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/Analysis/Convex/Basic.lean | convex_halfspace_gt | [
345,
1
] | [
346,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_sum | [
240,
1
] | [
241,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Matrix.lean | Matrix.reindexLieEquiv_apply | [
96,
1
] | [
98,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.conjTranspose_zpow | [
338,
1
] | [
340,
95
] | [{"tactic": "rw [zpow_ofNat, zpow_ofNat, conjTranspose_pow]", "annotated_tactic": ["rw [<a>zpow_ofNat</a>, <a>zpow_ofNat</a>, <a>conjTranspose_pow</a>]", [{"full_name": "zpow_ofNat", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [948, 9], "def_end_pos": [948, 19]}, {"full_name": "zpow_ofNat", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Relation.lean | Equivalence.eqvGen_iff | [
724,
1
] | [
733,
21
] | [{"tactic": "intro h", "annotated_tactic": ["intro h", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\na b : \u03b1\nh : Equivalence r\n\u22a2 EqvGen r a b \u2192 r a b", "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | Summable.div_const | [
85,
1
] | [
86,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.endofunctorMonoidalCategory_tensorUnit_map | [
51,
9
] | [
52,
34
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.natAbs_add_le | [
1337,
1
] | [
1352,
27
] | [{"tactic": "suffices \u2200 a b : Nat, natAbs (subNatNat a b.succ) \u2264 (a + b).succ by\n match a, b with\n | (a:Nat), (b:Nat) => simp\n | (a:Nat), -[b+1] => simp; apply this\n | -[a+1], (b:Nat) => simp [Nat.succ_add, Nat.add_comm a b]; apply this\n | -[a+1], -[b+1] => simp [Nat.succ_add]; apply Nat.le_refl... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.get?_set | [
922,
1
] | [
924,
56
] | [{"tactic": "by_cases m = n <;> simp [*, get?_set_eq, get?_set_ne]", "annotated_tactic": ["by_cases m = n <;> simp [*, <a>get?_set_eq</a>, <a>get?_set_ne</a>]", [{"full_name": "List.get?_set_eq", "def_path": "lake-packages/std/Std/Data/List/Lemmas.lean", "def_pos": [913, 9], "def_end_pos": [913, 20]}, {"full_name": "Li... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.finite_edist_eq | [
222,
1
] | [
223,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_inf | [
1538,
1
] | [
1539,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_inj | [
93,
1
] | [
94,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/DFinsupp.lean | DFinsupp.lsingle_apply | [
91,
1
] | [
92,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/VecNotation.lean | Matrix.tail_cons | [
157,
1
] | [
159,
17
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b1 : Type u\nm n o : \u2115\nm' : Type u_1\nn' : Type u_2\no' : Type u_3\nx : \u03b1\nu : Fin m \u2192 \u03b1\n\u22a2 vecTail (vecCons x u) = u", "state_after": "case h\n\u03b1 : Type u\nm n o : \u2115\nm' : Type u_1\nn' : Type u_2\no' : Type u_3\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_pow_sub_C | [
399,
1
] | [
401,
70
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rel.lean | Rel.core_inter | [
225,
1
] | [
226,
52
] | [{"tactic": "simp [mem_core, imp_and, forall_and]", "annotated_tactic": ["simp [<a>mem_core</a>, <a>imp_and</a>, <a>forall_and</a>]", [{"full_name": "Rel.mem_core", "def_path": "Mathlib/Data/Rel.lean", "def_pos": [214, 9], "def_end_pos": [214, 17]}, {"full_name": "imp_and", "def_path": "lake-packages/std/Std/Logic.lean... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | iff_self_and | [
214,
9
] | [
215,
41
