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/Algebra/Module/Torsion.lean | Submodule.torsionBySet_le_torsionBySet_of_subset | [] | [
277,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Data/Num/Lemmas.lean | ZNum.add_one | [
{
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"tactic": "cases p <;> rfl"
}
] | [
1173,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
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Mathlib/Algebra/Order/Floor.lean | Int.floor_lt | [] | [
657,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
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Mathlib/Algebra/Module/Submodule/Basic.lean | SMulMemClass.coeSubtype | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.monotone_eapprox | [] | [
909,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
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Mathlib/Data/Fintype/Card.lean | Fintype.card_of_isEmpty | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_toOuterMeasure | [
{
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1238,
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Mathlib/Data/Bool/Basic.lean | Bool.true_eq_decide_iff | [] | [
55,
30
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Mathlib/Data/Nat/Set.lean | Nat.range_casesOn | [] | [
54,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.isEquiv_iff_val_eq_one | [
{
"state_after": "case mp\nK : Type u_3\nF : Type ?u.3253919\nR : Type ?u.3253922\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type u_2\nΓ''₀ : Type ?u.3253934\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : LinearOrderedCommGroupWithZero Γ'₀\nv : Valuation ... | [
483,
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toOpens_inf | [] | [
234,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Basic.lean | OrderIso.map_top' | [] | [
1179,
24
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1177,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π | [
{
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402,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_univ | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ ... | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.mk_inl | [] | [
855,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
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Mathlib/Order/LiminfLimsup.lean | Filter.IsBoundedUnder.mono_ge | [] | [
114,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.le_def | [] | [
538,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.IsSeparatedFor.ext | [] | [
418,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean | CategoryTheory.HomOrthogonal.matrixDecomposition_id | [
{
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151,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Typ... | [
1097,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translate_zpow | [
{
"state_after": "no goals",
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"tactic": "simp only [← zsmul_eq_mul, ofAdd_zsmul, MonoidHom.map_zpow]"
}
] | [
310,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_eq_zero | [] | [
665,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
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Mathlib/Topology/ExtendFrom.lean | tendsto_extendFrom | [] | [
50,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | dist_comm | [] | [
192,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.linearEquiv_det_conjLie | [] | [
37,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/Order/CountableDenseLinearOrder.lean | Order.iso_of_countable_dense | [
{
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235,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.compl_congr | [
{
"state_after": "ι : Type u_1\nM : Type ?u.58340\nn : ℕ\nI J : Box ι\ni : ι\nx : ℝ\ninst✝ : Finite ι\nπ₁ π₂ : Prepartition I\nh : Prepartition.iUnion π₁ = Prepartition.iUnion π₂\n⊢ Exists.choose (_ : ∃ π', Prepartition.iUnion π' = ↑I \\ Prepartition.iUnion π₁) =\n Exists.choose (_ : ∃ π', Prepartition.iUnio... | [
378,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ContinuousMap.measurable | [] | [
939,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
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] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_comap | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.sInf_empty | [] | [
1019,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iUnion_Ioc_coe_nat | [
{
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"state_before": "α : Type ?u.133965\nβ : Type ?u.133968\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ (⋃ (n : ℕ), Ioc a ↑n) = Ioi a \\ {⊤}",
"tactic": "simp only [← Ioi_inter_Iic, ← inter_iUnion, iUnion_Iic_coe_nat, diff_eq]"
}
] | [
874,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.smul | [] | [
1525,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
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] |
Mathlib/Data/Finset/Basic.lean | Finset.not_mem_sdiff_of_not_mem_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.223921\nγ : Type ?u.223924\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\nh : ¬a ∈ s\n⊢ ¬a ∈ s \\ t",
"tactic": "simp [h]"
}
] | [
2064,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2064,
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Mathlib/Algebra/Hom/Group.lean | MulHom.map_mul | [] | [
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17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_cthickening_of_dist_le | [
{
"state_after": "ι : Sort ?u.98897\nα✝ : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α✝\nδ✝ ε : ℝ\ns t : Set α✝\nx✝ : α✝\nα : Type u_1\ninst✝ : PseudoMetricSpace α\nx y : α\nδ : ℝ\nE : Set α\nh : y ∈ E\nh' : dist x y ≤ δ\n⊢ edist x y ≤ ENNReal.ofReal δ",
"state_before": "ι : Sort ?u.98897\nα✝ : Type u\... | [
1041,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.NeBot.map | [] | [
2457,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2456,
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Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.facets_bot | [] | [
