file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/List/Infix.lean | List.mem_tails | [
{
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},
{
"state_after": "α : Type u_1\nβ : Type ?u.37187\nl l₁ l₂ l₃ : List α\na✝ b :... | [
369,
82
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355,
1
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Mathlib/Data/Finset/Image.lean | Disjoint.of_image_finset | [] | [
549,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.colimit_presheaf | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_map_eq_count | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.415864\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\ns : Multiset α\nhf : Set.InjOn f {x | x ∈ s}\nx : α\nH : x ∈ s\n⊢ count x (filter (fun a => f x = f a) s) = ↑card (filter (fun a => f x = f a) s)",
"state_before": "α : Type u_2\nβ : T... | [
2549,
92
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2542,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | not_surjective_of_ordinal_of_small | [] | [
2132,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2131,
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Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.support_zero | [] | [
135,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Computability/Reduce.lean | OneOneReducible.mk | [] | [
90,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.count_support_eq_one | [] | [
1311,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | nhds_translation_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nx : G\n⊢ comap (fun x_1 => x_1 / x) (𝓝 1) = 𝓝 x",
"tactic": "simpa only [div_eq_mul_inv] using nhds_translation_mul_inv x"
}
] | [
1205,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_iff_exists_fin_generating_family | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nN : Submodule R M\n⊢ (∃ S, Set.Finite S ∧ span R S = N) ↔ ∃ n s, span R (range s) = N",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module ... | [
79,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.reindex_apply | [
{
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602,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
11
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Std/Data/Int/DivMod.lean | Int.mul_ediv_cancel_left | [] | [
220,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
219,
9
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_inf | [] | [
1693,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1692,
1
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Mathlib/Order/SymmDiff.lean | Disjoint.le_symmDiff_sup_symmDiff_right | [
{
"state_after": "ι : Type ?u.94740\nα : Type u_1\nβ : Type ?u.94746\nπ : ι → Type ?u.94751\ninst✝ : BooleanAlgebra α\na b c d : α\nh : Disjoint b c\n⊢ a ≤ b ∆ a ⊔ c ∆ a",
"state_before": "ι : Type ?u.94740\nα : Type u_1\nβ : Type ?u.94746\nπ : ι → Type ?u.94751\ninst✝ : BooleanAlgebra α\na b c d : α\nh : D... | [
803,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_dvd_prod_of_subset_of_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nι : Type ?u.593251\nγ : Type ?u.593254\nA : Type ?u.593257\nB : Type ?u.593260\nC : Type ?u.593263\ninst✝⁴ : AddCommMonoid A\ninst✝³ : AddCommMonoid B\ninst✝² : AddCommMonoid C\nt : ι → A → C\nh0 : ∀ (i : ι), t i 0 = 0\nh1✝ : ∀ (i : ι) (x y : A), t... | [
601,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ioc | [] | [
648,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_left | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ : List α✝\n⊢ Disjoint l₁ l₂ ↔ ∀ ⦃a : α✝⦄, a ∈ l₁ → ¬a ∈ l₂",
"tactic": "simp [Disjoint]"
}
] | [
1354,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1354,
1
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Std/Data/String/Lemmas.lean | String.any_iff | [
{
"state_after": "no goals",
"state_before": "s : String\np : Char → Bool\n⊢ any s p = true ↔ ∃ c, c ∈ s.data ∧ p c = true",
"tactic": "simp [any_eq]"
}
] | [
720,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
720,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst | [] | [
2166,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2164,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_le_iff_inv_le | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.268745\nβ : Type ?u.268748\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a⁻¹ ≤ b ↔ b⁻¹ ≤ a",
"tactic": "simpa only [inv_inv] using @ENNReal.inv_le_inv a b⁻¹"
}
] | [
1496,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.iUnion_eq | [] | [
738,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Tactic/NormNum/NatFib.lean | Mathlib.Meta.NormNum.isFibAux_two_mul_add_one_done | [] | [
76,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_le | [] | [
1497,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.Hereditarily.mem | [] | [
1431,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.isConnected | [] | [
