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/Equivalence.lean | CategoryTheory.Equivalence.functor_map_inj_iff | [] | [
745,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_const_mul_pow_nhds_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nα : Type ?u.41734\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nn : ℕ\nc d : 𝕜\nhc : c ≠ 0\n⊢ Tendsto (fun x => c * x ^ n) atTop (𝓝 d) ↔ n = 0 ∧ c = d",
"tactic": "simp [... | [
190,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.toEnumFinset_mono | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nm m₁ m₂ : Multiset α\nh : m₁ ≤ m₂\np : α × ℕ\n⊢ p ∈ toEnumFinset m₁ → p ∈ toEnumFinset m₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm m₁ m₂ : Multiset α\nh : m₁ ≤ m₂\n⊢ toEnumFinset m₁ ⊆ toEnumFinset m₂",
"tactic": "intro p"
},
{
... | [
139,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.self_mem_cylinder | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type u_1\nx : (n : ℕ) → E n\nn : ℕ\n⊢ x ∈ cylinder x n",
"tactic": "simp"
}
] | [
133,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Order/Basic.lean | countable_of_isolated_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n⊢ Set.Countable {x | ∃ y, x < y ∧ Ioo x y = ∅}",
"tactic": "simpa only [← covby_iff_Ioo_eq] using countable_... | [
1418,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
src/lean/Init/Core.lean | ofBoolUsing_eq_false | [] | [
713,
35
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
712,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepFun_iff_indepSet_preimage | [
{
"state_after": "Ω : Type u_3\nι : Type ?u.3148409\nβ : Type u_1\nβ' : Type u_2\nγ : Type ?u.3148418\nγ' : Type ?u.3148421\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf : Ω → β\ng : Ω → β'\nmβ : MeasurableSpace β\nmβ' : MeasurableSpace β'\ninst✝ : IsProbabilityMeasure μ\nhf : Measurable f\nhg : Measu... | [
705,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.inv_def | [] | [
895,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.prodMap | [] | [
389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
8
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.transFiberHomeomorph_apply | [] | [
659,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_one_iff | [
{
"state_after": "case inl\ny z : ℝ\nhx : 0 ≤ 0\n⊢ 0 ^ y < 1 ↔ 0 = 0 ∧ y ≠ 0 ∨ 1 < 0 ∧ y < 0 ∨ 0 < 1 ∧ 0 < y\n\ncase inr\nx y z : ℝ\nhx✝ : 0 ≤ x\nhx : 0 < x\n⊢ x ^ y < 1 ↔ x = 0 ∧ y ≠ 0 ∨ 1 < x ∧ y < 0 ∨ x < 1 ∧ 0 < y",
"state_before": "x y z : ℝ\nhx : 0 ≤ x\n⊢ x ^ y < 1 ↔ x = 0 ∧ y ≠ 0 ∨ 1 < x ∧ y < 0 ∨ x ... | [
564,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Order/Heyting/Basic.lean | Disjoint.sdiff_eq_left | [
{
"state_after": "ι : Type ?u.139347\nα : Type u_1\nβ : Type ?u.139353\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\nh : Disjoint a b\n⊢ a \\ b = a \\ ⊥",
"state_before": "ι : Type ?u.139347\nα : Type u_1\nβ : Type ?u.139353\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\nh : Disjoint a b\n⊢ a \... | [
694,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Algebra/Homology/Additive.lean | CochainComplex.single₀MapHomologicalComplex_hom_app_succ | [] | [
436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.ge_on_segment' | [] | [
648,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_le_add_add_tsub | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9485\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ a + b ≤ a + (c + (b - c))",
"state_before": "α : Type u_1\nβ : Type ?u.9485\ninst✝... | [
149,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_image | [] | [
1700,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1699,
1
] |
Mathlib/Order/CompleteLattice.lean | Monotone.map_iInf₂_le | [] | [
1021,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_center | [] | [
480,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.of_left_adjoint | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : IsCofiltered C\nO : Finset C\nH : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))\nJ : Type w\ninst✝² : SmallCategory J\ninst✝¹ : FinCategory J\nD : Type u₁\ninst✝ : Category D\nL : C ⥤ D\nR : D ⥤ C\... | [
736,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_map_map_zero | [] | [
497,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.inter_indicator_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.128368\nι : Type ?u.128371\nM : Type u_2\nN : Type ?u.128377\ninst✝ : MulZeroOneClass M\ns t : Set α\nx✝ : α\n⊢ indicator (s ∩ t) 1 x✝ = indicator (s ∩ t) (fun x => 1) x✝",
"state_before": "α : Type u_1\nβ : Type ?u.128368\nι : Type ?u.128371\nM : Type u_2\nN : Ty... | [
720,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.coeFn_compLp | [] | [
951,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.eq_jacobson_iff_sInf_maximal' | [] | [
162,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf₂_le | [] | [
