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/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.eq_neg_self_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ θ = -θ ↔ θ = 0 ∨ θ = ↑π",
"tactic": "rw [← add_eq_zero_iff_eq_neg, ← two_nsmul, two_nsmul_eq_zero_iff]"
}
] | [
215,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.leftMoves_neg | [] | [
1242,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.mem_atBot_sets | [] | [
170,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.sigmaCongrRight_refl | [] | [
749,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | LinearIsometry.integral_comp_comm | [] | [
1134,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.one_mem_div_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.606313\nα : Type u_1\nβ : Type ?u.606319\nγ : Type ?u.606322\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq β\ninst✝² : Group α\ninst✝¹ : DivisionMonoid β\ninst✝ : MonoidHomClass F α β\nf : F\ns t : Finset α\na b : α\n⊢ 1 ∈ s / t ↔ ¬Disjoint s t",
... | [
1116,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/Control/Traversable/Instances.lean | Option.id_traverse | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα : Type u_1\nx : Option α\n⊢ Option.traverse pure x = x",
"tactic": "cases x <;> rfl"
}
] | [
37,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.integrable_of_boundedContinuous_to_real | [
{
"state_after": "Ω : Type u_1\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nf : Ω →ᵇ ℝ\n⊢ HasFiniteIntegral ↑f",
"state_before": "Ω : Type u_1\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasu... | [
682,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_split | [
{
"state_after": "case nil\nι : Type ?u.1166\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : List α\nh✝ : a ∈ l\nh : a ∈ []\n⊢ ∃ s t, [] = s ++ a :: t\n\ncase cons\nι : Type ?u.1166\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl✝ : List α\nh✝ : a ∈ l✝\nb : ... | [
110,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_upperSemicontinuous_lt_integral_gt | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : WeaklyRegular μ\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\... | [
563,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.range_coe' | [] | [
157,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Topology/Algebra/UniformFilterBasis.lean | AddGroupFilterBasis.uniformAddGroup | [] | [
42,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
11
] |
Mathlib/Data/List/Join.lean | List.drop_sum_join | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.6451\ni : ℕ\n⊢ drop (sum (take i (map length []))) (join []) = join (drop i [])\n\ncase cons\nα : Type u_1\nβ : Type ?u.6451\nhead✝ : List α\ntail✝ : List (List α)\ntail_ih✝ : ∀ (i : ℕ), drop (sum (take i (map length tail✝))) (join tail✝) = join (drop i tail... | [
103,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_eq_nnnorm_vsub' | [] | [
93,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.re_le_abs | [] | [
1043,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.rank_pow_quot | [
{
"state_after": "R : Type u\ninst✝⁵ : CommRing R\nS : Type v\ninst✝⁴ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhfp : NeZero e\ninst✝³ : IsDomain S\ninst✝² : IsDedekindDomain S\ninst✝¹ : IsMaximal p\ninst✝ : IsPrime P\nhP0 : P ≠ ⊥\ni : ℕ\nhi : i ≤ e\nQ : ℕ → Prop :=\n fun i => Module.rank (R ⧸ p) { ... | [
647,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_right_comm | [] | [
386,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.image_range_orderOf | [
{
"state_after": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nha : ∀ (x : α), x ∈ ↑(zpowers a)\n⊢ image (fun i => a ^ i) (range (orderOf a)) = univ",
"state_before": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nha : ∀ (x : α), x ∈ zpowe... | [
298,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.update_idem | [
{
"state_after": "case h\nα✝ : Sort u\nβ✝ : α✝ → Sort v\nα' : Sort w\ninst✝² : DecidableEq α✝\ninst✝¹ : DecidableEq α'\nf✝ g : (a : α✝) → β✝ a\na✝ : α✝\nb✝ : β✝ a✝\nα : Sort u_1\ninst✝ : DecidableEq α\nβ : α → Sort u_2\na : α\nv w : β a\nf : (a : α) → β a\nb : α\n⊢ update (update f a v) a w b = update f a w b",... | [
682,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FinitePresentation.of_surjective | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nC : Type ?u.1176485\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : CommRing C\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ninst✝ : Algebra R C\nf : A →ₐ[R] B\nhf : Surjective ↑f\nhker : Ideal.FG... | [
