]", "annotated_tactic": ["rw [<a>Int.add_mul</a>, <a>Int.one_mul</a>, <a>Int.mul_comm</a>]", [{"full_name": "Int.add_mul", "def_path": "lake-packages/std/Std/Data/Int/Lemmas.lean", "def_pos": [459, 19], "def_end_pos": [459, 26]}, {"full_name": "Int.one_mul", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousOn.clm_comp | [
535,
1
] | [
538,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonal_pullback_fst | [
354,
1
] | [
360,
25
] | [{"tactic": "ext <;> dsimp <;> simp", "annotated_tactic": ["ext <;> dsimp <;> simp", []], "state_before": "C : Type u_1\ninst\u271d\u2075 : Category.{u_2, u_1} C\nX\u271d Y\u271d Z\u271d : C\ninst\u271d\u2074 : HasPullbacks C\nS T : C\nf\u271d : X\u271d \u27f6 T\ng\u271d : Y\u271d \u27f6 T\ni : T \u27f6 S\ninst\u271d\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.comap_top | [
629,
1
] | [
630,
85
] | [{"tactic": "rw [comap_apply, top_apply hs, top_apply (hs.image _)]", "annotated_tactic": ["rw [<a>comap_apply</a>, <a>top_apply</a> hs, <a>top_apply</a> (hs.image _)]", [{"full_name": "MeasureTheory.OuterMeasure.comap_apply", "def_path": "Mathlib/MeasureTheory/Measure/OuterMeasure.lean", "def_pos": [541, 9], "def_end_... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.negSucc_ne_zero | [
76,
9
] | [
76,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.limNthHom_one | [
591,
1
] | [
592,
54
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.add_le_of_le_sub_left | [
961,
11
] | [
963,
71
] | [{"tactic": "have h := Int.add_le_add_left h a", "annotated_tactic": ["have h := <a>Int.add_le_add_left</a> h a", [{"full_name": "Int.add_le_add_left", "def_path": "lake-packages/std/Std/Data/Int/Lemmas.lean", "def_pos": [751, 19], "def_end_pos": [751, 34]}]], "state_before": "a b c : Int\nh : b \u2264 c - a\n\u22a2 a ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.choose_spec | [
3062,
1
] | [
3063,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Finiteness.lean | Submodule.FG.pow | [
453,
1
] | [
454,
90
] | [{"tactic": "simp [one_eq_span]", "annotated_tactic": ["simp [<a>one_eq_span</a>]", [{"full_name": "Submodule.one_eq_span", "def_path": "Mathlib/Algebra/Algebra/Operations.lean", "def_pos": [109, 9], "def_end_pos": [109, 20]}]], "state_before": "R : Type u_1\nA : Type u_2\ninst\u271d\u00b2 : CommSemiring R\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.erase_singleton | [
1024,
1
] | [
1025,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Matrix.lean | Matrix.nnnorm_def | [
80,
1
] | [
80,
74
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.ext_iff | [
100,
1
] | [
101,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.Mon_tensor_mul_assoc | [
429,
1
] | [
442,
29
] | [{"tactic": "rw [\u2190 Category.id_comp (\ud835\udfd9 (M.X \u2297 N.X)), tensor_comp]", "annotated_tactic": ["rw [\u2190 <a>Category.id_comp</a> (\ud835\udfd9 (M.X \u2297 N.X)), <a>tensor_comp</a>]", [{"full_name": "CategoryTheory.Category.id_comp", "def_path": "Mathlib/CategoryTheory/Category/Basic.lean", "def_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_empty | [
122,
1
] | [
123,
71
] | [{"tactic": "rw [prehaar, Compacts.coe_bot, index_empty, Nat.cast_zero, zero_div]", "annotated_tactic": ["rw [<a>prehaar</a>, <a>Compacts.coe_bot</a>, <a>index_empty</a>, <a>Nat.cast_zero</a>, <a>zero_div</a>]", [{"full_name": "MeasureTheory.Measure.haar.prehaar", "def_path": "Mathlib/MeasureTheory/Measure/Haar/Basic.l... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Dist.lean | Nat.dist_mul_left | [
104,
1
] | [
105,
60
] | [{"tactic": "rw [mul_comm k n, mul_comm k m, dist_mul_right, mul_comm]", "annotated_tactic": ["rw [<a>mul_comm</a> k n, <a>mul_comm</a> k m, <a>dist_mul_right</a>, <a>mul_comm</a>]", [{"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [302, 9], "def_end_pos": [302, 17]}, {"full_name": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/PFilter.lean | Order.PFilter.isPFilter | [
