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/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryRightEquiv_symm_apply' | [] | [
1588,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_sub_self_eq | [
{
"state_after": "F : Type ?u.235278\nα : Type u_1\nβ : Type ?u.235284\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\nha : fract a ≠ 0\n⊢ ↑⌈a⌉ - a = 1 - (a + 1 - ↑⌈a⌉)",
"state_before": "F : Type ?u.235278\nα : Type u_1\nβ : Type ?u.235284\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing ... | [
1258,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.mono | [] | [
87,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Analysis/Normed/Order/UpperLower.lean | IsUpperSet.cthickening' | [
{
"state_after": "α : Type u_1\nι : Type ?u.1091\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsUpperSet s\nε : ℝ\n⊢ IsUpperSet (⋂ (ε_1 : ℝ) (_ : max 0 ε < ε_1), thickening ε_1 s)",
"state_before": "α : Type u_1\nι : Type ?u.1091\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsUpperSet s\nε : ℝ\n⊢ IsUppe... | [
56,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.frequently_ae_iff | [] | [
386,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.coe_inf | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.min_of_le_pred | [] | [
604,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Std/Data/String/Lemmas.lean | String.prev_of_valid' | [
{
"state_after": "no goals",
"state_before": "cs cs' : List Char\n⊢ prev { data := cs ++ cs' } { byteIdx := utf8Len cs } = { byteIdx := utf8Len (List.dropLast cs) }",
"tactic": "match cs, cs.eq_nil_or_concat with\n| _, .inl rfl => rfl\n| _, .inr ⟨cs, c, rfl⟩ => simp [prev_of_valid]"
},
{
"state_... | [
292,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
288,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.isoToPlus_hom | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_mul_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.818251\nβ : Type ?u.818254\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ ENNReal.toNNReal (a * ⊤) = 0",
"tactic": "simp"
}
] | [
2200,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2200,
1
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.traverse_map | [
{
"state_after": "t : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng✝ : α → F β\nh : β → G γ\nf✝ : β → γ\nx✝ : t β\nf : β → F γ\ng : α → β... | [
91,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inclusion_range | [] | [
2687,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2685,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_apply_eq_one_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.26301\nγ : Type ?u.26304\np : Pmf α\ns t : Set α\nh : (∑' (x : α), Set.indicator s (↑p) x) = 1\na : α\nhap : a ∈ support p\n⊢ a ∈ s\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.26301\nγ : Type ?u.26304\np : Pmf α\ns t : Set α\nh : support p ⊆ s\n⊢ (∑' ... | [
210,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.dominatedFinMeasAdditive_weightedSMul | [] | [
248,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_smul_of_mem_skewAdjoint | [] | [
550,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.eq_univ_of_unbounded | [
{
"state_after": "X : Type u\nα : Type v\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\ns : Set α\nhs : IsPreconnected s\nhb : ¬BddBelow s\nha : ¬BddAbove s\nx : α\n⊢ x ∈ s",
"state_before": "X : Type u\nα : Type v\ninst✝³ : TopologicalSpace... | [
239,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean | AbsoluteValue.IsAdmissible.exists_approx_aux | [
{
"state_after": "R : Type u_1\ninst✝ : EuclideanDomain R\nabv : AbsoluteValue R ℤ\nn : ℕ\nh : IsAdmissible abv\nthis : DecidableEq R\n⊢ ∀ {ε : ℝ},\n 0 < ε →\n ∀ {b : R},\n b ≠ 0 →\n ∀ (A : Fin (Nat.succ (IsAdmissible.card h ε ^ n)) → Fin n → R),\n ∃ i₀ i₁, i₀ ≠ i₁ ∧ ∀ (k : Fi... | [
123,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.Pushforward.id_hom_app' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : TopCat\nℱ : Presheaf C X\nU : Set ↑X\np : IsOpen U\n⊢ (whiskerRight (NatTrans.op (Opens.mapId X).inv) ℱ ≫ (Functor.leftUnitor ℱ).hom).app\n { carrier := U, is_open' := p }.op =\n ℱ.map (𝟙 { carrier := U, is_open' := p }.op)",
"state_before": "C ... | [
222,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.lipschitz_apply | [] | [
497,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.Prod.right_inv | [
{
"state_after": "case mk.mk\nB : Type u_1\ninst✝⁶ : TopologicalSpace B\nF₁ : Type u_3\ninst✝⁵ : TopologicalSpace F₁\nE₁ : B → Type u_4\ninst✝⁴ : TopologicalSpace (TotalSpace E₁)\nF₂ : Type u_2\ninst✝³ : TopologicalSpace F₂\nE₂ : B → Type u_5\ninst✝² : TopologicalSpace (TotalSpace E₂)\ne₁ : Trivialization F₁ To... | [
213,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.false_xor | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ xor false b = b",
"tactic": "cases b <;> simp"
}
] | [
63,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Hom.map_rel | [] | [
