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/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.span_right | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_eq_two | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.162338\ns t : Set α\na b x y : α\nf : α → β\nh : ncard s = 2\n⊢ ∃ x y, x ≠ y ∧ s = {x, y}\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.162338\ns t : Set α\na b x y : α\nf : α → β\n⊢ (∃ x y, x ≠ y ∧ s = {x, y}) → ncard s = 2",
"state_before": "α : T... | [
754,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.min_comm | [
{
"state_after": "a b : Nat\n⊢ (if a ≤ b then a else b) = if b ≤ a then b else a",
"state_before": "a b : Nat\n⊢ min a b = min b a",
"tactic": "simp [Nat.min_def]"
},
{
"state_after": "case inl.inl\na b : Nat\nh✝¹ : a ≤ b\nh✝ : b ≤ a\n⊢ a = b\n\ncase inr.inr\na b : Nat\nh✝¹ : ¬a ≤ b\nh✝ : ¬b ≤ a... | [
175,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
172,
11
] |
Mathlib/Data/List/Nodup.lean | List.nodup_iff_nthLe_inj | [] | [
113,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.of_le | [] | [
219,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.rev_injective | [] | [
459,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_cons_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.492391\nγ : Type ?u.492394\na : α\ns t : Multiset α\n⊢ Disjoint {a} t ∧ Disjoint s t ↔ ¬a ∈ t ∧ Disjoint s t",
"tactic": "rw [singleton_disjoint]"
}
] | [
2961,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2959,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_eq_one_iff | [] | [
353,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_finset_image_atTop_atTop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.269970\nι' : Type ?u.269973\nα : Type ?u.269976\nβ : Type u_1\nγ : Type u_2\ninst✝ : DecidableEq β\ni : β → γ\nj : γ → β\nh : Function.LeftInverse j i\na : β\n⊢ a ∈ Finset.image j {i a}",
"tactic": "simp only [Finset.image_singleton, h a, Finset.... | [
1389,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1386,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.find_eq_top_iff | [] | [
819,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.sizeUpTo_length | [] | [
229,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.4425879\nβ : Type u_1\nβ' : Type ?u.4425885\nγ : Type ?u.4425888\nE : Type ?u.4425891\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' :... | [
314,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.Final.hasColimit_of_comp | [] | [
351,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodCongrRight_trans_prodComm | [
{
"state_after": "case H.mk\nα₁ : Type u_3\nβ₁ : Type u_2\nβ₂ : Type u_1\ne : α₁ → β₁ ≃ β₂\na : α₁\nb : β₁\n⊢ ↑((prodCongrRight e).trans (prodComm α₁ β₂)) (a, b) = ↑((prodComm α₁ β₁).trans (prodCongrLeft e)) (a, b)",
"state_before": "α₁ : Type u_3\nβ₁ : Type u_2\nβ₂ : Type u_1\ne : α₁ → β₁ ≃ β₂\n⊢ (prodCong... | [
753,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Order/Atoms.lean | covby_iff_coatom_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8894\ninst✝ : PartialOrder α\na b : α\nh : a ≤ b\n⊢ a ⋖ b ↔ IsCoatom { val := a, property := h }",
"tactic": "simp"
}
] | [
202,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_inv_app_left | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.add_compl | [] | [
358,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.join | [
{
"state_after": "case h.e'_6\nX : Type u_2\ninst✝³ : NormedAddCommGroup X\nM : Type u_1\ninst✝² : Ring M\ninst✝¹ : Module M X\ninst✝ : FaithfulSMul M X\nP Q : M\nh₁ : IsLprojection X P\nh₂ : IsLprojection X Q\n⊢ P + Q - P * Q = 1 - (1 - P) * (1 - Q)",
"state_before": "X : Type u_2\ninst✝³ : NormedAddCommGr... | [
171,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_eq_iff_eq_sin | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : y ∈ Ioo (-(π / 2)) (π / 2)\n⊢ arcsin x = y ↔ x = sin y",
"tactic": "simp only [le_antisymm_iff, arcsin_le_iff_le_sin' (mem_Ico_of_Ioo hy),\n le_arcsin_iff_sin_le' (mem_Ioc_of_Ioo hy)]"
}
] | [
198,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.473672\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\n⊢ ↑(restrict v ∅) i = ↑0 i",
"tactic": "rw... | [
713,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.left_cancel | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ x ◃ y = x ◃ y' → y = y'\n\ncase mpr\nR : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ y = y' → x ◃ y = x ◃ y'",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ x ◃ y = x ◃ y' ↔ y = y'",
"tactic": "constructor"
},
{
"s... | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_subset_mul_left | [] | [
422,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_toFinset_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.201320\nι : Type ?u.201323\nG : Type ?u.201326\nM : Type u_2\nN : Type ?u.201332\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\nf : α → M\ns : Set α\ninst✝ : Fintype ↑s\n⊢ (s ∩ mulSupport fun i => f i) = ↑(toFinset s) ∩ mulSupport fun i... | [
