file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.degree_eq_one_iff_unique_adj | [
{
"state_after": "ι : Sort ?u.206794\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\nv : V\ninst✝ : Fintype ↑(neighborSet G' v)\n⊢ (∃! a, a ∈ Set.toFinset (neighborSet G' v)) ↔ ∃! w, Adj G' v w",
"state_before": "ι : Sort ?u.206794\nV : Type u\nW : Type v\nG : Simpl... | [
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48
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832,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_mono_left | [] | [
1607,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_zero_of_degree_lt | [
{
"state_after": "case pos\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhdeg : degree P < degree Q\nhP : P = 0\n⊢ Tendsto (fun x => eval x P / eval x Q) atTop (𝓝 0)\n\ncase neg\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopolo... | [
148,
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140,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_compl_eq_mk_compl_finite_same | [] | [
1190,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
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Mathlib/CategoryTheory/Monad/Adjunction.lean | CategoryTheory.Comonad.left_comparison | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/GroupTheory/OrderOfElement.lean | pow_ne_one_of_lt_orderOf' | [] | [
209,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_equivSentence | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.259032\nP : Type ?u.259035\ninst✝⁴ : Structure L M\ninst✝³ : Structure L N\ninst✝² : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\ninst✝¹ : Structure (L[[α]]) M\ninst✝ : LHom.IsExpansionOn (lhomWithConstants... | [
751,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.preimage_closedBall | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1110676\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nh✝ h : α ≃ᵢ β\nx : β\nr : ℝ\n⊢ ↑h ⁻¹' Metric.closedBall x r = Metric.closedBall (↑(IsometryEquiv.symm h) x) r",
"tactic": "rw [← h.isometry.pr... | [
624,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
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Mathlib/Data/Finset/Basic.lean | Finset.filter_eq | [
{
"state_after": "case inl\nα : Type ?u.409796\nβ : Type u_1\nγ : Type ?u.409802\np q : α → Prop\ninst✝³ : DecidablePred p\ninst✝² : DecidablePred q\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Finset β\nb : β\nh : b ∈ s\n⊢ filter (Eq b) s = {b}\n\ncase inr\nα : Type ?u.409796\nβ : Type u_1\nγ : Type ?u.... | [
2926,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2915,
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Mathlib/Init/Algebra/Order.lean | le_of_not_gt | [] | [
333,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
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Mathlib/GroupTheory/Commutator.lean | conjugate_commutatorElement | [] | [
71,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/RingTheory/Valuation/Quotient.lean | AddValuation.self_le_supp_comap | [] | [
122,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/GroupTheory/OrderOfElement.lean | vadd_eq_self_of_mem_zmultiples | [] | [
623,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_zero_right | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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Mathlib/Data/Finset/Fold.lean | Finset.fold_map | [
{
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"tactic": "simp only [fold, map, Mul... | [
68,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_image_continuousLinearEquiv | [] | [
318,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Mathlib/Algebra/Group/Conj.lean | ConjClasses.mk_eq_mk_iff_isConj | [] | [
177,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/GroupPower/Identities.lean | sq_add_sq_mul_sq_add_sq | [
{
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"tactic": "ring"
}
] | [
29,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean | AlgebraicTopology.DoldKan.MorphComponents.postComp_φ | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX X' : SimplicialObject C\nn : ℕ\nZ Z' : C\nf : MorphComponents X n Z\ng : X' ⟶ X\nh : Z ⟶ Z'\n⊢ HomologicalComplex.Hom.f PInfty (n + 1) ≫ { a := f.a ≫ h, b := fun i => b f i ≫ h }.a +\n ∑ i : Fin (n + 1),\n HomologicalCompl... | [
139,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Data/Stream/Init.lean | Stream'.interleave_eq | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\ns₁ s₂ : Stream' α\nt : Stream' α := tail s₁ ⋈ tail s₂\n⊢ s₁ ⋈ s₂ = head s₁ :: head s₂ :: (tail s₁ ⋈ tail s₂)",