356,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
11
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_eq_top | [] | [
241,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/Category/ModuleCat/EpiMono.lean | ModuleCat.ker_eq_bot_of_mono | [] | [
33,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_const_add' | [] | [
151,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.pointwise_smul_def | [] | [
276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroidWeights_apply | [] | [
795,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Order/Lattice.lean | inf_le_right | [] | [
398,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Ico | [] | [
353,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prod_ext | [] | [
305,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Basic.lean | Prod.swap_le_swap | [] | [
1203,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.antidiagonalTuple_zero_succ | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_neg_left | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ angle (-x) y = π - angle x y",
"tactic": "rw [← angle_neg_neg, neg_neg, angle_neg_right]"
}
] | [
115,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.diff | [] | [
210,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.sum_comm | [
{
"state_after": "case h.h\nα : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ✝ : { x // x ∈ kernel α β }\ninst✝ : Countable ι\nκ : ι → ι → { x // x ∈ kernel α β }\na : α\ns : Set β\n⊢ MeasurableSet s →\n ↑↑(↑(kernel.sum fun n => kernel.sum (κ n)) a) s = ↑↑(↑(kernel.s... | [
246,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.equicontinuousAt_iff | [
{
"state_after": "ι : Type u_5\nκ : Type ?u.123707\nX : Type u_3\nY : Type ?u.123713\nZ : Type ?u.123716\nα : Type u_4\nβ : Type ?u.123722\nγ : Type ?u.123725\n𝓕 : Type ?u.123728\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpa... | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.315442\nβ : Type ?u.315445\nγ : Type ?u.315448\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : (a : Ordinal) → a < 1 → Ordinal\n⊢ bsup 1 f = f 0 (_ : 0 < 1)",
"tactic": "simp_rw [← sup_eq_bsup, sup_unique, familyOfBFamily, familyOfBFam... | [
1561,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
1
] |
Mathlib/Algebra/Order/Ring/Canonical.lean | mul_add_mul_le_mul_add_mul | [
{
"state_after": "case intro\nα : Type u\nβ : Type ?u.1549\ninst✝¹ : StrictOrderedSemiring α\na c d : α\ninst✝ : ExistsAddOfLE α\nhcd : c ≤ d\nb : α\nhab : a ≤ a + b\n⊢ a * d + (a + b) * c ≤ a * c + (a + b) * d",
"state_before": "α : Type u\nβ : Type ?u.1549\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\ni... | [
59,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.memℒp | [] | [
220,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
11
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.le_comap_pow_of_le_comap | [
{
"state_after": "case zero\nR : Type u_1\nR₁ : Type ?u.610021\nR₂ : Type ?u.610024\nR₃ : Type ?u.610027\nR₄ : Type ?u.610030\nS : Type ?u.610033\nK : Type ?u.610036\nK₂ : Type ?u.610039\nM : Type u_2\nM' : Type ?u.610045\nM₁ : Type ?u.610048\nM₂ : Type ?u.610051\nM₃ : Type ?u.610054\nM₄ : Type ?u.610057\nN : T... | [
819,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.continuousOn_tan | [
{
"state_after": "⊢ ContinuousOn (fun x => sin x / cos x) {x | cos x ≠ 0}",
"state_before": "⊢ ContinuousOn tan {x | cos x ≠ 0}",
"tactic": "suffices ContinuousOn (fun x => sin x / cos x) {x | cos x ≠ 0} by\n have h_eq : (fun x => sin x / cos x) = tan := by ext1 x; rw [tan_eq_sin_div_cos]\n rwa [h_eq]... | [
67,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Set/MulAntidiagonal.lean | Set.MulAntidiagonal.eq_of_snd_eq_snd | [] | [
99,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.comp_apply | [] | [
332,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.biSup_add_biSup_le | [] | [
612,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Analysis/Convex/Basic.lean | AntitoneOn.convex_le | [] | [
362,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
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Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_zero | [] | [
112,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.cast_floor_eq_cast_int_floor | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.310443\nα : Type u_1\nβ : Type ?u.310449\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\na : α\nha : 0 ≤ a\n⊢ ↑⌊a⌋₊ = ↑⌊a⌋",
"tactic": "rw [← Nat.cast_floor_eq_int_floor ha, Int.cast_ofNat]"
}
] | [
1607,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_congr | [] | [
670,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cone.ofTrident_π | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝ : Category C\nX Y : C\nf : J → (X ⟶ Y)\nF : WalkingParallelFamily J ⥤ C\nt : Trident fun j => F.map (line j)\nj : WalkingParallelFamily J\n⊢ (parallelFamily fun j => F.map (line j)).obj j = F.obj j",