509,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_right_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.135344\nα : Type u_1\nβ : Type ?u.135350\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ (a \\ b) \\ c = (a \\ c) \\ b",
"tactic": "simp_rw [sdiff_sdiff, sup_comm]"
}
] | [
628,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_inner_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1721983\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 : E\n⊢ ‖inner x y‖ = ‖inner y x‖",
... | [
630,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Order/BooleanAlgebra.lean | disjoint_compl_left_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.59824\nw x y z : α\ninst✝ : BooleanAlgebra α\n⊢ Disjoint (xᶜ) y ↔ y ≤ x",
"tactic": "rw [← le_compl_iff_disjoint_left, compl_compl]"
}
] | [
735,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Fintype.card_le_card_of_leftTotal_unique | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nr : α → β → Prop\nh₁ : LeftTotal r\nh₂ : LeftUnique r\n⊢ ∀ (a : α), a ∈ univ → ∃ b, b ∈ univ ∧ r a b",
"tactic": "simpa using h₁"
}
] | [
144,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.equivalent_weightedSumSquares | [] | [
162,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/Bounds/Basic.lean | top_mem_upperBounds | [] | [
105,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_one | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\n✝ : Nontrivial α\n⊢ factors 1 = 0",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\n⊢ factors 1 =... | [
483,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Order/LocallyFinite.lean | Iic_ofDual | [] | [
944,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.isSelfAdjoint | [] | [
65,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Combinatorics/Quiver/ConnectedComponent.lean | Quiver.WeaklyConnectedComponent.eq | [] | [
63,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.compatible_of_mem_maximalAtlas | [
{
"state_after": "H : Type u\nH' : Type ?u.67678\nM : Type u_1\nM' : Type ?u.67684\nM'' : Type ?u.67687\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nG : StructureGroupoid H\ne e' : LocalHomeomorph M H\nhe : e ∈ maximalAtlas M G\nhe' : e' ∈ maximalAtlas M G\nx : H\nhx : x ... | [
954,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_self | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\np : Associates α\nhp : Irreducible p\n⊢ p =\n match some {{ val :=... | [
1674,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_ne_zero | [] | [
404,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.sup_apply | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.IsNormal.fp_iff_deriv | [
{
"state_after": "no goals",
"state_before": "f✝ : Ordinal → Ordinal\nf : Ordinal → Ordinal\nH : IsNormal f\na : Ordinal\n⊢ f a = a ↔ ∃ o, deriv f o = a",
"tactic": "rw [← H.le_iff_eq, H.le_iff_deriv]"
}
] | [
549,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Init/Algebra/Order.lean | le_of_eq | [] | [
76,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.mem_ofSet_self_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α\ninst✝¹ : DecidablePred fun x => x ∈ s✝\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\na : α\n⊢ (a ∈ if a ∈ s then some a else none) ↔ a ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α\ninst✝¹ :... | [
221,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.fin_insertNth | [] | [
1274,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_dotProduct | [
{
"state_after": "l : Type ?u.150094\nm : Type u_1\nn : Type ?u.150100\no : Type ?u.150103\nm' : o → Type ?u.150108\nn' : o → Type ?u.150113\nR : Type ?u.150116\nS : Type ?u.150119\nα : Type v\nβ : Type w\nγ : Type ?u.150126\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : DecidableEq m\ninst✝ : NonUnitalNonAs... | [
811,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_abs | [] | [
1063,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.relabel_bot | [] | [
612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Left.one_lt_mul' | [] | [
756,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.le_leftLim | [] | [
302,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_le_himp_left | [] | [
415,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd | [] | [
502,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.fg_unit | [] | [
880,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | List.Nodup.isCycleOn_formPerm | [
{
"state_after": "ι : Type ?u.3063559\nα : Type u_1\nβ : Type ?u.3063565\ninst✝¹ inst✝ : DecidableEq α\nl : List α\nh : List.Nodup l\na : α\nha : a ∈ {a | a ∈ l}\nb : α\nhb : b ∈ {a | a ∈ l}\n⊢ SameCycle (List.formPerm l) a b",
"state_before": "ι : Type ?u.3063559\nα : Type u_1\nβ : Type ?u.3063565\ninst✝¹ ... | [
1850,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1842,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.lastFun_of_subtype | [