] | [{"tactic": "rw [@Iff.comm p, and_iff_left_iff_imp]", "annotated_tactic": ["rw [@<a>Iff.comm</a> p, <a>and_iff_left_iff_imp</a>]", [{"full_name": "Iff.comm", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", "def_pos": [674, 9], "def_end_pos": [674, 17]}, {"full_name": "and_iff_left_iff_imp", "def_path": "lake... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_lift_le_max | [
57,
1
] | [
60,
74
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R : Type u\nA : Type v\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : CommRing A\ninst\u271d\u00b2 : IsDomain A\ninst\u271d\u00b9 : Algebra R A\ninst\u271d : NoZeroSMulDivisors R A\n\u22a2 lift.{v, u} (max #R \u2135\u2080) * \u2135\u2080 \u2264 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_neg_iff | [
710,
1
] | [
710,
95
] | [{"tactic": "simpa only [sinh_zero] using @sinh_lt_sinh x 0", "annotated_tactic": ["simpa only [<a>sinh_zero</a>] using @<a>sinh_lt_sinh</a> x 0", [{"full_name": "Real.sinh_zero", "def_path": "Mathlib/Data/Complex/Exponential.lean", "def_pos": [1347, 9], "def_end_pos": [1347, 18]}, {"full_name": "Real.sinh_lt_sinh", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Concept.lean | intentClosure_empty | [
83,
1
] | [
84,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Field/Basic.lean | one_div_neg_one_eq_neg_one | [
92,
1
] | [
94,
48
] | [{"tactic": "rw [neg_mul_neg, one_mul]", "annotated_tactic": ["rw [<a>neg_mul_neg</a>, <a>one_mul</a>]", [{"full_name": "neg_mul_neg", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [298, 9], "def_end_pos": [298, 20]}, {"full_name": "one_mul", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [464, 9]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_add_const_Ioi | [
84,
1
] | [
85,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Cover.lean | not_covby_iff | [
233,
1
] | [
234,
69
] | [{"tactic": "simp_rw [Covby, h, true_and_iff, not_forall, exists_prop, not_not]", "annotated_tactic": ["simp_rw [<a>Covby</a>, h, <a>true_and_iff</a>, <a>not_forall</a>, <a>exists_prop</a>, <a>not_not</a>]", [{"full_name": "Covby", "def_path": "Mathlib/Order/Cover.lean", "def_pos": [221, 5], "def_end_pos": [221, 10]}, ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Field/Basic.lean | norm_pow | [
544,
1
] | [
545,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_eq_map_powerset | [
85,
1
] | [
94,
47
] | [{"tactic": "induction' s using Multiset.induction_on with a s hs", "annotated_tactic": ["induction' s using <a>Multiset.induction_on</a> with a s hs", [{"full_name": "Multiset.induction_on", "def_path": "Mathlib/Data/Multiset/Basic.lean", "def_pos": [160, 19], "def_end_pos": [160, 31]}]], "state_before": "\u03b1 : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Star.lean | StarConvex.preimage_add_left | [
258,
1
] | [
261,
52
] | [{"tactic": "rw [add_comm] at hs", "annotated_tactic": ["rw [<a>add_comm</a>] at hs", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}]], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u2074 : OrderedSemiring \ud83... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/Linear.lean | LinearMap.hasDerivAtFilter | [
83,
11
] | [
84,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.twoBlockTriangular_det | [
201,
1
] | [
208,
28
] | [{"tactic": "rw [det_toBlock M p]", "annotated_tactic": ["rw [<a>det_toBlock</a> M p]", [{"full_name": "Matrix.det_toBlock", "def_path": "Mathlib/LinearAlgebra/Matrix/Block.lean", "def_pos": [187, 9], "def_end_pos": [187, 20]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nm : Type u_3\nn : Type u_4\no : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean | AlgebraicGeometry.compactSpace_iff_quasiCompact | [
223,
1
] | [
225,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Invertible/Basic.lean | div_self_of_invertible | [