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"tactic": "... | [
420,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.le_inf_support_multiset_prod | [
{
"state_after": "case refine'_1\nR : Type u_3\nA : Type u_2\nT : Type u_1\nB : Type ?u.80864\nι : Type ?u.80867\ninst✝¹¹ : SemilatticeSup B\ninst✝¹⁰ : OrderBot B\ninst✝⁹ : SemilatticeInf T\ninst✝⁸ : OrderTop T\ninst✝⁷ : CommSemiring R\ninst✝⁶ : AddCommMonoid A\ninst✝⁵ : AddCommMonoid B\ninst✝⁴ : CovariantClass... | [
159,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/Topology/ContinuousOn.lean | Continuous.if_const | [] | [
1199,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
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Mathlib/Data/Vector/Basic.lean | Vector.removeNth_val | [] | [
534,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_union_erase_cancel | [
{
"state_after": "no goals",
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"tactic": "simp_rw [erase_eq, sdiff_union_sdiff_cancel hts (singleton_subset_iff.2 ha)]"
}... | [
2299,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2298,
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Formula.sup_semanticallyEquivalent_not_inf_not | [] | [
569,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
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Mathlib/Data/Nat/PartENat.lean | PartENat.find_get | [] | [
782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.pair_preimage_singleton | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.64507\ninst✝ : MeasurableSpace α\nf : α →ₛ β\ng : α →ₛ γ\nb : β\nc : γ\n⊢ ↑(pair f g) ⁻¹' {b} ×ˢ {c} = ↑f ⁻¹' {b} ∩ ↑g ⁻¹' {c}",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.64507\ninst✝ : MeasurableSpace α\nf ... | [
429,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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Mathlib/Data/Seq/Computation.lean | Computation.empty_promises | [] | [
444,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/Order/PartialSups.lean | iSup_le_iSup_of_partialSups_le_partialSups | [
{
"state_after": "α : Type u_1\ninst✝ : CompleteLattice α\nf g : ℕ → α\nh : partialSups f ≤ partialSups g\n⊢ (⨆ (n : ℕ), ↑(partialSups f) n) ≤ ⨆ (n : ℕ), ↑(partialSups g) n",
"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nf g : ℕ → α\nh : partialSups f ≤ partialSups g\n⊢ (⨆ (n : ℕ), f n) ≤ ⨆ (n :... | [
188,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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] |
Mathlib/Data/Finset/Powerset.lean | Finset.empty_mem_ssubsets | [
{
"state_after": "α : Type u_1\ns✝ t : Finset α\ninst✝ : DecidableEq α\ns : Finset α\nh : Finset.Nonempty s\n⊢ ∅ ⊆ s ∧ ∅ ≠ s",
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"tactic": "rw [mem_ssubsets, ssubset_iff_subset_ne... | [
164,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.not_mem_bot | [] | [
173,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.closure_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.8596\nG : Type u_1\nA : Type ?u.8602\nS : Type ?u.8605\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns✝ s : Set G\n⊢ closure s⁻¹ = closure s",
"tactic": "simp only [← toSubmonoid_eq, closure_toSubmonoid, inv_inv, union_comm]"
}
] | [
93,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet.mk_smul | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
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Mathlib/Data/Real/NNReal.lean | NNReal.orderIsoIccZeroCoe_apply_coe_coe | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
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Mathlib/Data/Finset/Basic.lean | Finset.pairwise_cons' | [
{
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3735,
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Mathlib/RingTheory/PrincipalIdealDomain.lean | isCoprime_of_prime_dvd | [] | [
423,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
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Mathlib/Algebra/Parity.lean | IsSquare.zpow | [
{
"state_after": "case intro\nF : Type ?u.34433\nα : Type u_1\nβ : Type ?u.34439\nR : Type ?u.34442\ninst✝ : DivisionMonoid α\nn : ℤ\na : α\n⊢ IsSquare ((a * a) ^ n)",
"state_before": "F : Type ?u.34433\nα : Type u_1\nβ : Type ?u.34439\nR : Type ?u.34442\ninst✝ : DivisionMonoid α\na : α\nn : ℤ\n⊢ IsSquare a... | [
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181,
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Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Isδ₀.iff | [