{
"state_after": "case h\nn : ℕ\nα : TypeVec (n + 1)\np : α ⟹ repeat (n + 1) Prop\ni : last (Subtype_ p)\n⊢ lastFun (ofSubtype p) i = _root_.id i",
"state_before": "n : ℕ\nα : TypeVec (n + 1)\np : α ⟹ repeat (n + 1) Prop\n⊢ lastFun (ofSubtype p) = _root_.id",
"tactic": "ext i : 2"
},
{
"state_af... | [
730,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | card_nthRoots_subgroup_units | [
{
"state_after": "R : Type u_2\nG : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\ninst✝² : Group G\ninst✝¹ : Fintype G\ninst✝ : DecidableEq G\nf : G →* R\nhf : Injective ↑f\nn : ℕ\nhn : 0 < n\ng₀ : G\nthis : DecidableEq R\n⊢ card (filter (fun g => g ^ n = g₀) univ) ≤ ↑Multiset.card (nthRoots n (↑f g₀))",
... | [
136,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_caratheodory | [
{
"state_after": "G : Type w\ninst✝¹ : TopologicalSpace G\nμ : Content G\ninst✝ : T2Space G\nA : Set G\n⊢ MeasurableSet A ↔\n ∀ (U : Set G) (hU : IsOpen U),\n ↑(Content.outerMeasure μ) (↑{ carrier := U, is_open' := hU } ∩ A) +\n ↑(Content.outerMeasure μ) (↑{ carrier := U, is_open' := hU } \\ A)... | [
335,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.comp_f | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.rightUnitor_inv_app | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.mem_image₂_of_mem | [] | [
74,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_ndinsert | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ ∀ (a_1 : α), a_1 ∈ ndinsert a s ↔ a_1 ∈ a ::ₘ s",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : D... | [
121,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_one | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\n⊢ denom 1 = 1",
"tactic": "convert denom_div (1 : K[X]) one_ne_zero <;> simp"
}
] | [
1217,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.pow_smul_mem_adjoin_smul | [] | [
367,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_dvd_left | [] | [
160,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagram_right | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ext_iff | [
{
"state_after": "no goals",
"state_before": "z w : ℂ\nH : z = w\n⊢ z.re = w.re ∧ z.im = w.im",
"tactic": "simp [H]"
}
] | [
65,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.finite_of_finite_mul_right | [] | [
96,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_mul_dom | [] | [
724,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Icc_self | [] | [
514,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/Set/Prod.lean | Set.preimage_coe_coe_diagonal | [
{
"state_after": "case h.mk.mk.mk\nα : Type u_1\ns✝ t s : Set α\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\n⊢ ({ val := x, property := hx }, { val := y, property := hy }) ∈ (Prod.map (fun x => ↑x) fun x => ↑x) ⁻¹' diagonal α ↔\n ({ val := x, property := hx }, { val := y, property := hy }) ∈ diagonal ↑s",
"sta... | [
491,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.nat_cast_imJ | [] | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.isAdjointPair_inner | [
{
"state_after": "𝕜 : Type ?u.1264931\nE : Type ?u.1264934\nF : Type ?u.1264937\nG : Type ?u.1264940\ninst✝¹⁵ : IsROrC 𝕜\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : NormedAddCommGroup G\ninst✝¹¹ : InnerProductSpace 𝕜 E\ninst✝¹⁰ : InnerProductSpace 𝕜 F\ninst✝⁹ : InnerProductSpa... | [
266,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
src/lean/Init/SimpLemmas.lean | or_self | [] | [
87,
95
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
87,
9
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addEquiv_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type ?u.118278\nγ : Type ?u.118281\nι : Type ?u.118284\nM : Type u_1\nM' : Type ?u.118290\nN : Type u_2\nP : Type u_3\nG : Type ?u.118299\nH : Type ?u.118302\nR : Type ?u.118305\nS : Type ?u.118308\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMon... | [
271,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Algebra/Category/ModuleCat/Biproducts.lean | ModuleCat.biproductIsoPi_inv_comp_π | [] | [
147,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_cons_cons | [] | [
67,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.cast_eq_zero | [] | [
121,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | Real.tendsto_euler_sin_prod | [
{
"state_after": "case h.e'_3\nx : ℝ\n⊢ (fun n => π * x * ∏ j in Finset.range n, (1 - x ^ 2 / (↑j + 1) ^ 2)) =\n Complex.re ∘ fun n => ↑π * ↑x * ∏ j in Finset.range n, (1 - ↑x ^ 2 / (↑j + 1) ^ 2)\n\ncase h.e'_5\nx : ℝ\n⊢ 𝓝 (sin (π * x)) = 𝓝 (Complex.sin (↑π * ↑x)).re",
"state_before": "x : ℝ\n⊢ Tendsto... | [
348,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.toFun_eq_coe | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_hasBasis_closed | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.87316\ninst✝ : UniformSpace α\nt : Set (α × α)\nh : t ∈ 𝓤 α\n⊢ ∃ r, r ∈ 𝓤 α ∧ IsClosed r ∧ r ⊆ t",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.87316\ninst✝ : UniformSpace α\n⊢ HasBasis (�... | [