"tactic": "cases j <;> aesop... | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_range_le | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.39409\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝... | [
171,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_empty | [] | [
253,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Balanced.insertNew | [] | [
161,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
160,
11
] |
Mathlib/Algebra/Group/ULift.lean | ULift.pow_down | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.isGreatest_max' | [] | [
1363,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.eval₂_denom_ne_zero | [] | [
1483,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1481,
1
] |
Mathlib/Data/Multiset/Functor.lean | Multiset.naturality | [
{
"state_after": "F : Type u → Type u\ninst✝⁵ : Applicative F\ninst✝⁴ : CommApplicative F\nα' β' : Type u\nf✝ : α' → F β'\nG H : Type u_1 → Type u_1\ninst✝³ : Applicative G\ninst✝² : Applicative H\ninst✝¹ : CommApplicative G\ninst✝ : CommApplicative H\neta : ApplicativeTransformation G H\nα β : Type u_1\nf : α ... | [
144,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | two_mul_card_alternatingGroup | [
{
"state_after": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nontrivial α\nthis : Perm α ⧸ MonoidHom.ker sign ≃ ℤˣ :=\n (QuotientGroup.quotientKerEquivOfSurjective sign (_ : Function.Surjective ↑sign)).toEquiv\n⊢ 2 * card { x // x ∈ alternatingGroup α } = card (Perm α)",
"state_befor... | [
101,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.InfiniteNeg.lt_zero | [] | [
440,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.tendsto_lift_nhdsWithin_mk | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.102238\nZ : Type ?u.102241\nα : Type u_2\nι : Type ?u.102247\nπ : ι → Type ?u.102252\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx✝ y z : X\ns✝ : Set ... | [
550,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | Filter.Tendsto.eventually_intervalIntegrable_ae | [] | [
419,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_left_bijective | [] | [
769,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym_empty | [] | [
167,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Squarefree.lean | Squarefree.isRadical | [
{
"state_after": "case pos\nR : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : GCDMonoid R\nx : R\nhx : Squarefree x\ny : R\nhy : x ∣ y ^ 2\nh : gcd x y = 0\n⊢ x ∣ gcd x y\n\ncase neg\nR : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : GCDMonoid R\nx : R\nhx : Squarefree x\ny : R\nhy : x ∣ y ^ 2... | [
213,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.le_def | [
{
"state_after": "a✝ b✝ c✝ : ℚ\na b c d : ℤ\nb0 : 0 < b\nd0 : 0 < d\n⊢ Rat.Nonneg (c /. d - a /. b) ↔ a * d ≤ c * b",
"state_before": "a✝ b✝ c✝ : ℚ\na b c d : ℤ\nb0 : 0 < b\nd0 : 0 < d\n⊢ a /. b ≤ c /. d ↔ a * d ≤ c * b",
"tactic": "rw [Rat.le_iff_Nonneg]"
},
{
"state_after": "a✝ b✝ c✝ : ℚ\na b ... | [
158,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
11
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.80310\nγ : Type ?u.80313\nι : Sort ?u.80316\nπ : α → Type ?u.80321\nδ✝ : α → Sort ?u.80326\ns✝ : Set α\nf g✝ : (i : α) → δ✝ i\ninst✝² : (j : α) → Decidable (j ∈ s✝)\nδ : α → Type u_1\ninst✝¹ : (i : α) → Preorder (δ i)\ns : Set α\ninst✝ ... | [
1412,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ext_iff | [] | [
238,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.unique | [] | [
1093,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.smul | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type u_1\ninst✝³... | [
71,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.sup' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.39210\nγ : Type ?u.39213\nι : Sort u_2\nι' : Sort u_3\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt✝ : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nhl : HasBasis l p s\nhl' : HasBasis l' p' s'\nt : Set α\n⊢ t ∈ l ⊔ l' ↔ ∃ i, (p i.fst ∧ p' i.snd) ∧ s i.fs... | [
591,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.IndexSet.ext | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.931\ninst✝ : Category C\nΔ : SimplexCategoryᵒᵖ\nA A₁ A₂ : IndexSet Δ\nh₁ : A₁.fst = A₂.fst\n⊢ A₁.fst.unop = A₂.fst.unop",
"tactic": "rw [h₁]"
},
{
"state_after": "case mk.mk\nC : Type ?u.931\ninst✝ : Category C\nΔ : SimplexCategoryᵒᵖ\nA A... | [
87,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Fintype/Card.lean | univ_eq_singleton_of_card_one | [
{
"state_after": "α✝ : Type ?u.60858\nβ : Type ?u.60861\nγ : Type ?u.60864\nα : Type u_1\ninst✝ : Fintype α\nx : α\nh : Fintype.card α = 1\n⊢ {x} = univ",
"state_before": "α✝ : Type ?u.60858\nβ : Type ?u.60861\nγ : Type ?u.60864\nα : Type u_1\ninst✝ : Fintype α\nx : α\nh : Fintype.card α = 1\n⊢ univ = {x}",... | [