191,
1
] | [
192,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_mk' | [
283,
1
] | [
285,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/SimpleModule.lean | LinearMap.surjective_of_ne_zero | [
141,
1
] | [
143,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/QPF/Multivariate/Constructions/Cofix.lean | MvQPF.Cofix.bisim_rel | [
258,
1
] | [
280,
19
] | [{"tactic": "let r' (x y) := x = y \u2228 r x y", "annotated_tactic": ["let r' (x y) := x = y \u2228 r x y", []], "state_before": "n : \u2115\nF : TypeVec.{u} (n + 1) \u2192 Type u\nmvf : MvFunctor F\nq : MvQPF F\n\u03b1 : TypeVec.{u} n\nr : Cofix F \u03b1 \u2192 Cofix F \u03b1 \u2192 Prop\nh : \u2200 (x y : Cofix F \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_smul_le | [
287,
1
] | [
291,
69
] | [{"tactic": "erw [norm_smul, mul_assoc]", "annotated_tactic": ["erw [<a>norm_smul</a>, <a>mul_assoc</a>]", [{"full_name": "norm_smul", "def_path": "Mathlib/Analysis/Normed/MulAction.lean", "def_pos": [89, 9], "def_end_pos": [89, 18]}, {"full_name": "mul_assoc", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.filter_add | [
1942,
1
] | [
1943,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_bot | [
1518,
1
] | [
1519,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | min_mul_of_nonneg | [
980,
1
] | [
981,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.ext_iff | [
1373,
1
] | [
1374,
44
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | exists_eq' | [
457,
9
] | [
457,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Tropical/BigOperators.lean | trop_sum | [
53,
1
] | [
57,
6
] | [{"tactic": "convert Multiset.trop_sum (s.val.map f)", "annotated_tactic": ["convert <a>Multiset.trop_sum</a> (s.val.map f)", [{"full_name": "Multiset.trop_sum", "def_path": "Mathlib/Algebra/Tropical/BigOperators.lean", "def_pos": [48, 9], "def_end_pos": [48, 26]}]], "state_before": "R : Type u_1\nS : Type u_2\ninst\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_not_le_left | [
129,
1
] | [
129,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarAlgHom.restrictScalars_injective | [
840,
1
] | [
843,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasStrictFDerivAt_const | [
1136,
1
] | [
1138,
79
] | [{"tactic": "simp only [zero_apply, sub_self]", "annotated_tactic": ["simp only [<a>zero_apply</a>, <a>sub_self</a>]", [{"full_name": "ContinuousLinearMap.zero_apply", "def_path": "Mathlib/Topology/Algebra/Module/Basic.lean", "def_pos": [644, 9], "def_end_pos": [644, 19]}, {"full_name": "sub_self", "def_path": "Mathlib... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_rotate | [
1288,
1
] | [
1292,
40
] | [{"tactic": "simp only [rotate, tail_support_append]", "annotated_tactic": ["simp only [<a>rotate</a>, <a>tail_support_append</a>]", [{"full_name": "SimpleGraph.Walk.rotate", "def_path": "Mathlib/Combinatorics/SimpleGraph/Connectivity.lean", "def_pos": [1283, 5], "def_end_pos": [1283, 11]}, {"full_name": "SimpleGraph.W... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.exists_subset_of_mem_shadow | [
137,
1
] | [
139,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.piecewise_apply | [
235,
1
] | [
237,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Diffeomorph.lean | Diffeomorph.symm_image_eq_preimage | [
272,
1
] | [
273,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_mul_deriv''' | [
1462,
1
] | [
1469,
78
] | [{"tactic": "have hg2' : IntegrableOn (fun x => f' x \u2022 (g \u2218 f) x) [[a, b]] := by simpa [mul_comm] using hg2", "annotated_tactic": ["have hg2' : <a>IntegrableOn</a> (fun x => f' x \u2022 (g \u2218 f) x) [[a, b]] := by simpa [<a>mul_comm</a>] using hg2", [{"full_name": "MeasureTheory.IntegrableOn", "def_path": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_zero | [