84,
1
] | [
84,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.sSup_apply | [
367,
1
] | [
369,
32
] | [{"tactic": "simp [sSup, Sieve.sup, setOf]", "annotated_tactic": ["simp [<a>sSup</a>, <a>Sieve.sup</a>, <a>setOf</a>]", [{"full_name": "SupSet.sSup", "def_path": "Mathlib/Order/CompleteLattice.lean", "def_pos": [55, 3], "def_end_pos": [55, 7]}, {"full_name": "CategoryTheory.Sieve.sup", "def_path": "Mathlib/CategoryTheo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SumIntegralComparisons.lean | MonotoneOn.sum_le_integral_Ico | [
159,
1
] | [
162,
39
] | [{"tactic": "rw [\u2190 neg_le_neg_iff, \u2190 Finset.sum_neg_distrib, \u2190 intervalIntegral.integral_neg]", "annotated_tactic": ["rw [\u2190 <a>neg_le_neg_iff</a>, \u2190 <a>Finset.sum_neg_distrib</a>, \u2190 <a>intervalIntegral.integral_neg</a>]", [{"full_name": "neg_le_neg_iff", "def_path": "Mathlib/Algebra/Order/... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Pairwise.lean | List.Pairwise.imp_mem | [
87,
1
] | [
89,
68
] | [{"tactic": "simp (config := { contextual := true })", "annotated_tactic": ["simp (config := { contextual := <a>true</a> })", [{"full_name": "Bool.true", "def_path": "lake-packages/lean4/src/lean/Init/Prelude.lean", "def_pos": [549, 5], "def_end_pos": [549, 9]}]], "state_before": "\u03b1 : Type u_1\nR : \u03b1 \u2192 \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_nil | [
99,
1
] | [
99,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_dedup | [
95,
1
] | [
100,
61
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : CancelCommMonoidWithZero \u03b1\ninst\u271d\u00b9 : NormalizedGCDMonoid \u03b1\ninst\u271d : DecidableEq \u03b1\ns : Multiset \u03b1\n\u22a2 lcm (dedup 0) = lcm 0", "state_after": "no goals"}, {"tactic": "by_cas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/PathConnected.lean | Path.cast_coe | [
466,
1
] | [
467,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sequences.lean | isSeqClosed_iff_isClosed | [
198,
1
] | [
199,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_comm | [
385,
1
] | [
393,
59
] | [{"tactic": "rw [add_def]", "annotated_tactic": ["rw [<a>add_def</a>]", [{"full_name": "CategoryTheory.NonPreadditiveAbelian.add_def", "def_path": "Mathlib/CategoryTheory/Abelian/NonPreadditive.lean", "def_pos": [344, 9], "def_end_pos": [344, 16]}]], "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Tuple/Reflection.lean | FinVec.map_eq | [
69,
1
] | [
70,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.iSup_induction' | [
126,
1
] | [
135,
36
] | [{"tactic": "suffices : \u2203 h, C x h", "annotated_tactic": ["suffices : \u2203 h, C x h", []], "state_before": "\u03b1 : Type u_1\nG : Type u_2\nA : Type u_3\nS\u271d : Type u_4\ninst\u271d\u00b9 : Group G\ninst\u271d : AddGroup A\ns : Set G\n\u03b9 : Sort u_5\nS : \u03b9 \u2192 Subgroup G\nC : (x : G) \u2192 x \u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.null_iff_of_isMulLeftInvariant | [
596,
1
] | [
600,
60
] | [{"tactic": "by_cases h3\u03bc : \u03bc = 0", "annotated_tactic": ["by_cases h3\u03bc : \u03bc = 0", []], "state_before": "\ud835\udd5c : Type u_1\nG : Type u_2\nH : Type u_3\ninst\u271d\u2077 : MeasurableSpace G\ninst\u271d\u2076 : MeasurableSpace H\ninst\u271d\u2075 : TopologicalSpace G\ninst\u271d\u2074 : BorelSpace... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.zero_eq_coe | [
371,
20
] | [
371,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_def' | [
72,
1
] | [
74,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Diffeomorph.lean | Diffeomorph.coe_refl | [
191,
1
] | [
192,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Unitization.lean | Unitization.norm_def | [