547,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Order/Disjointed.lean | iSup_disjointed | [] | [
147,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_compl | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.gcd_pos_iff | [] | [
394,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddMonoidWithOne α\nm n : PosNum\n⊢ ↑(m + n) = ↑m + ↑n",
"tactic": "rw [← cast_to_nat, add_to_nat, Nat.cast_add, cast_to_nat, cast_to_nat]"
}
] | [
664,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Control/Traversable/Instances.lean | List.traverse_eq_map_id | [
{
"state_after": "case cons\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα β : Type u_1\nf : α → β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : List.traverse (pure ∘ f) tail✝ = pure (f <$> tail✝)\n⊢ (Seq.seq (cons (f head✝)) fun x =... | [
91,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.pow_one_cast | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ a ^ Nat.rawCast 1 = a",
"tactic": "simp"
}
] | [
761,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_congr | [] | [
1204,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_coe | [] | [
80,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_le_sinh | [] | [
696,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.opRingEquiv_symm_single | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.1569928\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nr : kᵐᵒᵖ\nx : Gᵐᵒᵖ\n⊢ ↑(RingEquiv.symm MonoidAlgebra.opRingEquiv) (single x r) = op (single (unop x) (unop r))",
"tactic": "simp"
}
] | [
1118,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Data/Set/Basic.lean | Set.empty_def | [] | [
558,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.zero_power | [] | [
579,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_add_nsmul_le | [
{
"state_after": "case inl\nα✝ : Type ?u.99967\ninst✝³ : CommGroup α✝\ninst✝² : DecidableEq α✝\nA B✝ C : Finset α✝\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : DecidableEq α\nB : Finset α\nn : ℕ\nhAB : ∀ (A' : Finset α), A' ⊆ ∅ → card (∅ + B) * card A' ≤ card (A' + B) * card ∅\n⊢ ↑(card (∅ + n • B)) ≤ (↑(car... | [
197,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.orthogonal_le | [] | [
1199,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.HasPoints.lineCount_le_pointCount | [] | [
224,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.singleton_mem_pure | [] | [
2595,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2594,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_epi_comp | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Epi f\nh✝ : f ≫ g = 0\nh : g = 0\n⊢ g = 0",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms... | [
147,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_finsupp | [
{
"state_after": "case intro.mk\nR : Type u\nM : Type v\nN : Type w\ninst✝⁷ : Ring R\ninst✝⁶ : StrongRankCondition R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : Module.Free R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : Module.Free R N\nι : Type w\nfst✝ : Type v\nbs : Basis fst✝ R M\n⊢ M... | [
45,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_of_forall_col_eq_smul_add_pred | [
{
"state_after": "m : Type ?u.1750254\nn✝ : Type ?u.1750257\ninst✝⁴ : DecidableEq n✝\ninst✝³ : Fintype n✝\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nn : ℕ\nA B : Matrix (Fin (n + 1)) (Fin (n + 1)) R\nc : Fin n → R\nA_zero : ∀ (i : Fin (n + 1)), A i 0 = B i 0\nA_succ : ∀ (i : Fi... | [
569,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.cast_nat_mul_left | [] | [
1040,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.mul_coe | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.limZero_sub_rev | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf g : CauSeq β abv\nhfg : LimZero (f - g)\n⊢ LimZero (g - f)",
"tactic": "simpa using neg_limZero hfg"
}
] | [
451,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_comp | [] | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.sup_toAddSubgroup | [
{
"state_after": "case h\nR✝ : Type ?u.111042\nR₂ : Type ?u.111045\nK : Type ?u.111048\nM✝ : Type ?u.111051\nM₂ : Type ?u.111054\nV : Type ?u.111057\nS : Type ?u.111060\ninst✝⁸ : Semiring R✝\ninst✝⁷ : AddCommMonoid M✝\ninst✝⁶ : Module R✝ M✝\nx✝ : M✝\np✝ p'✝ : Submodule R✝ M✝\ninst✝⁵ : Semiring R₂\nσ₁₂ : R✝ →+* ... | [
384,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.symm_apply_apply | [] | [
1269,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_left_comm | [
{
"state_after": "α : Type u_3\nα' : Type ?u.72811\nβ : Type u_5\nβ' : Type ?u.72817\nγ✝ : Type ?u.72820\nγ' : Type ?u.72823\nδ : Type u_4\nδ' : Type u_6\nε : Type u_2\nε' : Type ?u.72835\nζ : Type ?u.72838\nζ' : Type ?u.72841\nν : Type ?u.72844\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : Decida... | [
388,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.sigma_one_apply | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.522889\nn : ℕ\n⊢ ↑(σ 1) n = ∑ d in divisors n, d",
"tactic": "simp [sigma_apply]"
}
] | [