306,
1
] | [
307,
34
] | [{"tactic": "simp only [cyclotomic, dif_pos]", "annotated_tactic": ["simp only [<a>cyclotomic</a>, <a>dif_pos</a>]", [{"full_name": "Polynomial.cyclotomic", "def_path": "Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean", "def_pos": [255, 5], "def_end_pos": [255, 15]}, {"full_name": "dif_pos", "def_path": "lake-packa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | Filter.tendsto_inv_cobounded | [
475,
1
] | [
477,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.iUnion_union_distrib | [
643,
1
] | [
645,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/GDelta.lean | isGδ_singleton | [
169,
1
] | [
172,
63
] | [{"tactic": "rcases (nhds_basis_opens x).exists_antitone_subbasis with \u27e8U, hU, h_basis\u27e9", "annotated_tactic": ["rcases (<a>nhds_basis_opens</a> x).<a>exists_antitone_subbasis</a> with \u27e8U, hU, h_basis\u27e9", [{"full_name": "nhds_basis_opens", "def_path": "Mathlib/Topology/Basic.lean", "def_pos": [873, 9]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.invUnitsSub_mul_sub | [
55,
1
] | [
56,
33
] | [{"tactic": "simp [mul_sub, sub_sub_cancel]", "annotated_tactic": ["simp [<a>mul_sub</a>, <a>sub_sub_cancel</a>]", [{"full_name": "mul_sub", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [365, 7], "def_end_pos": [365, 14]}, {"full_name": "sub_sub_cancel", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Function.lean | Set.InvOn.symm | [
1197,
1
] | [
1198,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/PGame.lean | SetTheory.PGame.lt_congr_right | [
891,
1
] | [
892,
24
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Gcd.lean | Nat.lcm_self | [
207,
9
] | [
210,
49
] | [{"tactic": "match eq_zero_or_pos m with\n| .inl h => rw [h, lcm_zero_left]\n| .inr h => simp [lcm, Nat.mul_div_cancel _ h]", "annotated_tactic": ["match <a>eq_zero_or_pos</a> m with\n | .inl h => rw [h, <a>lcm_zero_left</a>]\n | .inr h => simp [<a>lcm</a>, <a>Nat.mul_div_cancel</a> _ h]", [{"full_name": "Nat.eq_zero... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.inseparable_iff | [
1237,
1
] | [
1238,
99
] | [{"tactic": "rw [EMetric.inseparable_iff, edist_nndist, dist_nndist, ENNReal.coe_eq_zero, NNReal.coe_eq_zero]", "annotated_tactic": ["rw [<a>EMetric.inseparable_iff</a>, <a>edist_nndist</a>, <a>dist_nndist</a>, <a>ENNReal.coe_eq_zero</a>, <a>NNReal.coe_eq_zero</a>]", [{"full_name": "EMetric.inseparable_iff", "def_path"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/GCD.lean | Int.gcd_mul_left | [
302,
1
] | [
304,
25
] | [{"tactic": "rw [Int.gcd, Int.gcd, natAbs_mul, natAbs_mul]", "annotated_tactic": ["rw [<a>Int.gcd</a>, <a>Int.gcd</a>, <a>natAbs_mul</a>, <a>natAbs_mul</a>]", [{"full_name": "Int.gcd", "def_path": "lake-packages/std/Std/Data/Int/Basic.lean", "def_pos": [120, 5], "def_end_pos": [120, 8]}, {"full_name": "Int.gcd", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.submatrix | [
138,
1
] | [
139,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_sup_comap_of_surjective | [
490,
1
] | [
492,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Cotangent.lean | Ideal.toCotangent_eq | [
73,
1
] | [
75,
30
] | [{"tactic": "rw [\u2190 sub_eq_zero]", "annotated_tactic": ["rw [\u2190 <a>sub_eq_zero</a>]", [{"full_name": "sub_eq_zero", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [801, 3], "def_end_pos": [801, 14]}]], "state_before": "R : Type u\nS : Type v\nS' : Type w\ninst\u271d\u2076 : CommRing R\ninst\u271d\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.rename_eq | [
