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/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.Subsingleton.stronglyMeasurable' | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.21646\nβ✝ : Type ?u.21649\nγ : Type ?u.21652\nι : Type ?u.21655\ninst✝³ : Countable ι\nα : Type u_1\nβ : Type u_2\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : Subsingleton α\nf : α → β\nx y : α\n⊢ f x = f y",
"tactic": "rw [... | [
186,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.zero_ne_trop_coe | [] | [
250,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.subset_closure_withConstants | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.681989\nP : Type ?u.681992\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\nA s : Set M\nh : A ⊆ ↑S\na : M\nha : a ∈ A\n⊢ a ∈ ↑(LowerAdjoint.toFun (closure (L[[↑A]])) s)",
"state_before": "L : Language\nM : ... | [
774,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.one_lt_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.135473\nβ : Type ?u.135476\nM : Type u_2\nN : Type ?u.135482\nG : Type ?u.135485\nk : Type ?u.135488\nR : Type ?u.135491\ninst✝ : OrderedCancelCommMonoid M\nf g : ι → M\ns t : Finset ι\nh : ∀ (i : ι), i ∈ s → 1 < f i\nhs : Finset.Nonemp... | [
509,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.sinh | [] | [
1185,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | Differentiable.dist | [] | [
257,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.quot_mk_eq_coe | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_add_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14902596\n𝕜 : Type ?u.14902599\nE : Type u_1\nF : Type ?u.14902605\nA : Type ?u.14902608\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nhc : c ≠ 0\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (d + x / ... | [
791,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | Filter.Tendsto.zero_mul_isBoundedUnder_le | [] | [
216,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_union_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.501362\nγ : Type ?u.501365\ninst✝ : DecidableEq α\ns t u : Multiset α\n⊢ Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u",
"tactic": "simp [Disjoint, or_imp, forall_and]"
}
] | [
2981,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2980,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_int_cast | [
{
"state_after": "no goals",
"state_before": "x : ℂ\nn : ℕ\n⊢ x ^ ↑↑n = x ^ ↑n",
"tactic": "simp"
},
{
"state_after": "x : ℂ\nn : ℕ\n⊢ x ^ ↑-[n+1] = (x ^ (n + 1))⁻¹",
"state_before": "x : ℂ\nn : ℕ\n⊢ x ^ ↑-[n+1] = x ^ -[n+1]",
"tactic": "rw [zpow_negSucc]"
},
{
"state_after": "no... | [
141,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/CategoryTheory/Abelian/Images.lean | CategoryTheory.Abelian.image.fac | [] | [
64,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_compRel | [] | [
158,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_ne_neg_one | [
{
"state_after": "z : 𝔻\n⊢ ↑abs ↑z ≠ 1",
"state_before": "z : 𝔻\n⊢ ↑abs ↑z ≠ ↑abs (-1)",
"tactic": "rw [abs.map_neg, map_one]"
},
{
"state_after": "no goals",
"state_before": "z : 𝔻\n⊢ ↑abs ↑z ≠ 1",
"tactic": "exact z.abs_ne_one"
}
] | [
68,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_vadd_apply | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV1 : Type u_3\nP1 : Type u_1\nV2 : Type ?u.423603\nP2 : Type ?u.423606\nV3 : Type ?u.423609\nP3 : Type ?u.423612\nV4 : Type ?u.423615\nP4 : Type ?u.423618\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 ... | [
538,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Filter.Tendsto.log | [] | [
383,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_inter_add_diff | [] | [
125,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.ker_mkQ | [
{
"state_after": "case h\nR : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type ?u.220917\nM₂ : Type ?u.220920\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nx✝ : M\n⊢ x✝ ∈ ker (mkQ p) ↔ x✝ ∈... | [
381,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_two | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11869\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\n⊢ a ^ 2 = a * a",
"tactic": "rw [pow_succ, pow_one]"
}
] | [
105,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | hasStrictDerivAt_of_hasDerivAt_of_continuousAt | [] | [
1357,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1353,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | is_const_of_fderiv_eq_zero | [
