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/Geometry/Manifold/VectorBundle/Basic.lean | Bundle.smooth_proj | [
224,
1
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225,
19
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left | [
428,
1
] | [
430,
70
] | [{"tactic": "simp_rw [setToSimpleFunc, ContinuousLinearMap.smul_apply, smul_sum]", "annotated_tactic": ["simp_rw [<a>setToSimpleFunc</a>, <a>ContinuousLinearMap.smul_apply</a>, <a>smul_sum</a>]", [{"full_name": "MeasureTheory.SimpleFunc.setToSimpleFunc", "def_path": "Mathlib/MeasureTheory/Integral/SetToL1.lean", "def_p... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.fill | [
268,
11
] | [
280,
88
] | [{"tactic": "simp [Ordered.fill, RBNode.Ordered, Ordered, RootOrdered, All_and]", "annotated_tactic": ["simp [Ordered.fill, <a>RBNode.Ordered</a>, <a>Ordered</a>, <a>RootOrdered</a>, <a>All_and</a>]", [{"full_name": "Std.RBNode.Ordered", "def_path": "lake-packages/std/Std/Data/RBMap/Basic.lean", "def_pos": [551, 5], "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.get?_terminates_le | [
891,
1
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894,
76
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Unitary.lean | unitary.to_units_injective | [
138,
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139,
36
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ne_zero_iff | [
1940,
1
] | [
1942,
16
] | [{"tactic": "rw [Ne, prod_eq_zero_iff]", "annotated_tactic": ["rw [<a>Ne</a>, <a>prod_eq_zero_iff</a>]", [{"full_name": "Ne", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", "def_pos": [560, 18], "def_end_pos": [560, 20]}, {"full_name": "Finset.prod_eq_zero_iff", "def_path": "Mathlib/Algebra/BigOperators/Bas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.canonicalEquiv_trans_canonicalEquiv | [
931,
1
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934,
59
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/MeanInequalities.lean | NNReal.geom_mean_le_arith_mean4_weighted | [
204,
1
] | [
210,
95
] | [{"tactic": "simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,\n Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, \u2190 add_assoc,\n mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w\u2081, w\u2082, w\u2083, w\u2084] ![p\u2081, p\u2082, p\u2083,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/Nim.lean | SetTheory.PGame.nim_one_equiv | [
199,
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200,
26
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Projection.lean | Submodule.quotientEquivOfIsCompl_symm_apply | [
80,
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82,
79
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.IsColimit.hom_ext | [
875,
1
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877,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.IsSeparableContraction.dvd_degree' | [
73,
1
] | [
77,
24
] | [{"tactic": "obtain \u27e8m, rfl\u27e9 := hf.2", "annotated_tactic": ["obtain \u27e8m, rfl\u27e9 := hf.2", []], "state_before": "F : Type u_1\ninst\u271d : CommSemiring F\nq : \u2115\nf : F[X]\nhf\u271d : HasSeparableContraction q f\ng : F[X]\nhf : IsSeparableContraction q f g\n\u22a2 \u2203 m, natDegree g * q ^ m = na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | lt_mul_self | [
573,
1
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574,
44
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_comp_monoidWithZeroHom | [
687,
1
] | [
689,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Zip.lean | List.nthLe_zip | [
366,
1
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369,
16
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https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.erase | [
457,
11
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458,
27
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Algebra/LeftInvariantDerivation.lean | LeftInvariantDerivation.coe_injective | [
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24
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https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.filterMap_some | [
1324,
9
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1325,
33
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.subsingleton_univ_iff | [