522,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Combinatorics/Derangements/Finite.lean | numDerangements_zero | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Computability/Primrec.lean | list_casesOn' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nH : Nat.Primrec fun n => encode (decode n)\nf : α → List β\ng : α → σ\nh : α → β × List β → σ\nhf : Primrec f\nhg : Primrec g\nhh : Primrec₂ h\nthis✝... | [
892,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
9
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.fundamentalDomain_bounded | [
{
"state_after": "case intro\nE : Type u_3\nι : Type u_1\nK : Type u_2\ninst✝⁵ : NormedLinearOrderedField K\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\nb : Basis ι K E\ninst✝² : FloorRing K\ninst✝¹ : Finite ι\ninst✝ : HasSolidNorm K\nval✝ : Fintype ι\n⊢ Metric.Bounded (fundamentalDomain b)",
"... | [
210,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/Cover.lean | Wcovby.wcovby_iff_le | [] | [
76,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.comp_sup_eq_sup_comp | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.63465\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Type ?u.63477\nκ : Type ?u.63480\ninst✝³ : SemilatticeSup α\ninst✝² : OrderBot α\ns✝ s₁ s₂ : Finset β\nf✝ g✝ : β → α\na : α\ninst✝¹ : SemilatticeSup γ\ninst✝ : OrderBot γ\ns : Finset β\nf : β → α\n... | [
204,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_bit1 | [] | [
243,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/Convex/Independent.lean | ConvexIndependent.range | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nι : Type u_3\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns t : Set E\np : ι → E\nhc : ConvexIndependent 𝕜 p\nf : ↑(Set.range p) → ι := fun x => Exists.choose (_ : ↑x ∈ Set.range p)\n⊢ ConvexIndependent 𝕜 Subtype.val",
"state_be... | [
106,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
11
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.proj_eq_iff | [] | [
419,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_mul_cancel | [
{
"state_after": "no goals",
"state_before": "n m : Nat\nH : n ∣ m\n⊢ m / n * n = m",
"tactic": "rw [Nat.mul_comm, Nat.mul_div_cancel' H]"
}
] | [
737,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
736,
11
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coord_repr_symm | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.177420\nR : Type u_2\nR₂ : Type ?u.177426\nK : Type ?u.177429\nM : Type u_3\nM' : Type ?u.177435\nM'' : Type ?u.177438\nV : Type u\nV' : Type ?u.177443\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCo... | [
266,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.restrict_extend | [
{
"state_after": "case h.h.h\nC : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y✝ : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nx : FamilyOfElements P R\nt : FamilyOfElements.Compatible x\nY : C\nf : Y ⟶ X\nhf : R f\n⊢ FamilyOfElements.restrict (_ : R ≤ (generate R).arrows) (FamilyOfE... | [
214,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Group/Conj.lean | ConjClasses.quot_mk_eq_mk | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.286346\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\na : R\nx : σ\n⊢ degreeOf x (↑C a) = 0",
"tactic": "classical simp [degreeOf_def, degrees_C]"
},
{
"state_afte... | [
517,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Data/Set/Sups.lean | Set.iUnion_image_inf_left | [] | [
334,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.coe_inv' | [
{
"state_after": "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\nA : { x // x ∈ symplecticGroup l R }\n⊢ (-J l R) ⬝ (↑A)ᵀ ⬝ J l R ⬝ ↑A = 1",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\nin... | [
206,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.realize_noBotOrder | [] | [
259,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | card_vector | [
{
"state_after": "α : Type u_1\nβ : Type ?u.13103\nγ : Type ?u.13106\ninst✝ : Fintype α\nn : ℕ\n⊢ Fintype.card (Fin n → α) = Fintype.card α ^ n",
"state_before": "α : Type u_1\nβ : Type ?u.13103\nγ : Type ?u.13106\ninst✝ : Fintype α\nn : ℕ\n⊢ Fintype.card (Vector α n) = Fintype.card α ^ n",
"tactic": "r... | [
157,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter_sublist | [] | [
150,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Set/Basic.lean | Set.top_eq_univ | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto | [] | [