{
"state_after": "E : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nF : Type ?u.251275\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\n𝕜 : Type u_1\nG : Type u_3\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → G\n... | [
602,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Embedding.isSeparable_preimage | [] | [
1949,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1947,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_right | [] | [
2909,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2908,
1
] |
Mathlib/Order/Atoms.lean | IsAtom.Iic_eq | [] | [
96,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_comp_map | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\ng : β → γ\nx : Option α\n⊢ (Option.map g ∘ Option.map f) x = Option.map (g ∘ f) x",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\ng : β → γ\n⊢ Option.map g ∘ Option.map f = Option.map (g ∘ f)",
"tactic... | [
152,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
151,
9
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_zsmulRec | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1031657\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : SeminormedAddCommGroup β\nf g : α →ᵇ β\nx : α\nC : ℝ\nn : ℕ\n⊢ ↑(zsmulRec (Int.ofNat n) f) = Int.ofNat n • ↑f",
"tactic": "rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul... | [
973,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.rotateR | [
{
"state_after": "α : Type u_1\ninst✝ : Preorder α\nl : Ordnode α\nx : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhl : Valid' o₁ l ↑x\nhr : Valid' (↑x) r o₂\nH1 : ¬size l + size r ≤ 1\nH2 : delta * size r < size l\nH3 : 2 * size l ≤ 9 * size r + 5 ∨ size l ≤ 3\n⊢ Valid' o₂ (Ordnode.dual (Ordnode.rotateR ... | [
1303,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_assoc_aux | [
{
"state_after": "ι : Sort ?u.52859\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns✝ t✝ u✝ : Set E\nx y : E\ns t u : Set E\n⊢ ∀ (x : E),\n (∃ a, (∃ a_1, a_1 ∈ s ∧ ∃ b, b ∈ t ∧ a ∈ segment 𝕜 a_1 b) ∧ ∃ b, b ∈ u ∧ x ∈ segment 𝕜 a b) →\n ∃ a, ... | [
154,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.X_pow_card_pow_sub_X_ne_zero | [] | [
257,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_one | [
{
"state_after": "x y : ℝ\n⊢ mk 1 = { cauchy := 1 }",
"state_before": "x y : ℝ\n⊢ mk 1 = 1",
"tactic": "rw [← ofCauchy_one]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ mk 1 = { cauchy := 1 }",
"tactic": "rfl"
}
] | [
331,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_comp | [] | [
2616,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2614,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.image_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.60024\nι : Sort ?u.60027\nπ : α → Type ?u.60032\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nhf : LeftInvOn f' f s\n⊢ f' '' (f '' s) = s",... | [
1088,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_top | [] | [
539,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.map_rootOfSplits | [] | [
317,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Topology/PathConnected.lean | IsPathConnected.isConnected | [
{
"state_after": "X : Type u_1\nY : Type ?u.695184\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.695199\nF : Set X\nhF : IsPathConnected F\n⊢ ConnectedSpace ↑F",
"state_before": "X : Type u_1\nY : Type ?u.695184\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y... | [
1165,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_ofReal | [] | [
458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.sub_apply | [] | [
892,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroMorphisms.ext | [
{
"state_after": "case w\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\nI J : HasZeroMorphisms C\n⊢ ∀ (X Y : C), Zero.zero = Zero.zero",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\nI J : HasZeroMorphisms C\n⊢ I = J",
"tactic": "apply ext_aux"
... | [
119,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.mclosure_subset | [] | [
616,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.closure_range | [] | [
62,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iInf_add | [] | [
2400,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2398,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.hasZeroObject_of_hasInitial_object | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasInitial C\nX : C\nf : X ⟶ ⊥_ C\n⊢ f = default",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasInitial C\n... | [
