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/Rat.lean | Int.closedEmbedding_coe_rat | [
80,
1
] | [
81,
93
] | [{"tactic": "simpa using Int.pairwise_one_le_dist", "annotated_tactic": ["simpa using <a>Int.pairwise_one_le_dist</a>", [{"full_name": "Int.pairwise_one_le_dist", "def_path": "Mathlib/Topology/Instances/Int.lean", "def_pos": [38, 9], "def_end_pos": [38, 29]}]], "state_before": "\u22a2 Pairwise fun x y => 1 \u2264 dist ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_neg | [
859,
1
] | [
860,
57
] | [{"tactic": "simpa only [zero_sub] using integral_comp_sub_left f 0", "annotated_tactic": ["simpa only [<a>zero_sub</a>] using <a>integral_comp_sub_left</a> f 0", [{"full_name": "zero_sub", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [317, 3], "def_end_pos": [317, 14]}, {"full_name": "intervalIntegral.in... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.mul_meas_ge_le_integral_of_nonneg | [
1695,
1
] | [
1705,
73
] | [{"tactic": "cases' eq_top_or_lt_top (\u03bc {x | \u03b5 \u2264 f x}) with h\u03bc h\u03bc", "annotated_tactic": ["cases' <a>eq_top_or_lt_top</a> (\u03bc {x | \u03b5 \u2264 f x}) with h\u03bc h\u03bc", [{"full_name": "eq_top_or_lt_top", "def_path": "Mathlib/Order/BoundedOrder.lean", "def_pos": [182, 9], "def_end_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Icc_eq_Iic | [
1477,
1
] | [
1479,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/Ergodic/Ergodic.lean | PreErgodic.of_iterate | [
79,
1
] | [
80,
79
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/String/Lemmas.lean | Substring.ValidFor.next | [
845,
1
] | [
854,
50
] | [{"tactic": "simp [Substring.next]", "annotated_tactic": ["simp [<a>Substring.next</a>]", [{"full_name": "Substring.next", "def_path": "lake-packages/lean4/src/lean/Init/Data/String/Basic.lean", "def_pos": [537, 15], "def_end_pos": [537, 19]}]], "state_before": "l m\u2081 : List Char\nc : Char\nm\u2082 r : List Char\n\... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | Bool.eq_iff_iff | [
812,
1
] | [
812,
78
] | [{"tactic": "cases b <;> simp", "annotated_tactic": ["cases b <;> simp", []], "state_before": "a b : Bool\n\u22a2 a = b \u2194 (a = true \u2194 b = true)", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_ofSubsemiring | [
508,
1
] | [
510,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.strongInductionOn_eq | [
821,
1
] | [
823,
25
] | [{"tactic": "rw [strongInductionOn]", "annotated_tactic": ["rw [<a>strongInductionOn</a>]", [{"full_name": "Multiset.strongInductionOn", "def_path": "Mathlib/Data/Multiset/Basic.lean", "def_pos": [813, 5], "def_end_pos": [813, 22]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type v\n\u03b3 : Type u_2\np : Multiset ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comapEquiv_symm_coe | [
122,
1
] | [
124,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Partial.lean | Filter.rtendsto_iff_le_rcomap | [
130,
1
] | [
136,
50
] | [{"tactic": "rw [rtendsto_def]", "annotated_tactic": ["rw [<a>rtendsto_def</a>]", [{"full_name": "Filter.rtendsto_def", "def_path": "Mathlib/Order/Filter/Partial.lean", "def_pos": [95, 9], "def_end_pos": [95, 21]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nr : Rel \u03b1 \u03b2\nl\u2081 : Fi... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.lift_of | [
291,
1
] | [
291,
83
] | [{"tactic": "rw [\u2190 mk_C x, lift_mk, eval\u2082_C]", "annotated_tactic": ["rw [\u2190 <a>mk_C</a> x, <a>lift_mk</a>, <a>eval\u2082_C</a>]", [{"full_name": "AdjoinRoot.mk_C", "def_path": "Mathlib/RingTheory/AdjoinRoot.lean", "def_pos": [203, 9], "def_end_pos": [203, 13]}, {"full_name": "AdjoinRoot.lift_mk", "def_pat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PullbackCone.op_inr | [