788,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.ofMulHom_coe | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.map_inr_inv_coprodComparison | [
{
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1379,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.IsCobounded.mk | [] | [
194,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.maximal_of_isField | [
{
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252,
77
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243,
1
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Mathlib/SetTheory/Lists.lean | Lists'.toList_cons | [
{
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] | [
90,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.mk_zero | [] | [
121,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_fromBlocks_iff | [] | [
127,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Data/Fintype/Basic.lean | Finset.map_univ_of_surjective | [] | [
265,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.eval_eq_rfindOpt | [
{
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{
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1158,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
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Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.exists_solution | [
{
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... | [
374,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
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Mathlib/Algebra/DirectSum/Algebra.lean | DirectSum.algebraMap_apply | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_mul | [
{
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154,
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142,
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.neg | [] | [
184,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_neg | [] | [
447,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_injective | [] | [
133,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/Analysis/Convex/StrictConvexBetween.lean | Collinear.wbtw_of_dist_eq_of_dist_le | [
{
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70,
38
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54,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_nsmul | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/Topology/Separation.lean | SeparatedNhds.disjoint | [] | [
138,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Data/Nat/Basic.lean | Nat.div_le_iff_le_mul_add_pred | [
{
"state_after": "m✝ n✝ k✝ m n k : ℕ\nn0 : 0 < n\n⊢ m < n * k + n ↔ m ≤ n * k + (n - 1)",
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},
{
"state_after": "case zero\nm✝ n k✝ m k : ℕ\... | [
249,
20
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244,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.MeasurePreserving.skew_product | [
{
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648,
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622,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_span | [
{
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148,
42
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146,
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Mathlib/Data/Num/Lemmas.lean | PosNum.pred_to_nat | [
{
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{
"state_after": "case zero\nn : PosNum\nh : 1 < n\ne : pred' n = zero\n⊢ ↑(Num.casesOn zero 1 id) = Nat.pred ↑n... | [
816,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
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Mathlib/Topology/Category/Locale.lean | Locale.coe_of | [] | [
46,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_single | [] | [
342,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ✝ σ : Perm α\nhσ : IsCycle σ\n⊢ (fun τ => cycleType τ⁻¹ = cycleType τ) σ",
"tactic": "simp only [hσ.cycleType, hσ.inv.cycleType, support_inv]"
},
{
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"state_before... | [
137,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.snd_prod | [
{
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539,
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538,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv'_mul | [] | [
501,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_ker | [
{
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287,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.expand' | [
{
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"tactic": "norm_cast"
},
{
"st... | [
127,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
11
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Std/Data/List/Lemmas.lean | List.range'_subset_right_1 | [
{
"state_after": "no goals",
"state_before": "s m n : Nat\n⊢ 0 < 1",
"tactic": "decide"
}
] | [
1868,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1867,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isOpen_iff_of_mem' | [
{
"state_after": "no goals",
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"tactic": "simp [isOpen_def, h]"
