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/Order/CompleteLattice.lean | lt_iSup_iff | [] | [
610,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_subset_Ioi | [] | [
428,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_algHom | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_iUnion_eq | [] | [
2731,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2728,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | aemeasurable_id' | [] | [
723,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_mul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz1 z2 : ℤ_[p]\n⊢ ‖z1 * z2‖ = ‖z1‖ * ‖z2‖",
"tactic": "simp [norm_def]"
}
] | [
271,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.hasBasis | [] | [
171,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
11
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.eq' | [] | [
477,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
11
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_div_norm_mul_norm_eq_one_iff | [
{
"state_after": "case mp\n𝕜 : Type ?u.3223425\nE : Type ?u.3223428\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\n⊢ inner x y / (‖x‖ * ‖y‖) = 1 → x ≠ 0 ∧ ∃ r, 0 < r... | [
1698,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1689,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_eq_of_trailingDegree_eq_some | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nh : trailingDegree 0 = ↑n\nhp0 : p = 0\n⊢ False",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nh : trailingDegree p = ↑n\nhp0 : p = 0\n⊢ False",... | [
140,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.generate_has_subset_generate_measurable | [] | [
700,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
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Std/Data/List/Lemmas.lean | List.reverse_sublist | [] | [
389,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
388,
9
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Mathlib/Data/ZMod/Basic.lean | ZMod.val_add | [
{
"state_after": "case zero\ninst✝ : NeZero Nat.zero\na b : ZMod Nat.zero\n⊢ val (a + b) = (val a + val b) % Nat.zero\n\ncase succ\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\na b : ZMod (Nat.succ n✝)\n⊢ val (a + b) = (val a + val b) % Nat.succ n✝",
"state_before": "n : ℕ\ninst✝ : NeZero n\na b : ZMod n\n⊢ val (a... | [
600,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/List/Basic.lean | List.map_eq_bind | [
{
"state_after": "ι : Type ?u.22232\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\n⊢ map f l = List.bind l fun x => map f [x]",
"state_before": "ι : Type ?u.22232\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : T... | [
509,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_one_iff_eq_one_of_mul_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.3131\nβ : Type ?u.3134\nG : Type ?u.3137\nM : Type u\ninst✝ : MulOneClass M\na b : M\nh : a * b = 1\n⊢ a = 1 ↔ b = 1",
"tactic": "constructor <;> (rintro rfl; simpa using h)"
},
{
"state_after": "case mpr\nα : Type ?u.3131\nβ : Type ?u.31... | [
74,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_inf | [] | [
845,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_union_right | [] | [
1377,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.hasEigenvalue_of_hasEigenvector | [
{
"state_after": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\nμ : R\nx : M\nh : HasEigenvector f μ x\n⊢ ∃ x, x ∈ eigenspace f μ ∧ x ≠ 0",
"state_before": "K R : Type v\nV M : Type w... | [
96,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_toOrderRingHom | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_mono | [] | [
212,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Data/List/Init/Lemmas.lean | List.reverse_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\n⊢ reverse (map f l) = map f (reverse l)",
"tactic": "induction l <;> simp [*]"
}
] | [
124,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
123,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Relations.realize_reflexive | [] | [
1000,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAdjointPair.add | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M\ninst✝¹⁸ : Module R M\nR₁ : Type ?u.1034553\nM₁ : Type ?u.1034556\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type ?u.1035165\nM₂ : Type ?u.1035168\ninst✝... | [
1051,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.fin_embedding | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nh : Set.Finite s\n⊢ range ↑(Equiv.asEmbedding (Fintype.equivFin ↑↑(Finite.toFinset h)).symm) = s",
"tactic": "simp only [Finset.coe_sort_coe, Equiv.asEmbedding_range, Finite.coe_toFinset, setOf_mem_e... | [
1082,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_neg | [] | [
280,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.rw | [] | [
1442,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.card_constantsOn | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\ninst✝ : Structure L M\nα : Type u'\n⊢ card (constantsOn α) = (#α)",