552,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.ne_neg_self | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁵ : StrictOrderedCommRing R\nM : Type u_2\nN : Type ?u.180935\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nx✝ y : M\ninst✝ : NoZeroSMulDivisors R M\nx : M\nhx : x ≠ 0\n⊢ rayOfNeZero R x hx ≠ -rayOfNeZero R x hx",
"s... | [
480,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.toConvexCone_le_iff | [] | [
528,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.zeta_apply | [] | [
453,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.liftHom_mk | [] | [
337,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk'_surjective | [] | [
97,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/ContinuousOn.lean | preimage_coe_mem_nhds_subtype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.304580\nγ : Type ?u.304583\nδ : Type ?u.304586\ninst✝ : TopologicalSpace α\ns t : Set α\na : ↑s\n⊢ Subtype.val ⁻¹' t ∈ 𝓝 a ↔ t ∈ 𝓝[s] ↑a",
"tactic": "rw [← map_nhds_subtype_val, mem_map]"
}
] | [
507,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Topology/Basic.lean | isClosed_imp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np✝ p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\np q : α → Prop\nhp : IsOpen {x | p x}\nhq : IsClosed {x | q x}\n⊢ IsClosed {x | p x → q x}",
"tactic": "simpa only [imp_iff_not_or] using hp.isClos... | [
267,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.suffix | [] | [
315,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.cmpLT.trans | [] | [
31,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
30,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_le_of_forall_set_integral_le | [
{
"state_after": "α : Type u_1\nE : Type ?u.79505\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf✝ f g : α → ℝ\nhf : Integrable f\nhg : Integrable g\nhf_le : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → (∫ (x : ... | [
303,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | LinearIsometry.extend_apply | [
{
"state_after": "ι : Type ?u.1751792\nι' : Type ?u.1751795\n𝕜 : Type u_1\ninst✝¹² : IsROrC 𝕜\nE : Type ?u.1751804\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : InnerProductSpace 𝕜 E\nE' : Type ?u.1751824\ninst✝⁹ : NormedAddCommGroup E'\ninst✝⁸ : InnerProductSpace 𝕜 E'\nF : Type ?u.1751842\ninst✝⁷ : NormedAddC... | [
963,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Algebra/Lie/SkewAdjoint.lean | skewAdjointMatricesLieSubalgebraEquivTranspose_apply | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousAt.inv₀ | [] | [
131,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
8
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.837272\nβ : Type ?u.837275\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\n⊢ ENNReal.toReal (a / b) = ENNReal.toReal a / ENNReal.toReal b",
"tactic": "rw [div_eq_mul_inv, toReal_mul, toReal_inv, div_eq_mul_inv]"
}
] | [
2326,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2325,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Reaches₀.refl | [] | [
788,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_add_right | [] | [
87,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
86,
11
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.FG.sup | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nN₁ N₂ : Submodule R M\nhN₁ : FG N₁\nhN₂ : FG N₂\nt₁ : Set M\nht₁ : Set.Finite t₁ ∧ span R t₁ = N₁\nt₂ : Set M\nht₂ : Set.Finite t₂ ∧ span R t₂ = N₂\n⊢ span R (t₁ ∪ t₂)... | [
185,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.map_roots_le | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b✝ : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\np : A[X]\nf : A →+* B\nh : map f p ≠ 0\nb : B\n⊢ Multiset.count b (Multiset.map (↑f) (roots p)) ≤ rootMultiplicity b (map f p)",
... | [
1186,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.compRel_gen_gen_subset_gen_compRel | [] | [
116,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
9
] |
Mathlib/Topology/SubsetProperties.lean | isIrreducible_irreducibleComponent | [] | [
1801,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1800,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_empty_eq | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.156154\n𝕜 : Type ?u.156157\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nx✝¹ x✝ : V\n⊢ Adj (deleteEdges G ∅) x✝¹ x✝ ↔ Adj G x✝¹ x✝",