133,
1
] | [
134,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.smul_mem | [
158,
1
] | [
159,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.Ring.polarBilin_pi | [
291,
9
] | [
293,
64
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b9 : Type u_1\nR : Type u_2\nM\u2081 : Type u_3\nM\u2082 : Type u_4\nN\u2081 : Type u_5\nN\u2082 : Type u_6\nM\u1d62 : \u03b9 \u2192 Type u_7\nN\u1d62 : \u03b9 \u2192 Type u_8\ninst\u271d\u2075 : CommRing R\ninst\u271d\u2074 : (i : \u03b9) \u219... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Prod.lean | Finset.offDiag_singleton | [
412,
1
] | [
412,
92
] | [{"tactic": "simp [\u2190 Finset.card_eq_zero]", "annotated_tactic": ["simp [\u2190 <a>Finset.card_eq_zero</a>]", [{"full_name": "Finset.card_eq_zero", "def_path": "Mathlib/Data/Finset/Card.lean", "def_pos": [70, 9], "def_end_pos": [70, 21]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupWithZero/Divisibility.lean | ne_zero_of_dvd_ne_zero | [
102,
1
] | [
104,
31
] | [{"tactic": "rcases h\u2082 with \u27e8u, rfl\u27e9", "annotated_tactic": ["rcases h\u2082 with \u27e8u, rfl\u27e9", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : MonoidWithZero \u03b1\np q : \u03b1\nh\u2081 : q \u2260 0\nh\u2082 : p \u2223 q\n\u22a2 p \u2260 0", "state_after": "case intro\n\u03b1 : Type u_1\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_zero_iff_eq_of_closed | [
414,
1
] | [
416,
80
] | [{"tactic": "rw [hausdorffEdist_zero_iff_closure_eq_closure, hs.closure_eq, ht.closure_eq]", "annotated_tactic": ["rw [<a>hausdorffEdist_zero_iff_closure_eq_closure</a>, hs.closure_eq, ht.closure_eq]", [{"full_name": "EMetric.hausdorffEdist_zero_iff_closure_eq_closure", "def_path": "Mathlib/Topology/MetricSpace/Hausdor... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MatrixExponential.lean | Matrix.exp_conjTranspose | [
91,
1
] | [
93,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_mem_haarProduct | [
364,
1
] | [
366,
90
] | [{"tactic": "rintro \u27e8K, hK\u27e9 _", "annotated_tactic": ["rintro \u27e8K, hK\u27e9 _", []], "state_before": "G : Type u_1\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : TopologicalSpace G\ninst\u271d : TopologicalGroup G\nK\u2080 : PositiveCompacts G\nU : Set G\nhU : Set.Nonempty (interior U)\n\u22a2 prehaar (\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiff_of_differentiable_iteratedDeriv | [
270,
1
] | [
272,
96
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/Cardinality.lean | IsLocalization.card | [
54,
1
] | [
55,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/ProbabilityMassFunction/Monad.lean | PMF.toOuterMeasure_pure_apply | [
73,
1
] | [
79,
87
] | [{"tactic": "refine' (toOuterMeasure_apply (pure a) s).trans _", "annotated_tactic": ["refine' (<a>toOuterMeasure_apply</a> (<a>pure</a> a) s).<a>trans</a> _", [{"full_name": "PMF.toOuterMeasure_apply", "def_path": "Mathlib/Probability/ProbabilityMassFunction/Basic.lean", "def_pos": [161, 9], "def_end_pos": [161, 29]},... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | Prod.nnorm_def | [
2459,
1
] | [
2460,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.ae_eq | [
2188,
1
] | [
2189,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Basic.lean | zsmul_eq_smul_cast | [
429,
1
] | [
433,
27
] | [{"tactic": "apply AddMonoidHom.ext_int", "annotated_tactic": ["apply <a>AddMonoidHom.ext_int</a>", [{"full_name": "AddMonoidHom.ext_int", "def_path": "Mathlib/Data/Int/Cast/Lemmas.lean", "def_pos": [224, 9], "def_end_pos": [224, 16]}]], "state_before": "\u03b1 : Type u_1\nR : Type u_2\nk : Type u_3\nS : Type u_4\nM : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/EReal.lean | EReal.sub_le_sub | [
873,
1
] | [