"tactic": "simp"
}
] | [
416,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.exists_eq_add_of_lt | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\nh : m < n\n⊢ n = m + (n - (m + 1)) + 1",
"tactic": "rw [add_right_comm, add_sub_of_le h]"
}
] | [
294,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.atTop_countable_basis | [] | [
264,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_mono | [
{
"state_after": "α : Type u_1\nE : Type ?u.381967\nF : Type ?u.381970\nF' : Type ?u.381973\nG : Type ?u.381976\n𝕜 : Type ?u.381979\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ... | [
565,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | isOfFinOrder_iff_coe | [
{
"state_after": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nH : Submonoid G\nx : { x // x ∈ H }\n⊢ (∃ n, 0 < n ∧ x ^ n = 1) ↔ ∃ n, 0 < n ∧ ↑x ^ n = 1",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid ... | [
98,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullback_fst_image_snd_preimage | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\nU : Set ↑Y\nx : (forget TopCat).obj X\n⊢ x ∈ (forget TopCat).map pullback.fst '' ((forget TopCat).map pullback.snd ⁻¹' U) ↔\n x ∈ (forget TopCat).map f ⁻¹' ((forget TopCat).map g '' U)",
"state_before": "... | [
395,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.blsub_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.40577\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nc : Ordinal\nho : card o < cof c\nhf : ∀ (i : Ordinal) (hi : i < o), f i hi < c\n⊢ Cardinal.lift (card o) < cof c",
"tactic": "rwa [o.card.lift_id]"
}
] | [
451,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | NormedAddGroupHom.lift_norm_le | [] | [
413,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | exists_nat_nat_continuous_surjective_of_completeSpace | [
{
"state_after": "E : ℕ → Type ?u.233694\nα : Type u_1\ninst✝³ : MetricSpace α\ninst✝² : CompleteSpace α\ninst✝¹ : SecondCountableTopology α\ninst✝ : Nonempty α\nthis : MetricSpace (ℕ → ℕ) := metricSpaceNatNat\n⊢ ∃ f, Continuous f ∧ Surjective f",
"state_before": "E : ℕ → Type ?u.233694\nα : Type u_1\ninst✝... | [
808,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean | CategoryTheory.IsKernelPair.pullback | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nR X✝ Y✝ Z✝ : C\nf✝ : X✝ ⟶ Y✝\na b : R ⟶ X✝\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\n⊢ f ≫ 𝟙 Z = 𝟙 X ≫ f",
"tactic": "simp"
},
... | [
195,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_mk | [] | [
614,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.map_hom_inv_app | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF✝ G H I : C ⥤ D\nF : C ⥤ D ⥤ E\nX Y : C\ne : X ≅ Y\nZ : D\n⊢ (F.map e.hom).app Z ≫ (F.map e.inv).app Z = 𝟙 ((F.obj X).obj Z)",
"tactic": "simp [← NatTrans.... | [
159,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_map_inr | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.nonempty | [] | [
906,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.exists_mem_algebraMap_eq | [] | [
305,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_sdiff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.175653\nι : Type ?u.175656\ninst✝¹ : CompleteBooleanAlgebra α\nf : Filter β\nu : β → α\ninst✝ : NeBot f\na : α\n⊢ liminf u f \\ a = liminf (fun b => u b \\ a) f",
"tactic": "simp only [sdiff_eq, inf_comm (b := aᶜ), inf... | [
1034,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.hom_comp_eq_id | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nf : Y ⟶ X\n⊢ α.hom ≫ f = 𝟙 X ↔ f = α.inv",
"tactic": "rw [← eq_inv_comp, comp_id]"
}
] | [
243,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Prod.norm_def | [] | [
2377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2376,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.zero_fst | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.mem_leadingCoeff | [
{
"state_after": "R : Type u\nS : Type ?u.182986\ninst✝¹ : CommSemiring R\ninst✝ : Semiring S\nI : Ideal R[X]\nx : R\n⊢ (∃ i, x ∈ leadingCoeffNth I i) ↔ ∃ p, p ∈ I ∧ Polynomial.leadingCoeff p = x\n\ncase H\nR : Type u\nS : Type ?u.182986\ninst✝¹ : CommSemiring R\ninst✝ : Semiring S\nI : Ideal R[X]\nx : R\n⊢ Dir... | [
612,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_mul_self | [] | [
155,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
153,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.radius_pos | [] | [
460,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.cons_bind | [
{
"state_after": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\na : Γ\nl✝ : ListBlank Γ\nf : Γ → List Γ'\nhf : ∃ n, f default = List.replicate n default\nl : List Γ\n⊢ bind (cons a (Quotient.mk (BlankRel.setoid Γ) l)) f hf = append (f a) (bind (Quotient.mk (BlankRel.setoid Γ) l) f hf)... | [
