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/GroupTheory/GroupAction/Basic.lean | MulAction.mem_stabilizer_submonoid_iff | [] | [
170,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.cInf_eq_min' | [] | [
49,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.exists_local_min_mem_ball | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.542746\nι : Type ?u.542749\ninst✝⁴ : PseudoMetricSpace α\ninst✝³ : ProperSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : ConditionallyCompleteLinearOrder β\ninst✝ : OrderTopology β\nf : α → β\na z : α\nr : ℝ\nhf : ContinuousOn f (closedBall a r)\nhz : z ∈ clo... | [
2774,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2768,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_subset_iff | [] | [
476,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.ker_prodMap | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.119528\nM₆ : Type ?u.119531\nS : Type ?u.119534\ninst✝¹³ : Semiring R\ninst✝¹² : Semiring S\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M₂\ninst... | [
331,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.extend_apply_coe | [] | [
188,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.sub | [] | [
113,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.continuous_sin | [] | [
317,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.smul_posPart | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.changeOriginSeries_summable_aux₁ | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.1492746\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinea... | [
1217,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.ext | [] | [
906,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.isNilpotent_iff_exists_ucs_eq_top | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk : ℕ\nN N₁ N₂ : LieSubmodule R L M\n⊢ (∃ k, LieModule.lowerCentralSeries R L M k = ⊥) ↔ ∃ k,... | [
427,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.map_piecewise_add | [] | [
361,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Seq/Parallel.lean | Computation.parallel_empty | [
{
"state_after": "α : Type u\nβ : Type v\nS : WSeq (Computation α)\nh : WSeq.head S ~> none\nx✝ : Terminates (parallel S)\na : α\nm : a ∈ parallel S\nc : Computation α\ncs : c ∈ S\nright✝ : a ∈ c\n⊢ False",
"state_before": "α : Type u\nβ : Type v\nS : WSeq (Computation α)\nh : WSeq.head S ~> none\nx✝ : Term... | [
322,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ext | [
{
"state_after": "case mk.mk\nM : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.212365\ninst✝ : CommMonoid P\ng : LocalizationMap S N\ntoOneHom✝ : OneHom M N\nmap_mul'✝ : ∀ (x y : M), OneHom.toFun toOneHom✝ (x * y) = OneHom.toFun toOneHom✝ x * OneHom.toFun to... | [
559,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_natCast | [
{
"state_after": "n : ℕ\nx✝ : Decidable (↑n).Dom\n⊢ toWithTop ↑n = toWithTop ↑n",
"state_before": "n : ℕ\nx✝ : Decidable (↑n).Dom\n⊢ toWithTop ↑n = ↑n",
"tactic": "simp only [← toWithTop_some]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nx✝ : Decidable (↑n).Dom\n⊢ toWithTop ↑n = ... | [
579,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.distrib_lattice_lemma | [
{
"state_after": "no goals",
"state_before": "X : Type u_2\ninst✝³ : NormedAddCommGroup X\nM : Type u_1\ninst✝² : Ring M\ninst✝¹ : Module M X\ninst✝ : FaithfulSMul M X\nP Q R : { P // IsLprojection X P }\n⊢ (↑P + ↑(Pᶜ) * ↑R) * (↑P + ↑Q * ↑R * ↑(Pᶜ)) = ↑P + ↑Q * ↑R * ↑(Pᶜ)",
"tactic": "rw [add_mul, mul_a... | [
279,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.map_linearMap_add_haar_pi_eq_smul_add_haar | [
{
"state_after": "case intro\nι : Type u_1\ninst✝¹ : Finite ι\nf : (ι → ℝ) →ₗ[ℝ] ι → ℝ\nhf : ↑LinearMap.det f ≠ 0\nμ : Measure (ι → ℝ)\ninst✝ : IsAddHaarMeasure μ\nval✝ : Fintype ι\n⊢ map (↑f) μ = ENNReal.ofReal (abs (↑LinearMap.det f)⁻¹) • μ",
"state_before": "ι : Type u_1\ninst✝¹ : Finite ι\nf : (ι → ℝ) →... | [
214,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.normalClosure_subset_iff | [] | [
741,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Logic/Basic.lean | exists_prop_congr' | [] | [
903,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciInf_iff' | [] | [
1061,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.id_comp | [] | [
424,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
9
] |
Mathlib/Algebra/AddTorsor.lean | vsub_add_vsub_cancel | [
{
"state_after": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 p3 : P\n⊢ p1 -ᵥ p2 + (p2 -ᵥ p3) +ᵥ p3 = p1 -ᵥ p3 +ᵥ p3",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 p3 : P\n⊢ p1 -ᵥ p2 + (p2 -ᵥ p3) = p1 -ᵥ p3",
"tactic": "apply vadd... | [