664,
1
] | [
665,
15
] | [{"tactic": "aesop_cat", "annotated_tactic": ["aesop_cat", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nJ : Type u\u2082\ninst\u271d : Category.{v\u2082, u\u2082} J\nX\u271d : Type v\u2082\nX Y Z : C\nf : X \u27f6 Z\ng : Y \u27f6 Z\nc : PullbackCone f g\n\u22a2 PushoutCocone... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.le_infsep | [
408,
1
] | [
410,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Fintype.lean | Multiset.card_toEnumFinset | [
247,
1
] | [
250,
31
] | [{"tactic": "rw [Finset.card, \u2190Multiset.card_map Prod.fst m.toEnumFinset.val]", "annotated_tactic": ["rw [<a>Finset.card</a>, \u2190<a>Multiset.card_map</a> <a>Prod.fst</a> m.toEnumFinset.val]", [{"full_name": "Finset.card", "def_path": "Mathlib/Data/Finset/Card.lean", "def_pos": [43, 5], "def_end_pos": [43, 9]}, ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/Defs.lean | Rat.divInt_zero_one | [
233,
1
] | [
236,
9
] | [{"tactic": "rw [divInt]", "annotated_tactic": ["rw [<a>divInt</a>]", [{"full_name": "Rat.divInt", "def_path": "lake-packages/std/Std/Data/Rat/Basic.lean", "def_pos": [98, 5], "def_end_pos": [98, 11]}]], "state_before": "a b c : \u211a\n\u22a2 0 /. 1 = 0", "state_after": "a b c : \u211a\n\u22a2 (match 0, 1 with\n | ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Ring/Defs.lean | RingHom.mul_def | [
698,
1
] | [
699,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X | [
517,
1
] | [
518,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/QPF/Multivariate/Constructions/Const.lean | MvQPF.Const.mk_get | [
53,
11
] | [
53,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | tendsto_measure_cthickening_of_isCompact | [
1840,
1
] | [
1845,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.cofork_ι_app_one | [
953,
1
] | [
954,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecificLimits/Basic.lean | summable_geometric_two_encode | [
232,
1
] | [
234,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_eq_empty | [
191,
1
] | [
192,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi | [
759,
1
] | [
762,
58
] | [{"tactic": "rw [\u2190 eq_sub_iff_add_eq, \u2190 two_nsmul_coe_div_two, \u2190 nsmul_sub, two_nsmul_eq_iff] at h", "annotated_tactic": ["rw [\u2190 <a>eq_sub_iff_add_eq</a>, \u2190 <a>two_nsmul_coe_div_two</a>, \u2190 <a>nsmul_sub</a>, <a>two_nsmul_eq_iff</a>] at h", [{"full_name": "eq_sub_iff_add_eq", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ZetaFunction.lean | differentiableAt_mellin_zetaKernel₁ | [
305,
1
] | [
308,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.isClosed_iff_sup | [
152,
1
] | [
159,
18
] | [{"tactic": "use fun hs \u03b9 h\u03b9 f hf => (mem_closed_iff_sup hs).2 \u27e8\u03b9, h\u03b9, f, hf, rfl\u27e9", "annotated_tactic": ["use fun hs \u03b9 h\u03b9 f hf => (<a>mem_closed_iff_sup</a> hs).2 \u27e8\u03b9, h\u03b9, f, hf, <a>rfl</a>\u27e9", [{"full_name": "Ordinal.mem_closed_iff_sup", "def_path": "Mathlib/S... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.pow_mulRight | [
234,
1
] | [
237,
86
] | [{"tactic": "simp only [mulRight, \u2190 Algebra.coe_lmul_eq_mul]", "annotated_tactic": ["simp only [<a>mulRight</a>, \u2190 <a>Algebra.coe_lmul_eq_mul</a>]", [{"full_name": "LinearMap.mulRight", "def_path": "Mathlib/Algebra/Algebra/Bilinear.lean", "def_pos": [51, 5], "def_end_pos": [51, 13]}, {"full_name": "Algebra.co... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.cos_sq_arctan | [
141,
1
] | [
142,
81