803,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.nonempty_range_succ | [] | [
3053,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3052,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_eq_of_le | [] | [
828,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Std/Data/List/Lemmas.lean | List.mem_iff_get? | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\n⊢ a ∈ l ↔ ∃ n, get? l n = some a",
"tactic": "simp [get?_eq_some, Fin.exists_iff, mem_iff_get]"
}
] | [
540,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
539,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : CommRing K\n⊢ { toFractionRing := 0 } = 0",
"tactic": "simp only [Zero.zero, OfNat.ofNat, RatFunc.zero]"
}
] | [
314,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearIsometry.toSpanSingleton_apply | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_congr_right | [] | [
1490,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_invOf | [] | [
280,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_eq | [
{
"state_after": "M : Type u_2\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_3\ninst✝¹ : CommMonoid N\nP : Type u_1\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nx : M\n⊢ ↑g (sec f (↑(toMap f) x)).fst = ↑g (↑(sec f (↑(toMap f) x)).snd * x)",
"... | [
1011,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/Order/BoundedOrder.lean | le_top | [] | [
100,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/List/AList.lean | AList.extract_eq_lookup_erase | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : AList β\n⊢ dlookup a s.entries = lookup a s ∧\n { entries := kerase a s.entries, nodupKeys := (_ : NodupKeys (kerase a s.entries)) } = erase a s",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns :... | [
410,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_le_compl_iff_le | [
{
"state_after": "α : Type u\nβ : Type ?u.56262\nw x y z : α\ninst✝ : BooleanAlgebra α\nh✝ : yᶜ ≤ xᶜ\nh : xᶜᶜ ≤ yᶜᶜ\n⊢ x ≤ y",
"state_before": "α : Type u\nβ : Type ?u.56262\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : yᶜ ≤ xᶜ\n⊢ x ≤ y",
"tactic": "have h := compl_le_compl h"
},
{
"state_after": ... | [
687,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_or_ssubset_of_subset | [] | [
400,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.ι_of_isLimit | [
{
"state_after": "J : Type w\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasZeroMorphisms C\nF f : J → C\nt : Bicone f\nht : IsLimit (toCone t)\nj : J\nj' : Discrete J\n⊢ ι t j ≫ (toCone t).π.app j' = (Fan.mk (f j) fun j' => if h : j = j' then eqToHom (_ : f j = f j') else 0).π.app j'",
"state_before": "J : T... | [
155,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Complex.continuous_ofReal_cpow_const | [] | [
424,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.smul_comp | [] | [
976,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Computability/Partrec.lean | Computable.list_ofFn | [
{
"state_after": "α : Type u_1\nβ : Type ?u.207104\nγ : Type ?u.207107\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nn : ℕ\nf : Fin (n + 1) → α → σ\nhf : ∀ (i : Fin (n + 1)), Computable (f i)\n⊢ Computable fun a => f 0 a :: List.ofFn fun i => f (Fi... | [
750,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.append_natAdd_aux | [
{
"state_after": "case mk\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nα : Type u_1\nm n : ℕ\na : Fin (Nat.succ m) → α\nb : Fin (Nat.succ n) → α\nval✝ : ℕ\nisLt✝ : val✝ < n\n⊢ Matrix.vecAppend (_ : Nat.succ (m + n) = m + Nat.succ n) (a ∘ ↑Fin.castSucc) b\n (↑Fin.castSucc (↑(Fin.natAdd m)... | [
486,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryLeftEquiv_symm_apply | [] | [
1430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.star_coe | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.314480\nT : Type ?u.314483\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ star ↑x = ↑x",
"tactic": "ext <;> simp"
}
] | [
671,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.map_floor | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedSemiring α\ninst✝³ : LinearOrderedSemiring β\ninst✝² : FloorSemiring α\ninst✝¹ : FloorSemiring β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\nn : ℕ\n⊢ ↑n ≤ ↑f a ↔ ↑n... | [
1509,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.eta | [] | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.attach_count_eq_count_coe | [] | [
2568,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2564,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lcs_zero | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.memℒ1_smul_of_L1_withDensity | [] | [
920,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | padicValNat.pow_add_pow | [
{
"state_after": "case zero\nR : Type ?u.883070\nn✝ x p : ℕ\nhp : Fact (Nat.Prime p)\nhp1 : Odd p\nhx : ¬p ∣ x\nn : ℕ\nhn : Odd n\nhxy : p ∣ x + Nat.zero\n⊢ padicValNat p (x ^ n + Nat.zero ^ n) = padicValNat p (x + Nat.zero) + padicValNat p n\n\ncase succ\nR : Type ?u.883070\nn✝ x p : ℕ\nhp : Fact (Nat.Prime p)... | [