107,
1
] | [
111,
6
] | [{"tactic": "simp only [rename, aeval_def, eval\u2082, Finsupp.mapDomain, algebraMap_eq, comp_apply,\n X_pow_eq_monomial, \u2190 monomial_finsupp_sum_index]", "annotated_tactic": ["simp only [<a>rename</a>, <a>aeval_def</a>, <a>eval\u2082</a>, <a>Finsupp.mapDomain</a>, <a>algebraMap_eq</a>, <a>comp_apply</a>,\n <a>... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.support_indicator | [
256,
1
] | [
258,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_lattice_hom | [
1296,
1
] | [
1298,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_summable_of_mem_ball | [
213,
1
] | [
216,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Reflection.lean | Matrix.mulVecᵣ_eq | [
185,
1
] | [
188,
6
] | [{"tactic": "simp [mulVec\u1d63, Function.comp]", "annotated_tactic": ["simp [<a>mulVec\u1d63</a>, <a>Function.comp</a>]", [{"full_name": "Matrix.mulVec\u1d63", "def_path": "Mathlib/Data/Matrix/Reflection.lean", "def_pos": [172, 5], "def_end_pos": [172, 12]}, {"full_name": "Function.comp", "def_path": "lake-packages/le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.essentiallySmallSelf | [
84,
1
] | [
85,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sups.lean | Finset.subset_infs | [
362,
1
] | [
364,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.sup_span | [
191,
1
] | [
192,
28
] | [{"tactic": "rw [span_union, span_coe]", "annotated_tactic": ["rw [<a>span_union</a>, <a>span_coe</a>]", [{"full_name": "Projectivization.Subspace.span_union", "def_path": "Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean", "def_pos": [179, 9], "def_end_pos": [179, 19]}, {"full_name": "Projectivization.Subspace.span... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Defs.lean | MeasurableSet.ite | [
217,
11
] | [
219,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.hom_ext | [
252,
1
] | [
255,
16
] | [{"tactic": "rw [lift_unique f, lift_unique g]", "annotated_tactic": ["rw [<a>lift_unique</a> f, <a>lift_unique</a> g]", [{"full_name": "SemidirectProduct.lift_unique", "def_path": "Mathlib/GroupTheory/SemidirectProduct.lean", "def_pos": [243, 9], "def_end_pos": [243, 20]}, {"full_name": "SemidirectProduct.lift_unique"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Integral.lean | MeasureTheory.Integrable.comp_mul_right | [
119,
1
] | [
121,
93
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Reverse.lean | Polynomial.trailingCoeff_mul | [
334,
1
] | [
337,
26
] | [{"tactic": "rw [\u2190 reverse_leadingCoeff, reverse_mul_of_domain, leadingCoeff_mul, reverse_leadingCoeff,\n reverse_leadingCoeff]", "annotated_tactic": ["rw [\u2190 <a>reverse_leadingCoeff</a>, <a>reverse_mul_of_domain</a>, <a>leadingCoeff_mul</a>, <a>reverse_leadingCoeff</a>,\n <a>reverse_leadingCoeff</a>]", [{... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_apply_ne' | [
439,
1
] | [
440,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivWithinAt.cosh | [
1062,
1
] | [
1064,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/ZMod/Basic.lean | Nat.le_div_two_iff_mul_two_le | [
984,
1
] | [
985,
86
] | [{"tactic": "rw [Nat.le_div_iff_mul_le zero_lt_two, \u2190 Int.ofNat_le, Int.ofNat_mul, Nat.cast_two]", "annotated_tactic": ["rw [<a>Nat.le_div_iff_mul_le</a> <a>zero_lt_two</a>, \u2190 <a>Int.ofNat_le</a>, <a>Int.ofNat_mul</a>, <a>Nat.cast_two</a>]", [{"full_name": "Nat.le_div_iff_mul_le", "def_path": "lake-packages/s... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Bernoulli.lean | bernoulli_zero | [
208,
1
] | [
208,
64