] | [{"tactic": "rw_mod_cast [one_div, \u2190 inv_one_add_tan_sq (cos_arctan_pos x).ne', tan_arctan]", "annotated_tactic": ["rw_mod_cast [<a>one_div</a>, \u2190 <a>inv_one_add_tan_sq</a> (<a>cos_arctan_pos</a> x).<a>ne'</a>, <a>tan_arctan</a>]", [{"full_name": "one_div", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IntegralClosure.lean | RingHom.isIntegral_of_surjective | [
1045,
1
] | [
1046,
74
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/CliffordAlgebra/Contraction.lean | CliffordAlgebra.changeFormEquiv_symm | [
386,
1
] | [
388,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/Floor.lean | Nat.coprime_sub_mul_floor_rat_div_of_coprime | [
99,
1
] | [
104,
41
] | [{"tactic": "have : (n : \u2124) % d = n - d * \u230a(n : \u211a) / d\u230b := Int.mod_nat_eq_sub_mul_floor_rat_div", "annotated_tactic": ["have : (n : \u2124) % d = n - d * \u230a(n : \u211a) / d\u230b := <a>Int.mod_nat_eq_sub_mul_floor_rat_div</a>", [{"full_name": "Int.mod_nat_eq_sub_mul_floor_rat_div", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.rank_eq_four | [
578,
1
] | [
580,
11
] | [{"tactic": "rw [rank_eq_card_basis (basisOneIJK c\u2081 c\u2082), Fintype.card_fin]", "annotated_tactic": ["rw [<a>rank_eq_card_basis</a> (<a>basisOneIJK</a> c\u2081 c\u2082), <a>Fintype.card_fin</a>]", [{"full_name": "rank_eq_card_basis", "def_path": "Mathlib/LinearAlgebra/Dimension.lean", "def_pos": [810, 9], "def_e... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Encodable/Basic.lean | Encodable.axiom_of_choice | [
595,
1
] | [
597,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_iSup_eq | [
949,
1
] | [
951,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.hσ'_eq_zero | [
105,
1
] | [
109,
18
] | [{"tactic": "simp only [h\u03c3', h\u03c3]", "annotated_tactic": ["simp only [<a>h\u03c3'</a>, <a>h\u03c3</a>]", [{"full_name": "AlgebraicTopology.DoldKan.h\u03c3'", "def_path": "Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean", "def_pos": [101, 5], "def_end_pos": [101, 8]}, {"full_name": "AlgebraicTopology.DoldKan.h... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset | [
279,
1
] | [
284,
87
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.paste_vert_iff | [
537,
1
] | [
541,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Dilation.lean | Dilation.id_comp | [
346,
1
] | [
347,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueFinset_mono | [
355,
1
] | [
356,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux | [
689,
1
] | [
699,
51
] | [{"tactic": "refine' f.tendsto_translationNumber_aux.congr_dist (squeeze_zero (fun _ => dist_nonneg) _ _)", "annotated_tactic": ["refine' f.tendsto_translationNumber_aux.congr_dist (<a>squeeze_zero</a> (fun _ => <a>dist_nonneg</a>) _ _)", [{"full_name": "squeeze_zero", "def_path": "Mathlib/Topology/MetricSpace/Basic.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.naturality_2 | [
172,
1
] | [
173,
7
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\nD : Type u\u2082\ninst\u271d\u00b9 : Category.{v\u2082, u\u2082} D\nE : Type u\u2083\ninst\u271d : Category.{v\u2083, u\u2083} E\nF G : C \u2964 D\nX Y : C\n\u03b1 : F \u2245 G\nf :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.swap_apply | [
374,
1
] | [
376,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Function/OfArity.lean | Function.OfArity.const_succ_apply | [
59,
1
] | [
60,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_ne_zero_iff | [
894,
1
] | [
895,
36
] | [{"tactic": "rw [\u2190 not_or, \u2190 sign_eq_zero_iff]", "annotated_tactic": ["rw [\u2190 <a>not_or</a>, \u2190 <a>sign_eq_zero_iff</a>]", [{"full_name": "not_or", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [340, 9], "def_end_pos": [340, 15]}, {"full_name": "Real.Angle.sign_eq_zero_iff", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Ordmap/Ordset.lean | Ordnode.delta_lt_false | [