955,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_subtype_coe_le_comap | [] | [
1419,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.exists_subgroup_card_pow_prime | [
{
"state_after": "no goals",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\ninst✝¹ : Fintype G\np n : ℕ\ninst✝ : Fact (Nat.Prime p)\nhdvd : p ^ n ∣ Fintype.card G\n⊢ 1 = p ^ 0",
"tactic": "simp"
}
] | [
658,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.top_ne_one | [] | [
101,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_triangle | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.3412\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.3444\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y z : (i : ι) → β i\n⊢ hammingDist x z ≤ hammingDist x y + hammingDist y z",
"tactic": "c... | [
71,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.vadd_vsub | [
{
"state_after": "case h.e'_5\n𝕜 : Type ?u.1931289\nV : Type u_4\nV₁ : Type ?u.1931295\nV₂ : Type u_3\nV₃ : Type ?u.1931301\nV₄ : Type ?u.1931304\nP₁ : Type ?u.1931307\nP : Type u_1\nP₂ : Type u_2\nP₃ : Type ?u.1931316\nP₄ : Type ?u.1931319\ninst✝²¹ : NormedField 𝕜\ninst✝²⁰ : SeminormedAddCommGroup V\ninst✝¹⁹... | [
767,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.37787\nm : MeasurableSpace α\nμ ν : Measure α\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf g : α → E\nhf : Integrable f\nhg : Integrable g\n⊢ withDensityᵥ μ (f - g) = withDensityᵥ μ ... | [
107,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.inverseAssociator_map_inr_inr | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousOn.add | [] | [
955,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_le_left | [] | [
956,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
11
] |
Mathlib/Data/Real/Irrational.lean | Irrational.sub_int | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℤ\n⊢ Irrational (x - ↑m)",
"tactic": "simpa only [Rat.cast_coe_int] using h.sub_rat m"
}
] | [
296,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_ofNat | [] | [
411,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_b_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.589386\nF : Type ?u.589389\nK : Type ?u.589392\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b ≠ 0\n⊢ natDegree (toPoly P) = 2",
"tactic": "rw [of_a_eq_zero ha, natDegree_quadratic hb]"
}
] | [
404,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.memℒp_indicator_iff_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.663273\nG : Type ?u.663276\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs✝ : MeasurableSet s\nc : E\nf... | [
673,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/Invertible.lean | isUnit_of_invertible | [] | [
195,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.nndist_single_same | [] | [
304,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.mul_val | [] | [
128,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
9
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_iInf_finite | [] | [
850,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_toAlgHom | [] | [
1623,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1621,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.196846\nα : Type u_2\nβ : Type ?u.196852\nE : Type ?u.196855\ninst✝¹⁰ : Group G\ninst✝⁹ : Group H\ninst✝⁸ : MulAction G α\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MulAction H β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : NormedAddCommGroup E\ns ... | [
265,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_div_eq_mul_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27922\nG : Type ?u.27925\ninst✝ : DivisionMonoid α\na b c : α\n⊢ a / (b / c) = a * c / b",
"tactic": "simp"
}
] | [
462,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Algebra/Parity.lean | odd_one | [] | [
349,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Topology/PathConnected.lean | pathConnectedSpace_iff_eq | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.692142\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.692157\nF : Set X\n⊢ PathConnectedSpace X ↔ ∃ x, pathComponent x = univ",
"tactic": "simp [pathConnectedSpace_iff_univ, isPathConnected_iff_eq]"... | [
1149,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.finset_sup_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → ℝ≥0\ns : Finset α\nr : ℝ≥0\n⊢ Finset.sup s f / r = Finset.sup s fun a => f a / r",
"tactic": "simp only [div_eq_inv_mul, mul_finset_sup]"
}
] | [
576,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_image₂ | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.15748\nG : Type ?u.15751\nι : Type ?u.15754\nπ : ι → Type ?u.15759\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\ns : Set E\nx✝ y✝ x y : E\n⊢ openSegment 𝕜 x y = (fun p => p.fst • x + p.snd • ... | [
74,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
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