466,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_pos | [] | [
98,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.eq_of_comm | [] | [
288,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/GroupTheory/Torsion.lean | IsTorsion.extension_closed | [
{
"state_after": "case intro.intro\nG : Type u_1\nH : Type u_2\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : Group H\nf : G →* H\nhN : N = MonoidHom.ker f\ntH : IsTorsion H\ntN : IsTorsion { x // x ∈ N }\ng : G\nngn : ℕ\nngnpos : 0 < ngn\nhngn : ↑f g ^ ngn = 1\n⊢ ∃ n, 0 < n ∧ g ^ n = 1",
"state_before": "G : T... | [
119,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subsingleton.strictAnti | [] | [
503,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
11
] |
Mathlib/Data/Set/Function.lean | Set.InvOn.bijOn | [] | [
1193,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.isOpenMap_mk | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.48723\nZ : Type ?u.48726\nα : Type ?u.48729\nι : Type ?u.48732\nπ : ι → Type ?u.48737\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns✝ : Set ... | [
458,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.toList_ne_nil | [] | [
3374,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3373,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.arg_expMapCircle | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ ↑(arg ↑(expMapCircle ↑x✝)) = ↑x✝",
"state_before": "θ : Angle\n⊢ ↑(arg ↑(expMapCircle θ)) = θ",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ ↑(arg ↑(expMapCircle ↑x✝)) = ↑x✝",
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154,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/GroupTheory/Sylow.lean | Sylow.conj_eq_normalizer_conj_of_mem | [] | [
395,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
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Mathlib/RingTheory/WittVector/Basic.lean | WittVector.map_injective | [] | [
285,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/Logic/Equiv/List.lean | Encodable.length_le_encode | [] | [
88,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
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Mathlib/Data/Finset/Pointwise.lean | Finset.image_mul_right' | [
{
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1175,
87
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1174,
1
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Mathlib/RingTheory/Nilpotent.lean | Module.End.IsNilpotent.mapQ | [
{
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"state_before": "R S : Type u\nx y : R\nM : Type v\nin... | [
249,
26
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246,
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Mathlib/Topology/UniformSpace/Equicontinuity.lean | UniformInducing.uniformEquicontinuous_iff | [
{
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369,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.comap_unop_pow | [] | [
531,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_or_equiv_or_gf | [
{
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"state_before": "x y : PGame\n⊢ x ⧏ y ∨ (x ≈ y) ∨ y ⧏ x",
"tactic": "by_cases h : x ⧏ y"
},
{
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"state_before": "case pos\n... | [
875,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
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Mathlib/Algebra/QuadraticDiscriminant.lean | quadratic_eq_zero_iff_of_discrim_eq_zero | [
{
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"state_before": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NeZero 2\na b c x✝ : K\nha : a ≠ 0\nh : discrim ... | [
111,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.zero_bot | [] | [
697,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
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Std/Data/List/Lemmas.lean | List.replicate_succ | [] | [
276,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
276,
1
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Mathlib/Computability/Primrec.lean | Primrec.vector_tail | [
{
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1305,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Data/List/Forall2.lean | Relator.LeftUnique.forall₂ | [] | [
144,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.comp_apply | [] | [
424,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Order/Antichain.lean | IsAntichain.image | [
{
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"state... | [