82,
1
] | [
84,
83
] | [{"tactic": "decide", "annotated_tactic": ["decide", []], "state_before": "\u03b1 : Type u_1\na b : \u2115\nh\u2081 : delta * a < b\nh\u2082 : delta * b < a\n\u22a2 0 < delta", "state_after": "no goals"}, {"tactic": "simpa [mul_assoc] using Nat.mul_le_mul_right a (by decide : 1 \u2264 delta * delta)", "annotated_tactic... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | Convex.affine_image | [
537,
1
] | [
539,
31
] | [{"tactic": "rintro _ \u27e8x, hx, rfl\u27e9", "annotated_tactic": ["rintro _ \u27e8x, hx, rfl\u27e9", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\n\u03b2 : Type u_4\ninst\u271d\u2074 : OrderedRing \ud835\udd5c\ninst\u271d\u00b3 : AddCommGroup E\ninst\u271d\u00b2 : AddCommGroup F\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | Function.Surjective.iSup_congr | [
707,
11
] | [
710,
20
] | [{"tactic": "convert h1.iSup_comp g", "annotated_tactic": ["convert h1.iSup_comp g", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b2\u2082 : Type u_3\n\u03b3 : Type u_4\n\u03b9 : Sort u_5\n\u03b9' : Sort u_6\n\u03ba : \u03b9 \u2192 Sort u_7\n\u03ba' : \u03b9' \u2192 Sort u_8\ninst\u271d : SupSet \u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.op_smul_set_mul_eq_mul_smul_set | [
855,
1
] | [
857,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/FunctionField.lean | FunctionField.inftyValuedFqt.def | [
247,
1
] | [
249,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Primrec.lean | Primrec.fin_val_iff | [
1268,
1
] | [
1270,
68
] | [{"tactic": "letI : Primcodable { a // id a < n } := Primcodable.subtype (nat_lt.comp .id (const _))", "annotated_tactic": ["letI : <a>Primcodable</a> { a // <a>id</a> a < n } := <a>Primcodable.subtype</a> (nat_lt.comp .id (<a>const</a> _))", [{"full_name": "Primcodable", "def_path": "Mathlib/Computability/Primrec.lean... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Lattice.lean | Nat.sInf_mem | [
69,
1
] | [
71,
24
] | [{"tactic": "rw [Nat.sInf_def h]", "annotated_tactic": ["rw [<a>Nat.sInf_def</a> h]", [{"full_name": "Nat.sInf_def", "def_path": "Mathlib/Data/Nat/Lattice.lean", "def_pos": [33, 9], "def_end_pos": [33, 17]}]], "state_before": "s : Set \u2115\nh : Set.Nonempty s\n\u22a2 sInf s \u2208 s", "state_after": "s : Set \u2115\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/WittVector/Verschiebung.lean | WittVector.verschiebungFun_coeff_succ | [
52,
1
] | [
54,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.ringHom_eval₂_cast_int_ringHom | [
138,
1
] | [
140,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Denumerable.lean | Denumerable.encode_ofNat | [
65,
1
] | [
67,
26
] | [{"tactic": "obtain \u27e8a, h, e\u27e9 := decode_inv (\u03b1 := \u03b1) n", "annotated_tactic": ["obtain \u27e8a, h, e\u27e9 := <a>decode_inv</a> (\u03b1 := \u03b1) n", [{"full_name": "Denumerable.decode_inv", "def_path": "Mathlib/Logic/Denumerable.lean", "def_pos": [32, 3], "def_end_pos": [32, 13]}]], "state_before":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Filtered/Basic.lean | CategoryTheory.IsFiltered.sup_exists | [
256,
1
] | [
285,
14
] | [{"tactic": "induction' H using Finset.induction with h' H' nmf h''", "annotated_tactic": ["induction' H using <a>Finset.induction</a> with h' H' nmf h''", [{"full_name": "Finset.induction", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1240, 19], "def_end_pos": [1240, 28]}]], "state_before": "C : Type u\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_norm_flip | [
792,
9
] | [
795,
35