] | [{"tactic": "simp [bernoulli]", "annotated_tactic": ["simp [<a>bernoulli</a>]", [{"full_name": "bernoulli", "def_path": "Mathlib/NumberTheory/Bernoulli.lean", "def_pos": [199, 5], "def_end_pos": [199, 14]}]], "state_before": "A : Type u_1\ninst\u271d\u00b9 : CommRing A\ninst\u271d : Algebra \u211a A\n\u22a2 bernoulli 0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_op_smul_set | [
427,
1
] | [
428,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_assoc | [
341,
1
] | [
347,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_sInf | [
307,
1
] | [
308,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Order.lean | le_max_of_sq_le_mul | [
322,
1
] | [
323,
69
] | [{"tactic": "simpa using min_le_max_of_mul_le_mul ((pow_two _).symm.trans_le h)", "annotated_tactic": ["simpa using <a>min_le_max_of_mul_le_mul</a> ((<a>pow_two</a> _).symm.trans_le h)", [{"full_name": "min_le_max_of_mul_le_mul", "def_path": "Mathlib/Algebra/Order/Monoid/Lemmas.lean", "def_pos": [350, 22], "def_end_pos... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.congr_mono | [
1019,
1
] | [
1022,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Exponential.lean | Complex.cosh_add_sinh | [
730,
1
] | [
731,
99
] | [{"tactic": "rw [\u2190 mul_right_inj' (two_ne_zero' \u2102), mul_add, two_cosh, two_sinh, add_add_sub_cancel, two_mul]", "annotated_tactic": ["rw [\u2190 <a>mul_right_inj'</a> (<a>two_ne_zero'</a> \u2102), <a>mul_add</a>, <a>two_cosh</a>, <a>two_sinh</a>, <a>add_add_sub_cancel</a>, <a>two_mul</a>]", [{"full_name": "mu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Unoriented/Conformal.lean | InnerProductGeometry.ConformalAt.preserves_angle | [
35,
1
] | [
38,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_mul | [
549,
1
] | [
550,
30
] | [{"tactic": "simp only [mul_def, coe_mk]", "annotated_tactic": ["simp only [<a>mul_def</a>, <a>coe_mk</a>]", [{"full_name": "FractionalIdeal.mul_def", "def_path": "Mathlib/RingTheory/FractionalIdeal.lean", "def_pos": [544, 9], "def_end_pos": [544, 16]}, {"full_name": "FractionalIdeal.coe_mk", "def_path": "Mathlib/RingT... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.monotone_sort | [
106,
1
] | [
108,
56
] | [{"tactic": "rw [self_comp_sort]", "annotated_tactic": ["rw [<a>self_comp_sort</a>]", [{"full_name": "Tuple.self_comp_sort", "def_path": "Mathlib/Data/Fin/Tuple/Sort.lean", "def_pos": [96, 9], "def_end_pos": [96, 23]}]], "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_int_cast_mul | [
614,
1
] | [
616,
53
] | [{"tactic": "induction' k with k ih generalizing f <;> simp [*]", "annotated_tactic": ["induction' k with k ih generalizing f <;> simp [*]", []], "state_before": "R : Type u\nS : Type v\nT : Type w\n\u03b9 : Type y\nA : Type z\na b : R\nn\u271d : \u2115\ninst\u271d : Ring R\nn : \u2124\nk : \u2115\nf : R[X]\n\u22a2 (\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/FiniteDimensional.lean | CompleteLattice.Independent.subtype_ne_bot_le_finrank_aux | [
405,
1
] | [
414,
66
] | [{"tactic": "suffices Cardinal.lift.{v} #{ i // p i \u2260 \u22a5 } \u2264 Cardinal.lift.{v} (finrank K V : Cardinal.{w}) by\n rwa [Cardinal.lift_le] at this", "annotated_tactic": ["suffices <a>Cardinal.lift</a>.{v} #{ i // p i \u2260 \u22a5 } \u2264 <a>Cardinal.lift</a>.{v} (<a>finrank</a> K V : <a>Cardinal</a>.{w}) ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.re | [
1196,
1
] | [
1198,
14
] | [{"tactic": "rw [\u2190 mem\u2112p_one_iff_integrable] at hf \u22a2", "annotated_tactic": ["rw [\u2190 <a>mem\u2112p_one_iff_integrable</a>] at hf \u22a2", [{"full_name": "MeasureTheory.mem\u2112p_one_iff_integrable", "def_path": "Mathlib/MeasureTheory/Function/L1Space.lean", "def_pos": [453, 9], "def_end_pos": [453, 3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime_pow_eq_geom_sum | [