{
"state_after": "case mp\nC : Type ?u.1149\ninst✝¹ : Category C\ninst✝ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\nj : ℕ\ni : Fin (j + 2)\n⊢ Isδ₀ (SimplexCategory.δ i) → i = 0\n\ncase mpr\nC : Type ?u.1149\ninst✝¹ : Category C\ninst✝ : Preadditive C\nK K' : ChainComplex C ... | [
61,
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Mathlib/Data/PNat/Interval.lean | PNat.Ioc_eq_finset_subtype | [] | [
40,
6
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39,
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Mathlib/Topology/Bases.lean | exists_countable_dense_bot_top | [
{
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"tactic": "simpa using dense_univ.exists_countable_dense_subset_bot_t... | [
542,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | norm_iteratedFDeriv_fderiv | [
{
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.real_toNNReal | [] | [
839,
54
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_mul | [] | [
352,
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350,
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Mathlib/Data/Nat/Prime.lean | Nat.prime_two | [
{
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}
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172,
41
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172,
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Mathlib/Data/Fintype/Option.lean | Finite.induction_empty_option | [
{
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53
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_eq_of_subset | [
{
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942,
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Mathlib/NumberTheory/Liouville/Basic.lean | Liouville.exists_pos_real_of_irrational_root | [
{
"state_after": "α : ℝ\nha : Irrational α\nf : ℤ[X]\nf0 : f ≠ 0\nfR : ℝ[X] := map (algebraMap ℤ ℝ) f\nfa : eval α fR = 0\n⊢ ∃ A, 0 < A ∧ ∀ (a : ℤ) (b : ℕ), 1 ≤ (↑b + 1) ^ natDegree f * (abs (α - ↑a / (↑b + 1)) * A)",
"state_before": "α : ℝ\nha : Irrational α\nf : ℤ[X]\nf0 : f ≠ 0\nfa : eval α (map (algebra... | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Order.lean | continuous_iInf_dom | [] | [
800,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nU : TopCat\nX : PresheafedSpace C\nf : U ⟶ ↑X\nh : OpenEmbedding ((CategoryTheory.forget TopCat).map f)\nV : Opens ↑U\nx : ↑U\nhx : x ∈ V\n⊢ germ X.presheaf\n { val := (CategoryTheory.forget TopCat).... | [
100,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/Separation.lean | isCompact_closure_of_subset_compact | [] | [
1302,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/Topology/Order.lean | continuous_sInf_rng | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.41516\nf : α → β\nι : Sort ?u.41523\nt₁ : TopologicalSpace α\nT : Set (TopologicalSpace β)\n⊢ Continuous f ↔ ∀ (t : TopologicalSpace β), t ∈ T → Continuous f",
"tactic": "simp only [continuous_iff_coinduced_le, le_sInf_iff... | [
795,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Order/LocallyFinite.lean | Ioi_toDual | [] | [
940,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Functor.pi_ext | [
{
"state_after": "case h_map\nI : Type w₀\nJ : Type w₁\nC : I → Type u₁\ninst✝² : (i : I) → Category (C i)\nD : I → Type u₁\ninst✝¹ : (i : I) → Category (D i)\nA : Type u₁\ninst✝ : Category A\nf f' : A ⥤ ((i : I) → C i)\nh : ∀ (i : I), f ⋙ Pi.eval C i = f' ⋙ Pi.eval C i\n⊢ autoParam\n (∀ (X Y : A) (f_1 : X ⟶... | [
277,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumLexAssoc_apply_inl_inl | [] | [
660,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.measure_Ioi_pos | [] | [
136,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.13993\nδ : Type ?u.13996\na : α\ns t : Multiset α\nf✝ g✝ : α → Multiset β\nf : α → β\ng : α → Multiset β\n⊢ (bind 0 fun a => f a ::ₘ g a) = map f 0 + bind 0 g",
"tactic": "simp"
},
{
"state_after": "no goals",
... | [
134,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | le_tsum' | [] | [
206,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_inv | [] | [
306,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
11
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vadd_cancel_left | [] | [
99,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.ind_aux | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\na : (P F).A\nf' : MvPFunctor.B (MvPFunctor.drop (P F)) a ⟹ α\nf : PFunctor.B (MvPFunctor.last (P F)) a → MvPFunctor.W (P F) α\nthis :\n mk (abs { fst := a, snd := MvPFunctor.appendContents (P F) f' fun x => ... | [