] | [{"tactic": "rw [mul_right_comm]", "annotated_tactic": ["rw [<a>mul_right_comm</a>]", [{"full_name": "mul_right_comm", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [102, 9], "def_end_pos": [102, 23]}]], "state_before": "\ud835\udd5c : Type u_1\n\ud835\udd5c\u2082 : Type u_2\n\ud835\udd5c\u2083 : Type u_3\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.add_mul_subset | [
1075,
1
] | [
1076,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Slice.lean | Set.sized_powersetCard | [
97,
1
] | [
98,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | BddAbove.mono | [
217,
1
] | [
218,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_iso_pullback | [
308,
1
] | [
312,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | isGreatest_Icc | [
687,
1
] | [
688,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Circumcenter.lean | Affine.Simplex.circumsphere_reindex | [
396,
1
] | [
400,
56
] | [{"tactic": "refine' s.circumsphere_unique_dist_eq.2 _ \u27e8_, _\u27e9 <;> rw [\u2190 s.reindex_range_points e]", "annotated_tactic": ["refine' s.circumsphere_unique_dist_eq.2 _ \u27e8_, _\u27e9 <;> rw [\u2190 s.reindex_range_points e]", []], "state_before": "V : Type u_1\nP : Type u_2\ninst\u271d\u00b3 : NormedAddCom... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.divMonomial_add_modMonomial_single | [
200,
1
] | [
202,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.cos_ne_zero_iff | [
42,
1
] | [
43,
50
] | [{"tactic": "rw [\u2190 not_exists, not_iff_not, cos_eq_zero_iff]", "annotated_tactic": ["rw [\u2190 <a>not_exists</a>, <a>not_iff_not</a>, <a>cos_eq_zero_iff</a>]", [{"full_name": "not_exists", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [422, 17], "def_end_pos": [422, 27]}, {"full_name": "not_iff_not",... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.lift_comp_residue | [
392,
1
] | [
394,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.get?_drop | [
2172,
1
] | [
2175,
81
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nl\u2081 l\u2082 L : List \u03b1\ni j : \u2115\n\u22a2 get? (drop i L) j = get? L (i + j)", "state_after": "case a\n\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/Basic.lean | Vector.exists_eq_cons | [
73,
1
] | [
74,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_inj | [
327,
1
] | [
328,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.exists_orthogonal_basis | [
1144,
1
] | [
1186,
39
] | [{"tactic": "induction' hd : finrank K V with d ih generalizing V", "annotated_tactic": ["induction' hd : <a>finrank</a> K V with d ih generalizing V", [{"full_name": "FiniteDimensional.finrank", "def_path": "Mathlib/LinearAlgebra/Finrank.lean", "def_pos": [58, 19], "def_end_pos": [58, 26]}]], "state_before": "S : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.deriv_arcsin | [
108,
1
] | [
114,
39
] | [{"tactic": "funext x", "annotated_tactic": ["funext x", []], "state_before": "\u22a2 deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2)", "state_after": "case h\nx : \u211d\n\u22a2 deriv arcsin x = 1 / sqrt (1 - x ^ 2)"}, {"tactic": "by_cases h : x \u2260 -1 \u2227 x \u2260 1", "annotated_tactic": ["by_cases h : x \u2260 -1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.binary_cofan_inr_toCocone | [
1215,
1
] | [
1216,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.inv' | [
628,
1
] | [
629,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Nodup.lean | Multiset.map_eq_map_of_bij_of_nodup | [
255,
1
] | [
270,
88
] | [{"tactic": "simp only [mem_map, true_and_iff, Subtype.exists, eq_comm, mem_attach]", "annotated_tactic": ["simp only [<a>mem_map</a>, <a>true_and_iff</a>, <a>Subtype.exists</a>, <a>eq_comm</a>, <a>mem_attach</a>]", [{"full_name": "Multiset.mem_map", "def_path": "Mathlib/Data/Multiset/Basic.lean", "def_pos": [1228, 9],... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.inter_sdiff_self | [