418,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | coe_basisOfOrthonormalOfCardEqFinrank | [] | [
990,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
987,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.span_univ | [] | [
693,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Topology/Inseparable.lean | subtype_specializes_iff | [] | [
202,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.nonneg_mul | [
{
"state_after": "a✝ b✝ c a b : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nd₁0 : 0 < ↑d₁\n⊢ Rat.Nonneg (n₁ /. ↑d₁) → Rat.Nonneg (n₂ /. ↑d₂) → Rat.Nonneg (n₁ /. ↑d₁ * (n₂ /. ↑d₂))",
"state_before": "a✝ b✝ c a b : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\n⊢ Rat.Nonneg (n₁ ... | [
74,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/Order/Lattice.lean | sup_le_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Lattice α\na b c d : α\n⊢ a ⊔ b ≤ a ⊓ b ↔ a = b",
"tactic": "simp [le_antisymm_iff, and_comm]"
}
] | [
679,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_cons | [] | [
881,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_span | [] | [
62,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnion | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nM : Type u_3\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : T2Space M\nv : VectorMeasure α M\nf✝ : ℕ → Set α\ninst✝ : Countable β\nf : β → Set α\nhf₁ : ∀ (i : β), MeasurableSet (f i)\nhf₂ : Pairwise (Disjoint on f... | [
180,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/ModelTheory/Quotients.lean | FirstOrder.Language.relMap_quotient_mk' | [
{
"state_after": "L : Language\nM : Type u_3\ns : Setoid M\nps : Prestructure L s\nn : ℕ\nr : Relations L n\nx : Fin n → M\n⊢ Quotient.lift (RelMap r) (_ : ∀ (x y : Fin n → M), x ≈ y → RelMap r x = RelMap r y)\n (Quotient.finChoice fun i => Quotient.mk s (x i)) ↔\n RelMap r x",
"state_before": "L : ... | [
73,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.multiset_prod_singleton | [] | [
151,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.apply_mem_iff | [] | [
363,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1385610\nG : Type ?u.1385613\n𝕜 : Type ?u.1385616\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\... | [
1353,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.WalkingParallelPairHom.id_comp | [] | [
101,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.isClosed_ball_top | [] | [
697,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_subset_union_right | [] | [
842,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.cons_dotProduct | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\nx : α\nv : Fin n → α\nw : Fin (Nat.succ n) → α\n⊢ vecCons x v ⬝ᵥ w = x * vecHead w + v ⬝ᵥ vecTail w",
"tactic": "simp [dotProduct, Fin.sum_univ... | [
149,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.preimage_null_of_map_null | [] | [
1276,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.isOpen_range | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.139510\nδ : Type ?u.139513\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nhf : IsOpenMap f\n⊢ IsOpen (f '' univ)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.139510\nδ : Type ?u.139513\... | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_inv_lt_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.37386\nα : Type u_1\nβ : Type ?u.37392\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : 0 < b\n⊢ a * b⁻¹ < c ↔ a < b * c",
"tactic": "rw [mul_comm, inv_mul_lt_iff h]"
}
] | [
204,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.extend_eq_at' | [] | [
163,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_le_succ_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\n⊢ b = a ∨ b = succ a → a ≤ b ∧ b ≤ succ a",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\n⊢ a ≤ b ∧ b ≤ succ a ↔ b = a ∨ b = succ a",
"tactic": "refine'\n ⟨fun h =>\n or_iff... | [
425,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_map_fst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1989\ns : Multiset α\nl : List α\n⊢ map Prod.fst (antidiagonal (Quotient.mk (isSetoid α) l)) = powerset (Quotient.mk (isSetoid α) l)",
"tactic": "simp [powersetAux']"
}
] | [
63,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.bddBelow_u_image | [] | [
130,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.support_sup | [
{
"state_after": "case a\nι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyLinearOrderedAddMonoid α\ninst✝ : DecidableEq ι\nf g : ι →₀ α\na✝ : ι\n⊢ a✝ ∈ (f ⊔ g).support ↔ a✝ ∈ f.support ∪ g.support",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyLinearOrderedAddMonoid α\ninst✝ : DecidableE... | [
238,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.of_mul_symm_eq | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toContinuousLinearEquiv_injective | [] | [