2408,
1
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2409,
71
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https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_tail? | [
143,
1
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147,
52
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ParametricIntervalIntegral.lean | intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le | [
55,
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68,
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ext | [
754,
11
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754,
87
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans_eventuallyEq | [
426,
1
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428,
31
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnityEquivNthRoots_apply | [
220,
1
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222,
6
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_iff_exists_left | [
438,
1
] | [
454,
32
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "R : Type u_1\nV : Type u_2\nV' : Type u_3\nP : Type u_4\nP' : Type u_5\ninst\u271d\u2076 : LinearOrderedField R\ninst\u271d\u2075 : AddCommGroup V\ninst\u271d\u2074 : Module R V\ninst\u271d\u00b3 : AddTorsor V P\ninst\u271d\u00b2 : Add... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality | [
300,
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301,
56
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "C\u271d : Type u\n\ud835\udc9e : Category.{v, u} C\u271d\ninst\u271d\u00b2 : MonoidalCategory C\u271d\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\ninst\u271d : MonoidalCategory C\nU V W X\u271d Y Z X X' : C\nf : X \u27f6 X'\n\u22a2 f \u226b (\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MatrixExponential.lean | Matrix.exp_add_of_commute | [
125,
8
] | [
130,
29
] | [{"tactic": "letI : SeminormedRing (Matrix m m \ud835\udd38) := Matrix.linftyOpSemiNormedRing", "annotated_tactic": ["letI : <a>SeminormedRing</a> (<a>Matrix</a> m m \ud835\udd38) := <a>Matrix.linftyOpSemiNormedRing</a>", [{"full_name": "SeminormedRing", "def_path": "Mathlib/Analysis/Normed/Field/Basic.lean", "def_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/PathConnected.lean | isPathConnected_singleton | [
985,
1
] | [
988,
26
] | [{"tactic": "refine \u27e8x, rfl, ?_\u27e9", "annotated_tactic": ["refine \u27e8x, <a>rfl</a>, ?_\u27e9", [{"full_name": "rfl", "def_path": "lake-packages/lean4/src/lean/Init/Prelude.lean", "def_pos": [281, 22], "def_end_pos": [281, 25]}]], "state_before": "X : Type u_1\nY : Type u_2\ninst\u271d\u00b9 : TopologicalSpac... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.to_from | [
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11
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardObj_obj | [
158,
1
] | [
160,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mono_of_isLimitMkIdId | [
713,
1
] | [
717,
9
] | [{"tactic": "rcases PullbackCone.IsLimit.lift' t _ _ eq with \u27e8_, rfl, rfl\u27e9", "annotated_tactic": ["rcases <a>PullbackCone.IsLimit.lift'</a> t _ _ eq with \u27e8_, rfl, rfl\u27e9", [{"full_name": "CategoryTheory.Limits.PullbackCone.IsLimit.lift'", "def_path": "Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_ne_top | [
105,
1
] | [
125,
87
] | [{"tactic": "let npf := (\u222b\u207b c : \u03b1, f c ^ p \u2202\u03bc) ^ (1 / p)", "annotated_tactic": ["let npf := (\u222b\u207b c : \u03b1, f c ^ p \u2202\u03bc) ^ (1 / p)", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : MeasurableSpace \u03b1\n\u03bc : Measure \u03b1\np q : \u211d\nhpq : Real.IsConjugateExpo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_eq_zero_of_differentiableOn | [
286,
1
] | [
293,
97
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nmul_le_iff | [
549,
1
] | [
550,
41
] | [{"tactic": "rw [\u2190 not_iff_not]", "annotated_tactic": ["rw [\u2190 <a>not_iff_not</a>]", [{"full_name": "not_iff_not", "def_path": "Mathlib/Logic/Basic.lean", "def_pos": [439, 9], "def_end_pos": [439, 20]}]], "state_before": "a b c d : Ordinal.{u}\n\u22a2 a \u2a33 b \u2264 c \u2194 \u2200 (a' : Ordinal.{u}), a' < ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | Filter.EventuallyLE.eventuallyLE_nhds | [
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1