95,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Combinatorics/Additive/Energy.lean | Finset.multiplicativeEnergy_mono | [] | [
56,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_im_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1286514\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⊢ ↑im (inner x y) = -↑im (inner y ... | [
472,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Order/Max.lean | isBot_toDual_iff | [] | [
233,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add | [] | [
173,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/RingTheory/Filtration.lean | Ideal.iInf_pow_eq_bot_of_localRing | [
{
"state_after": "case h.e'_2.h.e'_4.h\nR M : Type u\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nI : Ideal R\nF F' : Filtration I M\ninst✝¹ : IsNoetherianRing R\ninst✝ : LocalRing R\nh : I ≠ ⊤\nx✝ : ℕ\n⊢ I ^ x✝ = I ^ x✝ • ⊤",
"state_before": "R M : Type u\ninst✝⁴ : CommRing R\ninst✝³... | [
477,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Set/Equitable.lean | Set.equitableOn_iff_exists_eq_eq_add_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5357\ns : Set α\nf : α → ℕ\n⊢ EquitableOn s f ↔ ∃ b, ∀ (a : α), a ∈ s → f a = b ∨ f a = b + 1",
"tactic": "simp_rw [equitableOn_iff_exists_le_le_add_one, Nat.le_and_le_add_one_iff]"
}
] | [
67,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.isSatisfiable_iUnion_iff_isSatisfiable_iUnion_finset | [
{
"state_after": "no goals",
"state_before": "L : Language\nT✝ : Theory L\nα : Type w\nn : ℕ\nT' : Theory L\nι : Type u_1\nT : ι → Theory L\n⊢ IsSatisfiable (⋃ (i : ι), T i) ↔ ∀ (s : Finset ι), IsSatisfiable (⋃ (i : ι) (_ : i ∈ s), T i)",
"tactic": "classical\n refine'\n ⟨fun h s => h.mono (Set.iUni... | [
204,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_of_le_mul_of_le_one_of_nonneg_left | [] | [
946,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.comp' | [] | [
657,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.sSup_smul_of_nonneg | [
{
"state_after": "case inl\nι : Sort ?u.3544\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : MulActionWithZero α ℝ\ninst✝ : OrderedSMul α ℝ\na : α\nha : 0 ≤ a\n⊢ sSup (a • ∅) = a • sSup ∅\n\ncase inr\nι : Sort ?u.3544\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : MulActionWithZero α ℝ\ninst✝ : O... | [
64,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/Topology/Basic.lean | interior_iInter | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι✝ : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝¹ : TopologicalSpace α\nι : Type u_1\ninst✝ : Finite ι\nf : ι → Set α\nval✝ : Fintype ι\n⊢ interior (⋂ (i : ι), f i) = ⋂ (i : ι), interior (f i)",
"state_before": "α : Type u\nβ : Type v\nι✝... | [
370,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_mono | [] | [
662,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.coe_coe_fst | [] | [
235,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_sdiff_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.61968\nα : Type u_1\nβ : Type ?u.61974\nπ : ι → Type ?u.61979\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b \\ a = b \\ a",
"tactic": "rw [symmDiff_def, sup_sdiff, sdiff_idem, sdiff_sdiff_self, bot_sup_eq]"
}
] | [
425,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.bound | [] | [
100,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Symmetric.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.braiding_naturality | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX✝ Y✝ : C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX X' Y Y' : C\nf : X ⟶ Y\ng : X' ⟶ Y'\n⊢ IsLimit.lift (ℬ Y Y').isLimit (BinaryFan.mk (BinaryFan.fst (ℬ X X').cone ≫ f) (BinaryFan.snd (ℬ X X').cone ≫ g)) ≫\n (IsLimit.conePoi... | [
43,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
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src/lean/Init/Data/List/Basic.lean | List.length_dropLast_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nas : List α\n⊢ length (dropLast (a :: as)) = length as",
"tactic": "match as with\n| [] => rfl\n| b::bs =>\n have ih := length_dropLast_cons b bs\n simp[dropLast, ih]"
},
{
"state_after": "no goals",... | [
788,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
783,
9
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_mem_mul | [] | [
344,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nr : α → β → Prop\ns : Finset α\nt : Finset β\na a' : α\nb b' : β\ninst✝² : DecidablePred (r a)\ninst✝¹ : (a : α) → Decidable (r a b)\nm n : ℕ\ninst✝ : (a : α) → (b : β) → Decidable (r a b)\n⊢ (∑ x in s, ∑ a in t, if r x a then 1 else 0) = ∑ x in t, ∑ a in s, if r a ... | [