"state_before": "ι : Sort ?u.156154\n𝕜 : Type ?u.156157\nV : Type u\... | [
1141,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_conjTranspose | [] | [
354,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.induction_on' | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝ : Semiring R\nM : R[T;T⁻¹] → Prop\np : R[T;T⁻¹]\nh_add : ∀ (p q : R[T;T⁻¹]), M p → M q → M (p + q)\nh_C_mul_T : ∀ (n : ℤ) (a : R), M (↑C a * T n)\na : R\n⊢ M (↑C a)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nM : R[T;T⁻¹] → Prop\np : R[T;T⁻¹]\nh... | [
316,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
11
] |
Mathlib/Algebra/Group/Basic.lean | eq_div_iff_mul_eq'' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.70975\nβ : Type ?u.70978\nG : Type u_1\ninst✝ : CommGroup G\na b c d : G\n⊢ a = b / c ↔ c * a = b",
"tactic": "rw [eq_div_iff_mul_eq', mul_comm]"
}
] | [
953,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Algebra/Algebra/Pi.lean | Pi.constAlgHom_eq_algebra_ofId | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_eq_comap_nhds_zero | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nX : Type ?u.203876\nι : Type ?u.203879\ninst✝ : PseudoMetricSpace α\ns : Set (α × α)\n⊢ s ∈ 𝓤 α ↔ s ∈ comap (fun p => dist p.fst p.snd) (𝓝 0)",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.203876\nι : Type ?u.203879\ninst✝ : PseudoMetricSpace α\n⊢ ... | [
1455,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1451,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_eq_zero_iff_deg_eq_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.514960\n⊢ leadingCoeff p = 0 ↔ degree p = ⊥",
"tactic": "rw [leadingCoeff_eq_zero, degree_eq_bot]"
}
] | [
672,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.continuousAt_zero' | [
{
"state_after": "R : Type ?u.1359761\nR' : Type ?u.1359764\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1359770\n𝕜₃ : Type ?u.1359773\n𝕝 : Type ?u.1359776\nE : Type u_1\nE₂ : Type ?u.1359782\nE₃ : Type ?u.1359785\nF : Type ?u.1359788\nG : Type ?u.1359791\nι : Type ?u.1359794\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : S... | [
1125,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Combinatorics/SetFamily/Kleitman.lean | Finset.card_biUnion_le_of_intersecting | [
{
"state_after": "ι : Type u_1\nα : Type u_2\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nonempty α\ns : Finset ι\nf : ι → Finset (Finset α)\nhf : ∀ (i : ι), i ∈ s → Set.Intersecting ↑(f i)\nthis : DecidableEq ι\n⊢ card (Finset.biUnion s f) ≤ 2 ^ Fintype.card α - 2 ^ (Fintype.card α - card s)",
"st... | [
88,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.SpecialLinearGroup.coeToGL_det | [] | [
172,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.mono | [] | [
90,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.congr_of_eventuallyEq | [] | [
590,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.succ | [] | [
268,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inf_eq_inter | [] | [
1316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.one_kronecker | [] | [
356,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
src/lean/Init/Data/List/Basic.lean | List.of_concat_eq_concat | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas bs : List α\na b : α\nh : concat as a = concat bs b\n⊢ as = bs ∧ a = b",
"tactic": "match as, bs with\n| [], [] => simp [concat] at h; simp [h]\n| [_], [] => simp [concat] at h\n| _::_::_, [] => simp [concat] at h\n| []... | [
848,
78
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
841,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.to_of_int | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1062538\nn : ℤ\n⊢ ↑↑0 = 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.1062538\nn : ℤ\n⊢ ∀ (k : ℤ), 0 ≤ k → ↑↑k = k → ↑↑(k + 1) = k + 1",
"tactic": "simp"
},
{
"state_after": "no goals",
... | [
1556,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_assoc | [] | [
79,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
70,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.withDensity_rnDeriv_le | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.34335\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\nhl : HaveLebesgueDecomposition μ ν\n⊢ withDensity ν (rnDeriv μ ν) ≤ μ\n\ncase neg\nα : Type u_1\nβ : Type ?u.34335\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\nhl : ¬HaveLebesgueDecomposition μ ν\n⊢ with... | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.restrictScalars_apply | [] | [