263,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.chaar_mem_haarProduct | [] | [
415,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.mul_toMatrix_mul | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1640706\nM✝ : Type ?u.1640709\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M✝\ninst✝¹⁸ : Module R M✝\nR₁ : Type ?u.1640745\nM₁ : Type ?u.1640748\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\nin... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.coe_multiset_prod | [] | [
121,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.infsep_exists_of_finite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.77742\ninst✝¹ : PseudoMetricSpace α\nx y z : α\ns t : Set α\ninst✝ : Finite ↑s\nhs : Set.Nontrivial s\n⊢ ∃ x x_1 y x_2 _hxy, infsep s = dist x y",
"tactic": "classical\n cases nonempty_fintype s\n simp_rw [hs.infsep_of_fintype]\n ... | [
528,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_compl_iff | [] | [
162,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_ne_zero_iff' | [] | [
1972,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1971,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.mapsTo_cos | [] | [
638,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_apply_ne | [] | [
546,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulStrictMono_iff_mulPosStrictMono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : CommSemigroup α\ninst✝¹ : Zero α\ninst✝ : Preorder α\n⊢ PosMulStrictMono α ↔ MulPosStrictMono α",
"tactic": "simp only [PosMulStrictMono, MulPosStrictMono, mul_comm]"
}
] | [
1031,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_transpose_apply' | [] | [
763,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.hasFDerivAt | [] | [
122,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.comp | [
{
"state_after": "α : Type ?u.176030\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.176039\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nκ : Type u_3\nι : Type ?u.176054\nf✝ : κ → β\ng✝ g : β → γ\nf : κ → β\nhg : DenseRange g\nhf : DenseRange f\ncg : Continuous g\n⊢ Dense (g '... | [
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29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | AddGroupSeminorm.coe_smul | [] | [
483,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_max_right | [] | [
716,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
716,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.singleton_div_singleton | [] | [
678,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieSubmodule.lie_abelian_iff_lie_self_eq_bot | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\n⊢ IsLieAbelian { x // x ∈ ↑I } ↔ ∀ (y : L) (x ... | [
316,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.equivQuotient_index | [] | [
444,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.map_isometryOfOrthonormal | [
{
"state_after": "ι : Type ?u.1334907\nι' : Type ?u.1334910\n𝕜 : Type ?u.1334913\ninst✝⁹ : IsROrC 𝕜\nE : Type ?u.1334919\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.1334939\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type u_1\ninst✝⁴ : NormedAddComm... | [
663,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
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] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_eq_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45708\nγ : Type ?u.45711\nι : Sort ?u.45714\nκ : ι → Sort ?u.45719\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\n⊢ ↑s = univ ↔ s = ⊥",
"tactic": "simp [SetLike.ext'_iff]"
}
] | [
525,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | HasDerivWithinAt.inv | [
{
"state_after": "case h.e'_7\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter 𝕜\nc : 𝕜 → 𝕜\nh :... | [
138,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_mul'' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.60876\ninst✝ : StrictOrderedSemiring α\na b c d : α\n⊢ a < c → b < d → 0 ≤ a → 0 ≤ b → a * b < c * d",
"tactic": "classical\nexact Decidable.mul_lt_mul''"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Ty... | [
560,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.desc | [
{
"state_after": "X : Type u_3\nY : Type ?u.7897\nZ : Type ?u.7900\nα✝ : Type ?u.7903\ninst✝ : TopologicalSpace X\nα : Type u_1\nβ : Type u_2\nf : X → α\ng : α → β\nh : IsLocallyConstant (g ∘ f)\ninj : Function.Injective g\ns : Set α\n⊢ IsOpen ((fun x => g (f x)) ⁻¹' (g '' s))",
"state_before": "X : Type u_... | [
222,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_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⊢ Ioo (pred a) b = Ico a b",
"tactic": "rw [← Ioi_inter_Iio, Ioi_pred_of_not_isMin ha, Ici_inter_Iio]"
}
] | [
680,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Measurable.sup_const | [] | [
127,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
src/lean/Init/Data/List/Basic.lean | List.append_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas : List α\n⊢ as ++ nil = as",
"tactic": "induction as with\n| nil => rfl\n| cons a as ih =>\n simp_all [HAppend.hAppend, Append.append, List.append]"
},
{
"state_after": "no goals",
"state_before": "case nil... | [
97,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
93,
9
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.toList_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\n⊢ toList 1 x = []",
"tactic": "simp [toList, cycleOf_one]"
}
] | [
225,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/GroupTheory/Torsion.lean | Monoid.IsTorsion.torsionMulEquiv_apply | [] | [
284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.le_antisymm | [
{
"state_after": "case inl\nα : Type u_1\ninst✝ : LT α\ns : Antisymm fun x x_1 => ¬x < x_1\nas✝ bs✝ : List α\na : α\nas : List α\nb : α\nbs : List α\nh₁ : a :: as ≤ b :: bs\nh₂ : b :: bs ≤ a :: as\nhab : a < b\n⊢ a :: as = b :: bs\n\ncase inr\nα : Type u_1\ninst✝ : LT α\ns : Antisymm fun x x_1 => ¬x < x_1\nas✝ ... | [
182,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
168,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | Commute.zpow_zpow₀ | [] | [
132,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
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