699,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOn_of_seq_tendstoUniformlyOn | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nl : Filter ι\ninst✝ : IsCountablyGenerated l\nh : ∀ (u : ℕ → ι), Tendsto u atTop l → TendstoUniformlyOn (fun n => F (u n)) f atTop s\n... | [
566,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.coe_coe | [] | [
408,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_one | [
{
"state_after": "no goals",
"state_before": "S : Type u\ninst✝ : Semiring S\n⊢ pochhammer S 1 = X",
"tactic": "simp [pochhammer]"
}
] | [
58,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_dvd_mul_iff_left | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nha : 0 < a\nd : ℕ\n⊢ a * c = a * b * d ↔ c = b * d",
"tactic": "rw [mul_assoc, mul_right_inj' ha.ne']"
}
] | [
734,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
11
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.gcd_eq | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\na b : ℕ+\nleft✝² : gcdW a b * gcdZ a b = succPNat (gcdX a b * gcdY a b)\nh₁ : a = gcdA' a b * gcdD a b\nh₂ : b = gcdB' a b * gcdD a b\nleft✝¹ : gcdZ a b * gcdA' a b = succPNat (gcdX a b * ↑(gcdB' a b))\nleft✝ : gcdW a b * gcdB' a b = succPNat (gcdY a b... | [
519,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsOrthoᵢ.not_isOrtho_basis_self_of_separatingRight | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.596990\nR₂ : Type ?u.596993\nR₃ : Type ?u.596996\nM : Type u_2\nM₁ : Type ?u.597002\nM₂ : Type ?u.597005\nMₗ₁ : Type ?u.597008\nMₗ₁' : Type ?u.597011\nMₗ₂ : Type ?u.597014\nMₗ₂' : Type ?u.597017\nK : Type ?u.597020\nK₁ : Type ?u.597023\nK₂ : Type ?u.597026\nV : Type ... | [
791,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.mem_iff | [
{
"state_after": "no goals",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\n⊢ A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R",
"tactic": "simp [symplecticGroup]"
}
] | [
105,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_hom_app_right | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_sInf_iff | [] | [
748,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.smul_of | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Data/List/MinMax.lean | List.le_max_of_le | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.114493\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl✝ l : List α\na x : α\nhx✝ : x ∈ l\nh : a ≤ x\nhx : x ∈ []\n⊢ a ≤ foldr max ⊥ []\n\ncase cons\nα : Type u_1\nβ : Type ?u.114493\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl✝¹ l✝ : List α\na x : α\nhx✝ : ... | [
428,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformContinuous.div | [] | [
85,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_one | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/LinearAlgebra/DirectSum/TensorProduct.lean | TensorProduct.directSumRight_tmul_lof | [
{
"state_after": "R : Type u\ninst✝¹⁰ : CommRing R\nι₁ : Type v₁\nι₂ : Type v₂\ninst✝⁹ : DecidableEq ι₁\ninst✝⁸ : DecidableEq ι₂\nM₁ : ι₁ → Type w₁\nM₁' : Type w₁'\nM₂ : ι₂ → Type w₂\nM₂' : Type w₂'\ninst✝⁷ : (i₁ : ι₁) → AddCommGroup (M₁ i₁)\ninst✝⁶ : AddCommGroup M₁'\ninst✝⁵ : (i₂ : ι₂) → AddCommGroup (M₂ i₂)\... | [
183,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.OrdConnected.out | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Order/Circular.lean | sbtw_asymm | [] | [
251,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.tendsto_rightLim | [] | [
346,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_insert | [] | [
2049,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.lift_unique | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nr : Setoid α\nf : α → β\nH : r ≤ ker f\ng : Quotient r → β\nHg : f = g ∘ Quotient.mk''\nx✝ : Quotient r\nx : α\n⊢ Quotient.lift f H (Quot.mk Setoid.r x) = g (Quot.mk Setoid.r x)",
"state_before": "α : Type u_1\nβ : Type u_2\nr : Setoid α\nf : α → β\nH... | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.lastFun_subtypeVal | [] | [
702,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_inv | [] | [
946,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_le_map_commutator | [] | [
188,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.196339\nm : Type u_2\nn : Type ?u.196345\no : Type ?u.196348\nm' : o → Type ?u.196353\nn' : o → Type ?u.196358\nR : Type u_1\nS : Type ?u.196364\nα : Type v\nβ : Type w\nγ : Type ?u.196371\ninst✝⁶ : Fintype m\ninst✝⁵ : Fintype n\ninst✝⁴ : Monoid R\ni... | [
890,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.not | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\np : Prop\nL2 L3 : List (α × Bool)\nx✝¹ : α\nx✝ : Bool\nh : reduce [] = L2 ++ (x✝¹, x✝) :: (x✝¹, !x✝) :: L3\n⊢ p",
"tactic": "cases L2 <;> injections"
},
{
"state_after": "α : Type u\... | [
1185,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_option | [] | [
1094,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
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