874,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/IsROrC/Basic.lean | IsROrC.isCauSeq_im | [
793,
1
] | [
795,
87
] | [{"tactic": "simpa only [map_sub] using abs_im_le_norm (f j - f i)", "annotated_tactic": ["simpa only [<a>map_sub</a>] using <a>abs_im_le_norm</a> (f j - f i)", [{"full_name": "map_sub", "def_path": "Mathlib/Algebra/Hom/Group/Defs.lean", "def_pos": [428, 3], "def_end_pos": [428, 14]}, {"full_name": "IsROrC.abs_im_le_no... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.induction_on₂ | [
193,
1
] | [
196,
55
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLeast.csInf_eq | [
583,
1
] | [
584,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Trace.lean | Algebra.traceForm_isSymm | [
209,
1
] | [
209,
101
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_zero_pos | [
190,
1
] | [
193,
41
] | [{"tactic": "simp [volumeForm, Or.by_cases, if_pos]", "annotated_tactic": ["simp [<a>volumeForm</a>, <a>Or.by_cases</a>, <a>if_pos</a>]", [{"full_name": "Orientation.volumeForm", "def_path": "Mathlib/Analysis/InnerProductSpace/Orientation.lean", "def_pos": [181, 17], "def_end_pos": [181, 27]}, {"full_name": "Or.by_case... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/IsROrC/Basic.lean | IsROrC.isCauSeq_re | [
788,
1
] | [
790,
87
] | [{"tactic": "simpa only [map_sub] using abs_re_le_norm (f j - f i)", "annotated_tactic": ["simpa only [<a>map_sub</a>] using <a>abs_re_le_norm</a> (f j - f i)", [{"full_name": "map_sub", "def_path": "Mathlib/Algebra/Hom/Group/Defs.lean", "def_pos": [428, 3], "def_end_pos": [428, 14]}, {"full_name": "IsROrC.abs_re_le_no... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.getLastD_eq_getLast? | [
544,
1
] | [
545,
18
] | [{"tactic": "cases l <;> rfl", "annotated_tactic": ["cases l <;> rfl", []], "state_before": "\u03b1 : Type u_1\na : \u03b1\nl : List \u03b1\n\u22a2 getLastD l a = Option.getD (getLast? l) a", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.natDegree_finSuccEquiv | [
505,
1
] | [
511,
9
] | [{"tactic": "by_cases c : f = 0", "annotated_tactic": ["by_cases c : f = 0", []], "state_before": "R : Type u\nS\u2081 : Type v\nS\u2082 : Type w\nS\u2083 : Type x\n\u03c3 : Type u_1\na a' a\u2081 a\u2082 : R\ne : \u2115\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\nn : \u2115\nf : MvPolynomial (Fin (n ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.pow_right_injective | [
922,
1
] | [
932,
64
] | [{"tactic": "letI := Classical.decEq R", "annotated_tactic": ["letI := <a>Classical.decEq</a> R", [{"full_name": "Classical.decEq", "def_path": "Mathlib/Logic/Basic.lean", "def_pos": [983, 19], "def_end_pos": [983, 24]}]], "state_before": "\u03b1 : Type u_1\nR : Type u_2\ninst\u271d\u00b9 : CancelCommMonoidWithZero R\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Icc' | [
1482,
1
] | [
1488,
29
] | [{"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\n\u22a2 Iic b \u222a Icc c d = Iic (max b d)", "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | uniqueMDiffWithinAt_iff | [
340,
1
] | [
345,
75
] | [{"tactic": "apply uniqueDiffWithinAt_congr", "annotated_tactic": ["apply <a>uniqueDiffWithinAt_congr</a>", [{"full_name": "uniqueDiffWithinAt_congr", "def_path": "Mathlib/Analysis/Calculus/TangentCone.lean", "def_pos": [271, 9], "def_end_pos": [271, 33]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/ODE/Gronwall.lean | dist_le_of_trajectories_ODE | [
220,
1
] | [
227,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.of_le_Henstock_of_forall_isLittleO | [
813,
1
] | [
824,
64
] | [{"tactic": "decide", "annotated_tactic": ["decide", []], "state_before": "\u03b9 : Type u\nE : Type v\nF : Type w\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\nI J : Box \u03b9\n\u03c0 : TaggedPrepart... |
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