86,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.integral_circleTransform | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR : ℝ\nz w : ℂ\ninst✝ : CompleteSpace E\nf : ℂ → E\n⊢ (∫ (θ : ℝ) in 0 ..2 * π,\n (2 * ↑π * I)⁻¹ • ((0 + ↑R * exp (↑θ * I)) * I) • (z + ↑R * exp (↑θ * I) - w)⁻¹ • f (z + ↑R * exp (↑θ * I))) =\n (2 * ↑π * I)⁻¹ •\n ... | [
77,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_monoidHom_refl | [] | [
514,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
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] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.map_rename | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type u_4\nα : Type ?u.73427\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : R →+* S\ng : σ → τ\np : MvPolynomial σ R\n⊢ ↑(map f) (↑(rename g) p) = ↑(rename g) (↑(map f) p)",
"tactic": "apply MvPolynomial.in... | [
80,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_copy | [] | [
1256,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu : V\np : Walk G u u\n⊢ length p = 0 ↔ p = nil",
"tactic": "cases p <;> simp"
}
] | [
439,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.eq_of_separated_of_uniformContinuous | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : SeparatedSpace β\nf : α → β\nx y : α\nH : UniformContinuous f\nh : x ≈ y\n⊢ SeparatedSpace β",
"tactic": "infer_instance"
}
] | [
350,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.inverseImage | [
{
"state_after": "case left\nC : Type u\ninst✝¹ : Category C\nD : Type u_2\ninst✝ : Category D\nP : MorphismProperty D\nh : RespectsIso P\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} (e : X ≅ Y) (f : Y ⟶ Z),\n MorphismProperty.inverseImage P F f → MorphismProperty.inverseImage P F (e.hom ≫ f)\n\ncase right\nC : Type u\ninst✝... | [
376,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.isMin_of_apply | [] | [
579,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Data/List/Basic.lean | List.map₂Left'_nil_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.462573\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option β → γ\nas : List α\n⊢ map₂Left' f as [] = (map (fun a => f a none) as, [])",
"tactic": "cases as <;> rfl"
}
] | [
3996,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3995,
1
] |
Mathlib/Algebra/Module/Basic.lean | invOf_two_smul_add_invOf_two_smul | [] | [
116,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_min | [] | [
185,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
185,
11
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_eq_zero_iff | [
{
"state_after": "case mp\nR : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na : A\nh : mulRight R a = 0\n⊢ a = 0\n\ncase mpr\nR : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na : A\nh : a = 0\n⊢ mulRight R a = 0",
"s... | [
205,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.neg | [] | [
1270,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/Data/Set/Image.lean | Function.LeftInverse.image_image | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.108588\nα : Type u_1\nβ : Type u_2\nf : α → β\ng : β → α\nh : LeftInverse g f\ns : Set α\n⊢ g '' (f '' s) = s",
"tactic": "rw [← image_comp, h.comp_eq_id, image_id]"
}
] | [
1352,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1351,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_inv_eq_iff_eq_mul₀ | [] | [
48,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_le_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.261406\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng✝ g₁ g₂ : Filter β\nm✝ : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf g : Filter α\nm : α → β\nhm : Injective m\n⊢ map m f ≤ map m g ↔ f ≤ g",
"tactic": "rw [map_le_iff_l... | [
2320,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2319,
1
] |
Std/Data/List/Lemmas.lean | List.getLastD_nil | [] | [
461,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
461,
9
] |
Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.cderiv_sub | [
{
"state_after": "E : Type u_1\nι : Type ?u.20084\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nU K : Set ℂ\nz : ℂ\nM r δ : ℝ\nφ : Filter ι\nF : ι → ℂ → E\nf g : ℂ → E\nhr : 0 < r\nhf : ContinuousOn f (sphere z r)\nhg : ContinuousOn g (sphere z r)\nh1 : ContinuousOn (fun w =... | [
80,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
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