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1025,
20
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.monotone_setOf | [
2965,
1
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2966,
61
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.count_singleton_self | [
2385,
1
] | [
2386,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Lattice.lean | SupHom.coe_copy | [
366,
1
] | [
367,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.zero_apply | [
187,
1
] | [
187,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | tendsto_measure_thickening | [
1802,
1
] | [
1807,
48
] | [{"tactic": "rw [closure_eq_iInter_thickening]", "annotated_tactic": ["rw [<a>closure_eq_iInter_thickening</a>]", [{"full_name": "Metric.closure_eq_iInter_thickening", "def_path": "Mathlib/Topology/MetricSpace/HausdorffDistance.lean", "def_pos": [1400, 9], "def_end_pos": [1400, 37]}]], "state_before": "\u03b1 : Type u_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sheaves/PUnit.lean | TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscrete | [
25,
1
] | [
42,
17
] | [{"tactic": "obtain rfl | hne := eq_or_ne U \u22a5", "annotated_tactic": ["obtain rfl | hne := <a>eq_or_ne</a> U \u22a5", [{"full_name": "eq_or_ne", "def_path": "Mathlib/Logic/Basic.lean", "def_pos": [209, 9], "def_end_pos": [209, 17]}]], "state_before": "C : Type u\ninst\u271d : Category.{v, u} C\nX : TopCat\nhind : X... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/AddTorsor.lean | vsub_eq_zero_iff_eq | [
138,
1
] | [
139,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Composition.lean | Composition.length_le | [
198,
1
] | [
200,
65
] | [{"tactic": "conv_rhs => rw [\u2190 c.blocks_sum]", "annotated_tactic": ["conv_rhs => rw [\u2190 c.blocks_sum]", []], "state_before": "n : \u2115\nc : Composition n\n\u22a2 length c \u2264 n", "state_after": "n : \u2115\nc : Composition n\n\u22a2 length c \u2264 sum c.blocks"}, {"tactic": "exact length_le_sum_of_one_le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_copy | [
164,
1
] | [
165,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.max_eq_sup_withBot | [
1251,
1
] | [
1252,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | MonotoneOn.map_bddBelow | [
1201,
1
] | [
1202,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_l_inv | [
249,
1
] | [
250,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Lattice.lean | InfHom.withTop_id | [
1679,
1
] | [
1679,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_congr | [
166,
1
] | [
168,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finite/Card.lean | Finite.card_subtype_lt | [
185,
1
] | [
188,
84
] | [{"tactic": "haveI := Fintype.ofFinite \u03b1", "annotated_tactic": ["haveI := <a>Fintype.ofFinite</a> \u03b1", [{"full_name": "Fintype.ofFinite", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [448, 19], "def_end_pos": [448, 35]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/Defs.lean | Rat.zero_ne_one | [
287,
11
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289,
20
] | [{"tactic": "rw [ne_comm, \u2190 divInt_one_one, divInt_ne_zero one_ne_zero]", "annotated_tactic": ["rw [<a>ne_comm</a>, \u2190 <a>divInt_one_one</a>, <a>divInt_ne_zero</a> <a>one_ne_zero</a>]", [{"full_name": "ne_comm", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [814, 9], "def_end_pos": [814, 16]}, {"f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Card.lean | Finset.card_singleton | [
86,
1
] | [
87,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Finiteness.lean | Submodule.fg_iff_addSubmonoid_fg | [
58,
1
] | [
60,
65
] | [{"tactic": "simpa [\u2190 span_nat_eq_addSubmonoid_closure] using hS", "annotated_tactic": ["simpa [\u2190 <a>span_nat_eq_addSubmonoid_closure</a>] using hS", [{"full_name": "Submodule.span_nat_eq_addSubmonoid_closure", "def_path": "Mathlib/LinearAlgebra/Span.lean", "def_pos": [194, 9], "def_end_pos": [194, 41]}]], "s... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_neg | [
404,
11
] | [
405,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/CauSeq.lean | CauSeq.cauchy | [
159,
1
] | [
159,
93
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Arithmetic.lean | Finset.aemeasurable_prod' | [
943,
1
] | [
947,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_bot | [