493,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.of_le | [] | [
674,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_of_bddAbove_of_bddBelow | [] | [
2563,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2559,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_mulVec_apply | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.42278\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype V\ninst✝ : NonAssocSemiring α\nv : V\nvec : V → α\n⊢ mulVec (adjMatrix α G) vec v = ∑ u in neighborFinset G v, vec u",
"tactic": "rw [mulVec, adjM... | [
216,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.comp_F | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Independence.lean | Projectivization.independent_iff_completeLattice_independent | [
{
"state_after": "case refine'_1\nι : Type u_1\nK : Type u_2\nV : Type u_3\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : ι → ℙ K V\n⊢ Independent f → CompleteLattice.Independent fun i => Projectivization.submodule (f i)\n\ncase refine'_2\nι : Type u_1\nK : Type u_2\nV : Type u_3\ninst✝² : ... | [
74,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.tendstoUniformlyOnFilter_iff | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.79122\nι✝ : Type ?u.79125\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nι : Type u_1\nF : ι → β → α\nf : β → α\np : Filter ι\np' : Filter β\nH : ∀ (ε : ℝ), ε > 0 → ∀ᶠ (n : ι × β) in p ×ˢ p', dist (f n.snd) (F n.fst n.snd) < ε\nu : Set (α... | [
897,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_map | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.val_eq_zero | [] | [
589,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Analysis/SpecialFunctions/PolarCoord.lean | polarCoord_source_ae_eq_univ | [
{
"state_after": "A : polarCoord.sourceᶜ ⊆ ↑(LinearMap.ker (LinearMap.snd ℝ ℝ ℝ))\n⊢ polarCoord.source =ᵐ[volume] univ",
"state_before": "⊢ polarCoord.source =ᵐ[volume] univ",
"tactic": "have A : polarCoord.sourceᶜ ⊆ LinearMap.ker (LinearMap.snd ℝ ℝ ℝ) := by\n intro x hx\n simp only [polarCoord_source... | [
130,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | isAdjointPair_toBilin' | [
{
"state_after": "R : Type ?u.1916305\nM : Type ?u.1916308\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type ?u.1916344\nM₁ : Type ?u.1916347\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type ?u.1916956\nM₂ : Type ?u.1916959\ninst✝¹⁰ : CommSemiring ... | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_inv_eq_iff_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.55077\nβ : Type ?u.55080\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a * b⁻¹ = c\n⊢ a = c * b",
"tactic": "rw [← h, inv_mul_cancel_right]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.55077\nβ : Type ?u.55080\nG :... | [
711,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_homothetyHom | [] | [
846,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.subtypePerm | [
{
"state_after": "case inl\nι : Type ?u.1656340\nα : Type u_1\nβ : Type ?u.1656346\nf g : Perm α\ns t : Set α\na b x y : α\nhf : IsCycleOn f s\nhs : Set.Subsingleton s\n⊢ IsCycleOn (subtypePerm f (_ : ∀ (x : α), x ∈ s ↔ ↑f x ∈ s)) _root_.Set.univ\n\ncase inr\nι : Type ?u.1656340\nα : Type u_1\nβ : Type ?u.16563... | [
851,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_biUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.498743\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\n⊢ ↑(Finset.biUnion s t) = ⋃ (x : α) (_ : x ∈ ↑s), ↑(t x)",
"tactic": "simp [Set.ext_iff, mem_biUnion, Set.mem_iUnion, iff_self_iff, mem_coe, im... | [
3546,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3545,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioc_of_Icc | [] | [
219,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_image | [] | [
1173,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.map_extend_nhdsWithin | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.153300\nM' : Type ?u.153303\nH' : Type ?u.153306\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : Topologic... | [
903,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.mkContinuous₂_apply | [] | [
758,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.derivative_succ | [
{
"state_after": "case zero\nR : Type u_1\ninst✝ : CommRing R\nν : ℕ\n⊢ ↑Polynomial.derivative (bernsteinPolynomial R Nat.zero (ν + 1)) =\n ↑Nat.zero * (bernsteinPolynomial R (Nat.zero - 1) ν - bernsteinPolynomial R (Nat.zero - 1) (ν + 1))\n\ncase succ\nR : Type u_1\ninst✝ : CommRing R\nν n✝ : ℕ\n⊢ ↑Polynomi... | [
144,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toOpen_apply | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_multiplicative | [] | [
1466,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1466,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_singleton_self | [] | [
695,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Combinatorics/Composition.lean | List.join_splitWrtCompositionAux | [
{