465,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.of_smul_eq_one | [
{
"state_after": "R : Type u_2\nS : Type u_1\nM : Type u_3\na b : R\ns : S\ninst✝⁴ : Monoid S\ninst✝³ : SMul R M\ninst✝² : SMul R S\ninst✝¹ : MulAction S M\ninst✝ : IsScalarTower R S M\nh : a • s = 1\n⊢ IsSMulRegular M 1",
"state_before": "R : Type u_2\nS : Type u_1\nM : Type u_3\na b : R\ns : S\ninst✝⁴ : M... | [
180,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.map_comp | [] | [
595,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.equiv_block_det | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.40762\nβ : Type ?u.40765\nm : Type u_1\nn : Type ?u.40771\no : Type ?u.40774\nm' : α → Type ?u.40779\nn' : α → Type ?u.40784\nR : Type v\ninst✝⁶ : CommRing R\nM✝ N : Matrix m m R\nb : m → α\ninst✝⁵ : DecidableEq m\ninst✝⁴ : Fintype m\ninst✝³ : Decida... | [
157,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_eq_self_of_ae_mem | [] | [
1794,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1790,
1
] |
Mathlib/Order/Zorn.lean | zorn_nonempty_preorder | [] | [
115,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.subset_product_image_snd | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.6733\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\ninst✝ : DecidableEq β\ni : β\n⊢ i ∈ image Prod.snd (s ×ˢ t) → i ∈ t",
"tactic": "simp (config := { contextual := true }) [mem_image]"
}
] | [
75,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/List/Forall2.lean | List.sublistForall₂_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.158809\nδ : Type ?u.158812\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nl₁ : List α\nl₂ : List β\nh : SublistForall₂ R l₁ l₂\n⊢ ∃ l, Forall₂ R l₁ l ∧ l <+ l₂\n\ncase mpr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.158809\nδ : Type ?u.1... | [
349,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Order/Bounds/Basic.lean | not_bddAbove_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns t : Set α\na b : α\ninst✝ : NoMaxOrder α\n⊢ ¬BddAbove univ",
"tactic": "simp [BddAbove]"
}
] | [
850,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearDependent_comp_subtype' | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.174501\nR : Type u_1\nK : Type ?u.174507\nM : Type u_2\nM' : Type ?u.174513\nM'' : Type ?u.174516\nV : Type u\nV' : Type ?u.174521\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMon... | [
371,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_le_of_range_subset | [] | [
1328,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
1
] |
Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.of_eq | [] | [
152,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_toEquiv_symm | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.eq_univ | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\ninst✝ : Subsingleton α\nx : α\nhx : x ∈ s\n⊢ s = univ",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\ninst✝ : Subsingleton α\n⊢ Set.Nonempt... | [
699,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/List/Sigma.lean | List.nodupKeys_singleton | [] | [
133,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_sup' | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₂ : Type ?u.100784\nK : Type ?u.100787\nM : Type u_1\nM₂ : Type ?u.100793\nV : Type ?u.100796\nS : Type ?u.100799\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R... | [
363,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ringHom_ext | [] | [
542,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.div_atTop | [
{
"state_after": "𝕜 : Type u_2\nα : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\na : 𝕜\nh : Tendsto f l (𝓝 a)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x => f x * (g x)⁻¹) l (𝓝 0)",
"state_before": "𝕜 : Type u_2\nα : Type u_... | [
146,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_nodal_not_at_node | [
{
"state_after": "F : Type u_2\ninst✝ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\nhx : ∀ (i : ι), i ∈ s → x ≠ v i\n⊢ ∀ (a : ι), a ∈ s → x ≠ v a",
"state_before": "F : Type u_2\ninst✝ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\nhx : ∀ (i : ι), i ∈... | [
515,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.