560,
1
] | [
575,
95
] | [{"tactic": "have : \u2200 m, (cyclotomic (p ^ (m + 1)) R = \u2211 i in Finset.range p, (X ^ p ^ m) ^ i) \u2194\n ((\u2211 i in Finset.range p, (X ^ p ^ m) ^ i) *\n \u220f x : \u2115 in Finset.range (m + 1), cyclotomic (p ^ x) R) = X ^ p ^ (m + 1) - 1 := by\n intro m\n have := eq_cyclotomic_iff (R := R) (P :=... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Infix.lean | List.tails_eq_inits | [
398,
1
] | [
400,
58
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nl l\u2081 l\u2082 l\u2083 : List \u03b1\na b : \u03b1\nm n : \u2115\n\u22a2 tails [] = reverse (map reverse (inits (reverse [])))", "state_after": "no goals"}, {"tactic": "simp [tails_eq_inits l, append_left_inj... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left | [
238,
1
] | [
249,
13
] | [{"tactic": "subst x", "annotated_tactic": ["subst x", []], "state_before": "x y z : \u2124\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhx : x = 0\n\u22a2 IsPrimitiveClassified h", "state_after": "y z : \u2124\nh : PythagoreanTriple 0 y z\nhc : Int.gcd 0 y = 1\n\u22a2 IsPrimitiveClassified h"}, {"tactic": "chan... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.le_add_caratheodory | [
1102,
1
] | [
1104,
73
] | [{"tactic": "simp [hs\u2081 t, hs\u2082 t, add_left_comm, add_assoc]", "annotated_tactic": ["simp [hs\u2081 t, hs\u2082 t, <a>add_left_comm</a>, <a>add_assoc</a>]", [{"full_name": "add_left_comm", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [95, 3], "def_end_pos": [95, 14]}, {"full_name": "add_assoc", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/EReal.lean | EReal.le_coe_toReal | [
418,
1
] | [
421,
41
] | [{"tactic": "by_cases h' : x = \u22a5", "annotated_tactic": ["by_cases h' : x = \u22a5", []], "state_before": "x : EReal\nh : x \u2260 \u22a4\n\u22a2 x \u2264 \u2191(toReal x)", "state_after": "case pos\nx : EReal\nh : x \u2260 \u22a4\nh' : x = \u22a5\n\u22a2 x \u2264 \u2191(toReal x)\n\ncase neg\nx : EReal\nh : x \u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.Adjunction.hasLiftingProperty_iff | [
128,
1
] | [
134,
19
] | [{"tactic": "constructor <;> intro <;> constructor <;> intro f g sq", "annotated_tactic": ["constructor <;> intro <;> constructor <;> intro f g sq", []], "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b9 : Category.{u_3, u_1} C\ninst\u271d : Category.{u_4, u_2} D\nG : C \u2964 D\nF : D \u2964 C\nadj : G \u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Basic.lean | Real.le_mk_of_forall_le | [
612,
1
] | [
623,
82
] | [{"tactic": "intro h", "annotated_tactic": ["intro h", []], "state_before": "x y : \u211d\nf : CauSeq \u211a abs\n\u22a2 (\u2203 i, \u2200 (j : \u2115), j \u2265 i \u2192 x \u2264 \u2191(\u2191f j)) \u2192 x \u2264 mk f", "state_after": "x y : \u211d\nf : CauSeq \u211a abs\nh : \u2203 i, \u2200 (j : \u2115), j \u2265 i... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Free.lean | FreeMagma.mul_eq | [
64,
1
] | [
64,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.aemeasurable | [
206,
11
] | [
208,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/CancelDenoms/Core.lean | CancelDenoms.neg_subst | [
63,
1
] | [
63,
89
] | [{"tactic": "simp [*]", "annotated_tactic": ["simp [*]", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : Ring \u03b1\nn e t : \u03b1\nh1 : n * e = t\n\u22a2 n * -e = -t", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsMinOn.closure | [
32,
11
] | [
34,
20
] | [] |
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