2082,
1
] | [
2084,
70
] | [{"tactic": "simp only [mem_inter, mem_sdiff]", "annotated_tactic": ["simp only [<a>mem_inter</a>, <a>mem_sdiff</a>]", [{"full_name": "Finset.mem_inter", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1601, 9], "def_end_pos": [1601, 18]}, {"full_name": "Finset.mem_sdiff", "def_path": "Mathlib/Data/Finset/Bas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.apply_none | [
177,
1
] | [
178,
43
] | [{"tactic": "simp only [Option.getD_none, h, l.apply]", "annotated_tactic": ["simp only [<a>Option.getD_none</a>, h, l.apply]", [{"full_name": "Option.getD_none", "def_path": "lake-packages/std/Std/Data/Option/Init/Lemmas.lean", "def_pos": [16, 17], "def_end_pos": [16, 26]}]], "state_before": "\u03b1 : Type u_1\n\u03b9... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_const | [
313,
1
] | [
317,
77
] | [{"tactic": "by_cases h_top : p = \u221e", "annotated_tactic": ["by_cases h_top : p = \u221e", []], "state_before": "\u03b1 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nm m0 : MeasurableSpace \u03b1\np : \u211d\u22650\u221e\nq : \u211d\n\u03bc \u03bd : Measure \u03b1\ninst\u271d\u00b2 : NormedAddCommGroup E\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/GCD.lean | Int.gcd_one_right | [
290,
1
] | [
291,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/AddTorsor.lean | vadd_vsub | [
94,
1
] | [
95,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_disjoint_ball | [
550,
1
] | [
551,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/VectorBundle/SmoothSection.lean | ContMDiffSection.coe_smul | [
175,
1
] | [
176,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.polynomial_mul | [
128,
1
] | [
132,
61
] | [{"tactic": "simpa [add_mul] using hp.add hq", "annotated_tactic": ["simpa [<a>add_mul</a>] using hp.add hq", [{"full_name": "add_mul", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [91, 7], "def_end_pos": [91, 14]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nl : Filter \u03b1\nk f g g' : \u03b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Star.lean | starConvex_iff_segment_subset | [
74,
1
] | [
79,
40
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u2074 : OrderedSemiring \ud835\udd5c\ninst\u271d\u00b3 : AddCommMonoid E\ninst\u271d\u00b2 : AddCommMonoid F\ninst\u271d\u00b9 : SMul \ud835\udd5c E\ninst\u271d : SMul \ud... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.reApplyInnerSelf_continuous | [
2300,
1
] | [
2302,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_vsub | [
718,
1
] | [
719,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Finite.lean | Set.Infinite.of_image | [
1326,
1
] | [
1327,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Dimension.lean | rank_bot | [
286,
1
] | [
288,
32
] | [{"tactic": "have : (\u22a5 : Submodule R M) \u2243\u2097[R] PUnit := botEquivPUnit", "annotated_tactic": ["have : (\u22a5 : <a>Submodule</a> R M) \u2243\u2097[R] <a>PUnit</a> := <a>botEquivPUnit</a>", [{"full_name": "Submodule", "def_path": "Mathlib/Algebra/Module/Submodule/Basic.lean", "def_pos": [41, 11], "def_end_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Sort.lean | List.sorted_insertionSort | [
281,
1
] | [
283,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Instances/Sphere.lean | stereoInvFunAux_apply | [
128,
1
] | [
130,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.countable_not_continuousWithinAt_Ioi | [
240,
1
] | [
252,
34