890,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_arrow | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : HasImage f\n⊢ (imageSubobjectIso f).hom ≫ image.ι f = arrow (imageSubobject f)",
"tactic": "simp [imageSubobjectIso]"
}
] | [
313,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_one | [] | [
429,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_eq | [] | [
210,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Std/Data/List/Lemmas.lean | List.erase_append_left | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : a ∈ l₁\n⊢ eraseP (fun b => decide (a = b)) (l₁ ++ l₂) = eraseP (fun b => decide (a = b)) l₁ ++ l₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : a ∈ l₁\n⊢ List.erase (l₁ ++ l₂) a = List.eras... | [
1067,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1065,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.emptyGraph_eq_bot | [] | [
396,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.cons | [] | [
60,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
11
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_range | [] | [
496,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Order/Cover.lean | Covby.Ioi_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37583\ninst✝ : LinearOrder α\na b c : α\nh : a ⋖ b\n⊢ Ioi a = Ici b",
"tactic": "rw [← Ioo_union_Ici_eq_Ioi h.lt, h.Ioo_eq, empty_union]"
}
] | [
423,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.one_compl | [] | [
141,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_ofAdd | [] | [
3190,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3190,
9
] |
Mathlib/Data/Finset/LocallyFinite.lean | Set.Infinite.not_bddBelow | [] | [
468,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_pi_div_two_sub | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ sin (↑(π / 2) - ↑x✝) = cos ↑x✝",
"state_before": "θ : Angle\n⊢ sin (↑(π / 2) - θ) = cos θ",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ sin (↑(π / 2) - ↑x✝) = cos ↑x✝",
"tacti... | [
461,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_modifyGet | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nσ α : Type u_1\ninst✝ : Monad m\nf : σ → α × σ\ns : σ\n⊢ run (modifyGet f) s = pure ((f s).fst, (f s).snd)",
"tactic": "simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]"
}
] | [
264,
66
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
263,
9
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.tendsto_atBot_of_leadingCoeff_nonpos | [] | [
84,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_iff_Ioi_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.30000\nγ : Type ?u.30003\nι : Sort ?u.30006\nκ : ι → Sort ?u.30011\ninst✝ : PartialOrder α\ns : Set α\n⊢ IsUpperSet s ↔ ∀ ⦃a : α⦄, a ∈ s → Ioi a ⊆ s",
"tactic": "simp [isUpperSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]"
}... | [
376,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_zip | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.mem_ndinsert_self | [] | [
69,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_add | [] | [
157,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_add_right | [] | [
113,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioc_pred_left_of_not_isMin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : PredOrder α\na b : α\nha : ¬IsMin a\n⊢ Ioc (pred a) b = Icc a b",
"tactic": "rw [← Ioi_inter_Iic, Ioi_pred_of_not_isMin ha, Ici_inter_Iic]"
}
] | [
676,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.Factors.piQuotientEquiv_map | [] | [
786,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | sup_iInf_eq | [] | [
207,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sSameSide_iff_exists_right | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.250138\nP : Type u_3\nP' : Type ?u.250144\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y p₂ : P\n... | [
473,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.comp_assoc | [] | [
199,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_nthLe_length | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.667803\nβ : Type ?u.667806\ninst✝ : DecidableEq α\nl : List α\nx✝ x : α\nxs : List α\n⊢ length xs < length (x :: xs)",
"tactic": "simp"
},
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.667806\ninst✝ : DecidableEq α\nl : List α\nx✝ x... | [
145,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.sigma_eq_iff_blocks_eq | [
{
"state_after": "n : ℕ\nc✝ : Composition n\nc c' : (n : ℕ) × Composition n\nH : c.snd.blocks = c'.snd.blocks\n⊢ c = c'",
"state_before": "n : ℕ\nc✝ : Composition n\nc c' : (n : ℕ) × Composition n\n⊢ c = c' ↔ c.snd.blocks = c'.snd.blocks",
"tactic": "refine' ⟨fun H => by rw [H], fun H => _⟩"
},
{
... | [
483,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
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