715,
1
] | [
716,
30
] | [{"tactic": "simp [Set.ext_iff, mem_bot]", "annotated_tactic": ["simp [<a>Set.ext_iff</a>, <a>mem_bot</a>]", [{"full_name": "Set.ext_iff", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [241, 9], "def_end_pos": [241, 16]}, {"full_name": "StarSubalgebra.mem_bot", "def_path": "Mathlib/Algebra/Star/Subalgebra.lean"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.quotient_preimage_image_eq_union_mul | [
296,
1
] | [
314,
30
] | [{"tactic": "letI := orbitRel G \u03b1", "annotated_tactic": ["letI := <a>orbitRel</a> G \u03b1", [{"full_name": "MulAction.orbitRel", "def_path": "Mathlib/GroupTheory/GroupAction/Basic.lean", "def_pos": [275, 5], "def_end_pos": [275, 13]}]], "state_before": "G : Type u\n\u03b1 : Type v\ninst\u271d\u00b9 : Group G\nins... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.card_eq_two | [
796,
1
] | [
799,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Powerset.lean | Multiset.revzip_powersetAux' | [
133,
1
] | [
138,
46
] | [{"tactic": "rw [revzip, powersetAux', \u2190 map_reverse, zip_map, \u2190 revzip, List.mem_map] at h", "annotated_tactic": ["rw [<a>revzip</a>, <a>powersetAux'</a>, \u2190 <a>map_reverse</a>, <a>zip_map</a>, \u2190 <a>revzip</a>, <a>List.mem_map</a>] at h", [{"full_name": "List.revzip", "def_path": "lake-packages/std/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/BumpFunction/Basic.lean | ContDiffBump.nonneg | [
158,
1
] | [
159,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_add | [
189,
1
] | [
193,
7
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\nX\u271d Y\u271d Z : C\nD : Type u\u2082\ninst\u271d\u00b9 : Category.{v\u2082, u\u2082} D\ninst\u271d : Preadditive C\nX Y : C\nP : Subobject Y\nf g : X \u27f6 Y\nw : Factors P (f + g... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Nilpotent.lean | comap_center_subst | [
589,
9
] | [
590,
91
] | [{"tactic": "subst h", "annotated_tactic": ["subst h", []], "state_before": "G : Type u_1\ninst\u271d\u00b3 : Group G\nH : Subgroup G\ninst\u271d\u00b2 : Normal H\nH\u2081 H\u2082 : Subgroup G\ninst\u271d\u00b9 : Normal H\u2081\ninst\u271d : Normal H\u2082\nh : H\u2081 = H\u2082\n\u22a2 comap (mk' H\u2081) (center (G \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.degreeOf_coeff_finSuccEquiv | [
514,
1
] | [
521,
38
] | [{"tactic": "rw [degreeOf_eq_sup, degreeOf_eq_sup, Finset.sup_le_iff]", "annotated_tactic": ["rw [<a>degreeOf_eq_sup</a>, <a>degreeOf_eq_sup</a>, <a>Finset.sup_le_iff</a>]", [{"full_name": "MvPolynomial.degreeOf_eq_sup", "def_path": "Mathlib/Data/MvPolynomial/Variables.lean", "def_pos": [494, 9], "def_end_pos": [494, 2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.uniformContinuousOn | [
136,
11
] | [
142,
69
] | [{"tactic": "refine' EMetric.uniformContinuousOn_iff.2 fun \u03b5 \u03b5pos => _", "annotated_tactic": ["refine' <a>EMetric.uniformContinuousOn_iff</a>.2 fun \u03b5 \u03b5pos => _", [{"full_name": "EMetric.uniformContinuousOn_iff", "def_path": "Mathlib/Topology/EMetricSpace/Basic.lean", "def_pos": [279, 9], "def_end_po... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | dist_self_div_left | [
1476,
1
] | [
1477,
38
] | [{"tactic": "rw [dist_comm, dist_self_div_right]", "annotated_tactic": ["rw [<a>dist_comm</a>, <a>dist_self_div_right</a>]", [{"full_name": "dist_comm", "def_path": "Mathlib/Topology/MetricSpace/Basic.lean", "def_pos": [188, 9], "def_end_pos": [188, 18]}, {"full_name": "dist_self_div_right", "def_path": "Mathlib/Analys... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Inseparable.lean | SeparationQuotient.range_mk | [
437,
1
] | [
438,
25
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Array/Init/Lemmas.lean | Array.size_uset | [
229,
1
] | [
229,
82
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\na : Array \u03b1\nv : \u03b1\ni : USize\nh : USize.toNat i < size a\n\u22a2 size (uset a i v h) = size a", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/QuasiSeparated.lean | isQuasiSeparated_iff_quasiSeparatedSpace | [
100,
1
] | [
104,
7
] | [{"tactic": "rw [\u2190 isQuasiSeparated_univ_iff]", "annotated_tactic": ["rw [\u2190 <a>isQuasiSeparated_univ_iff</a>]", [{"full_name": "isQuasiSeparated_univ_iff", "def_path": "Mathlib/Topology/QuasiSeparated.lean", "def_pos": [54, 9], "def_end_pos": [54, 34]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.get?_eq_some | [