}
] | [
216,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Std/Data/String/Lemmas.lean | String.utf8Len_le_of_infix | [] | [
71,
34
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70,
1
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Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | inner_gramSchmidtOrthonormalBasis_eq_zero | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : IsWellOrder ι fun x x_1 => x < x_1\ninst✝¹ : Fintype ι\ninst✝ : FiniteDimensional 𝕜 E\nh : finrank ... | [
380,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target_aux2 | [
{
"state_after": "H : Type u_1\nM : Type ?u.18883\nH' : Type u_2\nM' : Type u_3\nX : Type ?u.18892\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : Struct... | [
281,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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Mathlib/Topology/Algebra/Group/Basic.lean | continuous_zpow | [
{
"state_after": "no goals",
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"tactic": "simpa using continu... | [
494,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
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Mathlib/Topology/Basic.lean | closure_eq_iff_isClosed | [] | [
481,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_sum | [
{
"state_after": "α β : Type u\nι : Type u_1\nf : ι → Cardinal\ni : ι\n⊢ Quotient.mk isEquivalent (Quotient.out (f i)) ≤ sum f",
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"tactic": "rw [← Quotient.out_eq (f i)]"
},
{
"state_after": "no goals",
"sta... | [
863,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
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] |
Mathlib/Data/Matrix/Notation.lean | Matrix.one_fin_three | [
{
"state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : Zero α\ninst✝ : One α\ni j : Fin 3\n⊢ OfNat.ofNat 1 i j = ↑of ![![1, 0, 0], ![0, 1, 0], ![0, 0, 1]] i j",
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418,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_self_hom_app | [
{
"state_after": "no goals",
"state_before": "C : Type u\nA : Type u_1\ninst✝² : Category C\ninst✝¹ : AddGroup A\ninst✝ : HasShift C A\nX✝ Y : C\nf : X✝ ⟶ Y\nn : A\nX : C\n⊢ (shiftFunctor C (-n)).map ((shiftFunctorCompIsoId C (-n) n (_ : -n + n = 0)).hom.app X) =\n (shiftFunctorCompIsoId C n (-n) (_ : n ... | [
538,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finiteAt_nhds | [] | [
3896,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3894,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.Mem.left_unique | [] | [
345,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addEquiv_toEquiv | [] | [
291,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Algebra/Order/Invertible.lean | invOf_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedSemiring α\na : α\ninst✝ : Invertible a\n⊢ 0 < a * ⅟a",
"tactic": "simp only [mul_invOf_self, zero_lt_one]"
}
] | [
34,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
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Mathlib/Topology/Constructions.lean | nhds_toDual | [] | [
178,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_mono' | [
{
"state_after": "case inl\nα : Type ?u.796201\nβ : Type ?u.796204\nb c d : ℝ≥0∞\nr p q : ℝ≥0\nh : ⊤ ≤ b\nht : b = ⊤ → ⊤ = ⊤\n⊢ ENNReal.toReal ⊤ ≤ ENNReal.toReal b\n\ncase inr\nα : Type ?u.796201\nβ : Type ?u.796204\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≤ b\nht : b = ⊤ → a = ⊤\nha : a ≠ ⊤\n⊢ ENNReal.toReal a ≤ EN... | [
1998,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1995,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_add | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\na b : ℕ\nthis : Disjoint (filter p (range a)) (filter p (map (addLeftEmbedding a) (range b)))\n⊢ count p (a + b) = count p a + count (fun k => p (a + k)) b",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\na b : ℕ\n⊢ count p (a + b) = count p ... | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_set_iff_linearIndependent_vsub | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.62032\ns : Set P\np₁ : P\nhp₁ : p₁ ∈ s\n⊢ (LinearIndependent k fun i => ↑↑i -ᵥ ↑{ val := p₁, property := hp₁ }) ↔ LinearIndependent k fun v => ↑v",
... | [
163,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_eq_normalizedFactors | [
{
"state_after": "α : Type ?u.479911\ninst✝⁷ : CancelCommMonoidWithZero α\ninst✝⁶ : DecidableEq α\ninst✝⁵ : NormalizationMonoid α\ninst✝⁴ : UniqueFactorizationMonoid α\nM : Type u_1\ninst✝³ : CancelCommMonoidWithZero M\ninst✝² : DecidableEq M\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : Unique Mˣ\nx : M\n⊢ fa... | [
567,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Order/Lattice.lean | inf_inf_distrib_right | [] | [
540,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuousMul_sInf | [] | [
845,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_one | [] | [
204,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
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