258,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_comp_linearEquiv_eq_iff_det_pos | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁴ : LinearOrderedCommRing R\nM : Type u_3\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ne : Basis ι R M\nf : M ≃ₗ[R] M\n⊢ Basis.orientation (Basis.map e f) = Basis.orientation e ↔ 0 < ↑... | [
252,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/CategoryTheory/Preadditive/Schur.lean | CategoryTheory.isIso_iff_nonzero | [
{
"state_after": "C : Type u_2\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\ninst✝² : HasKernels C\nX Y : C\ninst✝¹ : Simple X\ninst✝ : Simple Y\nf : X ⟶ Y\nI : IsIso f\nh : f = 0\n⊢ False",
"state_before": "C : Type u_2\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\ninst✝² : HasKernels C\nX Y : C\ninst✝¹ : ... | [
61,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_div | [] | [
1315,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1314,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_mul_right_self | [] | [
487,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_comapDomain | [
{
"state_after": "α : Type u_3\nM : Type u_4\nN : Type ?u.454082\nP : Type ?u.454085\nR : Type u_2\nS : Type ?u.454091\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R P\nα' : T... | [
752,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | upperCentralSeries_eq_top_iff_nilpotencyClass_le | [
{
"state_after": "case mp\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nhG : Group.IsNilpotent G\nn : ℕ\n⊢ upperCentralSeries G n = ⊤ → nilpotencyClass G ≤ n\n\ncase mpr\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nhG : Group.IsNilpotent G\nn : ℕ\n⊢ nilpotencyClass G ≤... | [
383,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.lt_iff_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.27670\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.27679\nπ : ι → Type ?u.27684\nr : α → α → Prop\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\nhf : StrictMonoOn f s\na b : α\nha : a ∈ s\nhb : b ∈ s\n⊢ f a < f b ↔ a < b",
... | [
798,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_orthogonalProjection | [
{
"state_after": "case a\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np : P\n⊢ ↑(↑(orthogonalProjection s... | [
405,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_diff_union | [] | [
1929,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.smul_closure | [] | [
262,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/Instances/RatLemmas.lean | Rat.not_firstCountableTopology_opc | [
{
"state_after": "p q : ℚ\ns t : Set ℚ\na✝ : FirstCountableTopology ℚ∞\n⊢ False",
"state_before": "p q : ℚ\ns t : Set ℚ\n⊢ ¬FirstCountableTopology ℚ∞",
"tactic": "intro"
},
{
"state_after": "no goals",
"state_before": "p q : ℚ\ns t : Set ℚ\na✝ : FirstCountableTopology ℚ∞\n⊢ False",
"tact... | [
77,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.support_conj | [
{
"state_after": "case a\nι : Type ?u.3038576\nα : Type u_1\nβ : Type ?u.3038582\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ τ : Perm α\na✝ : α\n⊢ a✝ ∈ support (σ * τ * σ⁻¹) ↔ a✝ ∈ map (Equiv.toEmbedding σ) (support τ)",
"state_before": "ι : Type ?u.3038576\nα : Type u_1\nβ : Type ?u.3038582\ninst✝¹ : Dec... | [
1763,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1759,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.basis_sets | [] | [
407,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_toAlgHom | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_word_prod_nontrivial_of_head_card | [
{
"state_after": "case intro.intro\nι : Type u_1\nM : ι → Type ?u.798766\ninst✝⁴ : (i : ι) → Monoid (M i)\nN : Type ?u.798777\ninst✝³ : Monoid N\nhnontriv : Nontrivial ι\nG : Type u_3\ninst✝² : Group G\nH : ι → Type u_2\ninst✝¹ : (i : ι) → Group (H i)\nf : (i : ι) → H i →* G\nhcard✝ : 3 ≤ (#ι) ∨ ∃ i, 3 ≤ (#H i)... | [
768,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_mono | [] | [
1630,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1629,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Measurable.sup' | [] | [
144,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.sigma_zero_apply | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.524469\nn : ℕ\n⊢ ↑(σ 0) n = card (divisors n)",
"tactic": "simp [sigma_apply]"
}
] | [
791,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.smul | [] | [
357,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.abs_cos_le_one | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ cos x * cos x ≤ 1",