600,
1
] | [
604,
35
] | [{"tactic": "cases get?_len_le hn \u25b8 e", "annotated_tactic": ["cases <a>get?_len_le</a> hn \u25b8 e", [{"full_name": "List.get?_len_le", "def_path": "lake-packages/std/Std/Data/List/Lemmas.lean", "def_pos": [592, 9], "def_end_pos": [592, 20]}]], "state_before": "\u03b1\u271d : Type u_1\na : \u03b1\u271d\nl : List \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_eq_sum_range' | [
248,
1
] | [
252,
28
] | [{"tactic": "rw [eval\u2082_eq_sum, p.sum_over_range' _ _ hn]", "annotated_tactic": ["rw [<a>eval\u2082_eq_sum</a>, p.sum_over_range' _ _ hn]", [{"full_name": "Polynomial.eval\u2082_eq_sum", "def_path": "Mathlib/Data/Polynomial/Eval.lean", "def_pos": [49, 9], "def_end_pos": [49, 21]}]], "state_before": "R : Type u\nS :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_sub_le_iff_right | [
335,
1
] | [
336,
97
] | [{"tactic": "rwa [natDegree_sub, natDegree_sub_le_iff_left]", "annotated_tactic": ["rwa [<a>natDegree_sub</a>, <a>natDegree_sub_le_iff_left</a>]", [{"full_name": "Polynomial.natDegree_sub", "def_path": "Mathlib/Data/Polynomial/Degree/Lemmas.lean", "def_pos": [326, 9], "def_end_pos": [326, 22]}, {"full_name": "Polynomia... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.SpecialLinear.sl_bracket | [
101,
1
] | [
102,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq_lem1 | [
644,
1
] | [
653,
46
] | [{"tactic": "suffices xn a1 j % xn a1 n < xn a1 (j + 1) % xn a1 n from\n (lt_or_eq_of_le (Nat.le_of_succ_le_succ ij)).elim\n (fun h => lt_trans (eq_of_xn_modEq_lem1 h (le_of_lt jn)) this) fun h => by\n rw [h]; exact this", "annotated_tactic": ["suffices <a>xn</a> a1 j % <a>xn</a> a1 n < <a>xn</a> a1 (j + 1) % <a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/OrderOfElement.lean | mem_powers_iff_mem_range_orderOf | [
727,
1
] | [
729,
100
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Irreducible.lean | SupIrred.finset_sup_eq | [
111,
1
] | [
117,
30
] | [{"tactic": "induction' s using Finset.induction with i s _ ih", "annotated_tactic": ["induction' s using <a>Finset.induction</a> with i s _ ih", [{"full_name": "Finset.induction", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1240, 19], "def_end_pos": [1240, 28]}]], "state_before": "\u03b9 : Type u_1\n\u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/Basic.lean | IsConnected.union | [
147,
1
] | [
152,
22
] | [{"tactic": "rcases H with \u27e8x, hx\u27e9", "annotated_tactic": ["rcases H with \u27e8x, hx\u27e9", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Type u_1\n\u03c0 : \u03b9 \u2192 Type u_2\ninst\u271d : TopologicalSpace \u03b1\ns\u271d t\u271d u v s t : Set \u03b1\nH : Set.Nonempty (s \u2229 t)\nHs... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/MapLemmas.lean | Vector.map₂_flip | [
387,
1
] | [
389,
64
] | [{"tactic": "induction xs, ys using Vector.inductionOn\u2082 <;> simp_all[flip]", "annotated_tactic": ["induction xs, ys using <a>Vector.inductionOn\u2082</a> <;> simp_all[<a>flip</a>]", [{"full_name": "Vector.inductionOn\u2082", "def_path": "Mathlib/Data/Vector/Basic.lean", "def_pos": [475, 5], "def_end_pos": [475, 17... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/HomeomorphBall.lean | LocalHomeomorph.univUnitBall_apply_zero | [
76,
1
] | [
77,
44
] | [{"tactic": "simp [LocalHomeomorph.univUnitBall_apply]", "annotated_tactic": ["simp [<a>LocalHomeomorph.univUnitBall_apply</a>]", [{"full_name": "LocalHomeomorph.univUnitBall_apply", "def_path": "Mathlib/Analysis/NormedSpace/HomeomorphBall.lean", "def_pos": [41, 3], "def_end_pos": [41, 8]}]], "state_before": "E : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.continuous_eval | [
164,
1
] | [
165,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_assoc₁ | [
186,
1
] | [
192,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_iff | [
710,
1
] | [
711,
42
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.prefix_refl | [
1752,
1
] | [
1752,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂Measurable_toGerm | [
471,
1
] | [
477,
47