"state_after": "case nil\nn : ℕ\nα : Type u_1\nl : List α\nh : 0 = length l\n⊢ join (splitWrtCompositionAux l []) = l\n\ncase cons\nn✝ : ℕ\nα : Type u_1\nn : ℕ\nns : List ℕ\nIH : ∀ {l : List α}, sum ns = length l → join (splitWrtCompositionAux l ns) = l\nl : List α\nh : n + sum ns = length l\n⊢ join (splitWrt... | [
760,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_toAddMonoidHom | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.add_one_le_of_lt | [] | [
189,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.eventually_or | [] | [
191,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_apply' | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.190515\nι : Type ?u.190518\nM : Type u_2\nM' : Type ?u.190524\nN : Type ?u.190527\nP : Type ?u.190530\nG : Type ?u.190533\nH : Type ?u.190536\nR : Type ?u.190539\nS✝ : Type ?u.190542\ninst✝ : AddCommMonoid M\nv v₁ v₂ : α →₀ M\nS : Set α\nf : α → β\nx : α... | [
558,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRelAux.ret_left | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nC : Computation α → Computation β → Prop\na : α\ncb : Computation β\n⊢ ∀ (b : β), LiftRelAux R C (Sum.inl a) (destruct (pure b)) ↔ ∃ b_1, b_1 ∈ pure b ∧ R a b_1\n\nα : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nC : Computation α → Co... | [
1271,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_closure_singleton_self | [] | [
341,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/BinaryHeap.lean | BinaryHeap.size_mkHeap | [] | [
55,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
9
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_self_iff | [] | [
244,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.prod_rightr | [] | [
976,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.intervalIntegrable_of_integral_ne_zero | [] | [
514,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.subperm | [] | [
423,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.map_mul | [] | [
390,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
11
] |
Mathlib/Algebra/Order/Group/Abs.lean | apply_abs_le_mul_of_one_le' | [] | [
256,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Order/Partition/Equipartition.lean | Finpartition.top_isEquipartition | [] | [
78,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.symmetry' | [] | [
1121,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.comp_apply | [] | [
1113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_toContinuousLinearEquiv | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_center | [] | [
1349,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_le_factorization_mul_left | [
{
"state_after": "case inl\nb : ℕ\nhb : b ≠ 0\n⊢ factorization 0 ≤ factorization (0 * b)\n\ncase inr\na b : ℕ\nhb : b ≠ 0\nha : a ≠ 0\n⊢ factorization a ≤ factorization (a * b)",
"state_before": "a b : ℕ\nhb : b ≠ 0\n⊢ factorization a ≤ factorization (a * b)",
"tactic": "rcases eq_or_ne a 0 with (rfl | ... | [
481,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.equiv_lim | [] | [
347,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardEq_rfl | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf : X ⟶ Y\nℱ : Presheaf C X\nU : Opens ↑Y\n⊢ ℱ.map (𝟙 ((Opens.map f).obj U).op) = 𝟙 (ℱ.obj ((Opens.map f).obj U).op)",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf : X ⟶ Y\nℱ : Presheaf C X\nU : Opens ↑Y\n⊢ (pushforwardEq ... | [
190,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_zero | [] | [
33,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
33,
25
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_zero' | [] | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Iic_of_monotone_surjective | [] | [
89,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/Height.lean | Set.wellFoundedLT_of_chainHeight_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.52761\ns✝ t : Set α\ninst✝ : Preorder α\ns : Set α\nhs : chainHeight s ≠ ⊤\n⊢ chainHeight (↑ofDual ⁻¹' s) ≠ ⊤",
"tactic": "rwa [chainHeight_dual]"
}
] | [
377,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.not_modEq_iff_toIcoDiv_eq_toIocDiv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ ¬a ≡ b [PMOD p] ↔ toIcoDiv hp a b = toIocDiv hp a b",
"tactic": "rw [not_modEq_iff_toIcoMod_eq_toIocMod hp, toIcoMod, toIocMod, sub_right_inj,\n (z... | [
666,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.toDual_def | [] | [
1470,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.Regular.smul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.71015\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace α\nμ : Measure α\ninst✝ : Regular μ\nx : ℝ≥0∞\nhx : x ≠ ⊤\nthis : OuterRegular (x • μ)\n⊢ Regular (x • μ)",
"state_before": "α : Type u_1\nβ : Type ?u.71015\ninst✝² : MeasurableSpace α\ninst✝¹ : Topologi... | [
547,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
11
] |
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