"tactic": "simp only [← sq, cos_sq_le_one]"
}
] | [
1263,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.IsRegular.disjoint_compl_left_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : HeytingAlgebra α\na b : α\nha : IsRegular a\n⊢ Disjoint (aᶜ) b ↔ b ≤ a",
"tactic": "rw [← le_compl_iff_disjoint_left, ha.eq]"
}
] | [
82,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.π_of_isColimit | [
{
"state_after": "J : Type w\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasZeroMorphisms C\nF f : J → C\nt : Bicone f\nht : IsColimit (toCocone t)\nj : J\nj' : Discrete J\n⊢ (toCocone t).ι.app j' ≫ π t j = (Cofan.mk (f j) fun j' => if h : j' = j then eqToHom (_ : f j' = f j) else 0).ι.app j'",
"state_before"... | [
172,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.symm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1189\nδ : Type ?u.1192\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nμa✝ : Measure α\nμb✝ : Measure β\nμc : Measure γ\nμd : Measure δ\ne : α ≃ᵐ β\nμa : Meas... | [
71,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasFDerivWithinAt.snd | [] | [
274,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
18
] |
Mathlib/Algebra/Jordan/Basic.lean | commute_rmul_rmul_sq | [] | [
163,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_succ' | [
{
"state_after": "no goals",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p (n + 1) = count (fun k => p (k + 1)) n + if p 0 then 1 else 0",
"tactic": "rw [count_add', count_one]"
}
] | [
99,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_insert_swap | [
{
"state_after": "case neg\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx y : α\nl : List α\nxl : ¬x ∈ l\nyl : ¬y ∈ l\n⊢ List.insert x (y :: l) ~ List.insert y (x :: l)",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx y : α\nl : List α\n⊢ List.insert... | [
973,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_add_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.484252\nγ : Type ?u.484255\ns t u : Multiset α\n⊢ Disjoint (s + t) u ↔ Disjoint s u ∧ Disjoint t u",
"tactic": "simp [Disjoint, or_imp, forall_and]"
}
] | [
2949,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2948,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.comp_continuousOn | [] | [
340,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_zero | [] | [
2115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2114,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_div | [] | [
796,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.exists_succ_nth_stream_of_fr_zero | [
{
"state_after": "case intro.intro.intro\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nifp_n : IntFractPair K\nseq_nth_eq : IntFractPair.stream v n = some ifp_n\nleft✝ : ifp_n.fr ≠ 0\nstream_succ_nth_eq : IntFractPair.stream v (n + 1) = some (IntFractPair.of ifp_n.fr⁻¹)\nsucc_... | [
124,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.add_pos | [] | [
682,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_periodic | [
{
"state_after": "no goals",
"state_before": "⊢ Function.Periodic tan ↑π",
"tactic": "simpa only [tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic"
}
] | [
1299,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.image_relEmbedding | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nr r₁ r₂ : α → α → Prop\nr' : β → β → Prop\ns t : Set α\na b✝ : α\nhs : IsAntichain r s\nφ : r ↪r r'\nb : β\nhb : b ∈ ↑φ '' s\nb' : β\nhb' : b' ∈ ↑φ '' s\nh₁ : b ≠ b'\nh₂ : r' b b'\n⊢ False",
"state_before": "α : Type u_1\nβ : Type u_2\nr r₁ r₂ : α → α → Prop\nr'... | [
127,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.card_sigma | [] | [
1855,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1853,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_iff_le' | [] | [
950,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Deprecated/Subring.lean | Ring.closure.isSubring | [] | [
184,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.gcd_rel_left' | [] | [
535,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.high_scores | [
{
"state_after": "ι : Type ?u.70456\nι' : Type ?u.70459\nα : Type ?u.70462\nβ : Type u_1\nγ : Type ?u.70468\ninst✝¹ : LinearOrder β\ninst✝ : NoMaxOrder β\nu : ℕ → β\nhu : Tendsto u atTop atTop\nN : ℕ\n⊢ ∃ n, n ≥ N ∧ ∀ (k : ℕ), k < n → u k < u n",
"state_before": "ι : Type ?u.70456\nι' : Type ?u.70459\nα : T... | [
561,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
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