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\ninst\u271d\u00b9\u2074 : MeasurableSpace \u03b1\n\u03bc \u03bd : Measure \u03b1\ninst\u271d\u00b9\u00b3 : TopologicalSpace \u03b2\ninst\u271d\u00b9\u00b2 : TopologicalSpace ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ioi_iff_exists_Ioo_subset | [
1712,
1
] | [
1715,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ici_eq_Ioi | [
1351,
1
] | [
1352,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Submonoid/Membership.lean | ofMul_image_powers_eq_multiples_ofMul | [
755,
1
] | [
764,
20
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "M : Type u_1\nA : Type u_2\nB : Type u_3\ninst\u271d : Monoid M\nx : M\n\u22a2 \u2191Additive.ofMul '' \u2191(Submonoid.powers x) = \u2191(AddSubmonoid.multiples (\u2191Additive.ofMul x))", "state_after": "case h\nM : Type u_1\nA : Type u_2\nB : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Field.lean | Subfield.le_topologicalClosure | [
62,
1
] | [
63,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.sup_disjoint | [
99,
1
] | [
101,
51
] | [{"tactic": "simp [apply_eq_coe_toFun, \u03bc.sup_disjoint' _ _ h]", "annotated_tactic": ["simp [<a>apply_eq_coe_toFun</a>, \u03bc.sup_disjoint' _ _ h]", [{"full_name": "MeasureTheory.Content.apply_eq_coe_toFun", "def_path": "Mathlib/MeasureTheory/Measure/Content.lean", "def_pos": [91, 9], "def_end_pos": [91, 27]}]], "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | SL_reduction_mod_hom_val | [
40,
1
] | [
42,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_injective | [
1956,
1
] | [
1961,
10
] | [{"tactic": "cases f", "annotated_tactic": ["cases f", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nG : Type w\nH : Type x\ninst\u271d : Group \u03b1\nf g : GroupTopology \u03b1\nh : f.toTopologicalSpace = g.toTopologicalSpace\n\u22a2 f = g", "state_after": "case mk\n\u03b1 : Type u\n\u03b2 : Type v\nG : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_eq_empty_of_neg | [
503,
1
] | [
504,
87
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Divisibility/Units.lean | IsUnit.dvd_mul_left | [
102,
1
] | [
104,
27
] | [{"tactic": "rcases hu with \u27e8u, rfl\u27e9", "annotated_tactic": ["rcases hu with \u27e8u, rfl\u27e9", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : CommMonoid \u03b1\na b u : \u03b1\nhu : IsUnit u\n\u22a2 a \u2223 u * b \u2194 a \u2223 b", "state_after": "case intro\n\u03b1 : Type u_1\ninst\u271d : CommMon... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Field/Basic.lean | div_add_div | [
205,
1
] | [
207,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_induction' | [
536,
1
] | [
548,
75
] | [{"tactic": "refine' Exists.elim _ fun (hb : b \u2208 adjoin R s) (hc : p \u27e8b, hb\u27e9) => hc", "annotated_tactic": ["refine' <a>Exists.elim</a> _ fun (hb : b \u2208 <a>adjoin</a> R s) (hc : p \u27e8b, hb\u27e9) => hc", [{"full_name": "Exists.elim", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_a | [
208,
1
] | [
209,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_eq_span_image2 | [
139,
1
] | [
141,
42
] | [{"tactic": "rw [\u2190 map\u2082_span_span, span_eq, span_eq]", "annotated_tactic": ["rw [\u2190 <a>map\u2082_span_span</a>, <a>span_eq</a>, <a>span_eq</a>]", [{"full_name": "Submodule.map\u2082_span_span", "def_path": "Mathlib/Algebra/Module/Submodule/Bilinear.lean", "def_pos": [63, 9], "def_end_pos": [63, 23]}, {"fu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sym/Basic.lean | Sym.exists_eq_cons_of_succ | [
301,
1
] | [
303,
58
] | [{"tactic": "obtain \u27e8a, ha\u27e9 := exists_mem s", "annotated_tactic": ["obtain \u27e8a, ha\u27e9 := <a>exists_mem</a> s", [{"full_name": "Sym.exists_mem", "def_path": "Mathlib/Data/Sym/Basic.lean", "def_pos": [297, 9], "def_end_pos": [297, 19]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nn n' m : \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_const | [
344,
1
] | [
350,
54
] | [{"tactic": "classical\ncalc\n (const \u03b1 y).integral \u03bc = \u2211 z in {y}, (\u03bc (const \u03b1 y \u207b\u00b9' {z})).toReal \u2022 z :=\n integral_eq_sum_of_subset <| (filter_subset _ _).trans (range_const_subset _ _)\n _ = (\u03bc univ).toReal \u2022 y := by simp [Set.preimage]", "annotated_tactic": ["c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.subset_def | [
345,
1
] | [
346,
6
] | [] |
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