] | [{"tactic": "apply (countable_image_lt_image_Ioi f).mono", "annotated_tactic": ["apply (<a>countable_image_lt_image_Ioi</a> f).<a>mono</a>", [{"full_name": "countable_image_lt_image_Ioi", "def_path": "Mathlib/Topology/Order/Basic.lean", "def_pos": [1435, 9], "def_end_pos": [1435, 37]}, {"full_name": "Set.Countable.mono... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Bimod.lean | Bimod.comp_hom' | [
151,
1
] | [
153,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.ext | [
60,
1
] | [
66,
87
] | [{"tactic": "cases P", "annotated_tactic": ["cases P", []], "state_before": "C : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nP Q : Karoubi C\nh_X : P.X = Q.X\nh_p : P.p \u226b eqToHom h_X = eqToHom h_X \u226b Q.p\n\u22a2 P = Q", "state_after": "case mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nQ : Karoubi C\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/Computation.lean | Computation.corec_eq | [
253,
1
] | [
267,
26
] | [{"tactic": "dsimp [corec, destruct]", "annotated_tactic": ["dsimp [<a>corec</a>, <a>destruct</a>]", [{"full_name": "Computation.corec", "def_path": "Mathlib/Data/Seq/Computation.lean", "def_pos": [219, 5], "def_end_pos": [219, 10]}, {"full_name": "Computation.destruct", "def_path": "Mathlib/Data/Seq/Computation.lean",... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/CliffordAlgebra/Even.lean | CliffordAlgebra.even_toSubmodule | [
64,
1
] | [
65,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_X | [
410,
1
] | [
412,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/ModEq.lean | Nat.odd_of_mod_four_eq_three | [
520,
1
] | [
522,
31
] | [{"tactic": "simpa [ModEq, show 2 * 2 = 4 by norm_num, show 3 % 4 = 3 by norm_num] using\n @ModEq.of_mul_left 2 n 3 2", "annotated_tactic": ["simpa [<a>ModEq</a>, show 2 * 2 = 4 by norm_num, show 3 % 4 = 3 by norm_num] using\n @<a>ModEq.of_mul_left</a> 2 n 3 2", [{"full_name": "Nat.ModEq", "def_path": "Mathlib/Data... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basis.lean | Basis.reindex_refl | [
441,
1
] | [
442,
34
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b9 : Type u_1\n\u03b9' : Type u_2\nR : Type u_3\nR\u2082 : Type u_4\nK : Type u_5\nM : Type u_6\nM' : Type u_7\nM'' : Type u_8\nV : Type u\nV' : Type u_9\ninst\u271d\u2074 : Semiring R\ninst\u271d\u00b3 : AddCommMonoid M\ninst\u271d\u00b2 : Modu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.nonsing_inv_mul_cancel_right | [
285,
1
] | [
286,
47
] | [{"tactic": "simp [Matrix.mul_assoc, nonsing_inv_mul A h]", "annotated_tactic": ["simp [<a>Matrix.mul_assoc</a>, <a>nonsing_inv_mul</a> A h]", [{"full_name": "Matrix.mul_assoc", "def_path": "Mathlib/Data/Matrix/Basic.lean", "def_pos": [1145, 19], "def_end_pos": [1145, 28]}, {"full_name": "Matrix.nonsing_inv_mul", "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_smul | [
442,
1
] | [
444,
92
] | [{"tactic": "simp only [circleIntegral, \u2190 smul_comm a (_ : \u2102) (_ : E), intervalIntegral.integral_smul]", "annotated_tactic": ["simp only [<a>circleIntegral</a>, \u2190 <a>smul_comm</a> a (_ : \u2102) (_ : E), <a>intervalIntegral.integral_smul</a>]", [{"full_name": "circleIntegral", "def_path": "Mathlib/Measur... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Interval.lean | Fin.Iic_eq_finset_subtype | [
167,
1
] | [
168,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_add_prod_le' | [
667,
1
] | [
677,
17
] | [{"tactic": "classical\n simp_rw [prod_eq_mul_prod_diff_singleton hi]\n refine' le_trans _ (mul_le_mul_right' h2i _)\n rw [right_distrib]\n apply add_le_add <;> apply mul_le_mul_left' <;> apply prod_le_prod' <;>\n simp only [and_imp, mem_sdiff, mem_singleton] <;>\n intros <;>\n apply_assumption... |
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