151,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.305334\nδ : Type ?u.305337\nι : Type ?u.305340\nR : Type ?u.305343\nR' : Type ?u.305346\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\nf... | [
1781,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1779,
1
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | difference_quotients_converge_uniformly | [
{
"state_after": "case this\nι : Type u_3\nl : Filter ι\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx : E... | [
300,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Equalizer.Presieve.w | [
{
"state_after": "case w\nC : Type u₁\ninst✝¹ : Category C\nP : Cᵒᵖ ⥤ Type (max v₁ u₁)\nX : C\nR : Presieve X\nS : Sieve X\ninst✝ : HasPullbacks C\n⊢ ∀ (j : Discrete (((Y : C) × { f // R f }) × (Z : C) × { g // R g })),\n (forkMap P R ≫ firstMap P R) ≫\n limit.π (Discrete.functor fun fg => P.obj (Limi... | [
971,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.tendsto_atTop' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.142783\nι : Type ?u.142786\ninst✝³ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝² : Nonempty β\ninst✝¹ : SemilatticeSup β\ninst✝ : NoMaxOrder β\nu : β → α\na : α\n⊢ (∀ (ib : ℝ), 0 < ib → ∃ ia, True ∧ ∀ (x :... | [
1110,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.neg_of_mul_neg_right | [] | [
592,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.dualPairing_separatingLeft | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type ?u.39284\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\n⊢ Function.Injective ↑(dualPairing 𝕜 E)",
"state_before": "𝕜 : Type u_1\ninst✝⁴ : No... | [
126,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_union_distrib_left | [] | [
1757,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1756,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.54485\ninst✝¹ : Preorder α\ninst✝ : OrderTop α\na : α\n⊢ Ioc a ⊤ = Ioi a",
"tactic": "simp [← Ioi_inter_Iic]"
}
] | [
1002,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mul_coe_eq_smul | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.265744\nT : Type ?u.265747\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ a * ↑r = r • a",
"tactic": "rw [← coe_commutes, coe_mul_eq_smul]"
}
] | [
602,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_def | [] | [
233,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | ProbabilityMeasure.toFiniteMeasure_normalize_eq_self | [
{
"state_after": "case h\nΩ : Type u_1\ninst✝ : Nonempty Ω\nm0✝ : MeasurableSpace Ω\nμ✝ : FiniteMeasure Ω\nm0 : MeasurableSpace Ω\nμ : ProbabilityMeasure Ω\n⊢ ∀ (s : Set Ω),\n MeasurableSet s →\n (fun s => ENNReal.toNNReal (↑↑↑(normalize (ProbabilityMeasure.toFiniteMeasure μ)) s)) s =\n (fun s =>... | [
384,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_ratCast | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.add_linear | [] | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.diam_image | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.60676\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf : α → β\nhf : Isometry f\ns : Set α\n⊢ Metric.diam (f '' s) = Metric.diam s",
"tactic": "rw [Metric.diam, Metric.diam, hf.ediam_image]"
}
] | [
226,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_succ_right_eq | [
{
"state_after": "case e\nn k : ℕ\n⊢ (n + 1) * choose n k = choose n k * (k + 1) + choose n (k + 1) * (k + 1)\n\nn k : ℕ\ne : (n + 1) * choose n k = choose n k * (k + 1) + choose n (k + 1) * (k + 1)\n⊢ choose n (k + 1) * (k + 1) = choose n k * (n - k)",
"state_before": "n k : ℕ\n⊢ choose n (k + 1) * (k + 1)... | [
218,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.Subcanonical.of_yoneda_isSheaf | [
{
"state_after": "case intro\nC : Type u\ninst✝ : Category C\nP : Cᵒᵖ ⥤ Type v\nX✝ Y : C\nS : Sieve X✝\nR : Presieve X✝\nJ✝ J₂ J : GrothendieckTopology C\nh : ∀ (X : C), Presieve.IsSheaf J (yoneda.obj X)\nX : C\n⊢ Presieve.IsSheaf J (yoneda.obj X)",
"state_before": "C : Type u\ninst✝ : Category C\nP : Cᵒᵖ ⥤... | [
246,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.natDegree_map_of_leadingCoeff_ne_zero | [] | [
884,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.smul_apply | [
{
"state_after": "case h_add\nR : Type u_1\nM : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nI : Ideal R\nS : Type ?u.304250\ninst✝³ : CommSemiring S\ninst✝² : Algebra S R\ninst✝¹ : Module S M\ninst✝ : IsScalarTower S R M\ng : PolynomialModule R M\nn : ℕ\np q : R[X]\nhp : ↑(p • g... | [
194,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative | [
{
"state_after": "α : Type u_1\nβ : Type ?u.127949\ninst✝³ : MeasurableSpace α\nM : Type ?u.127955\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns✝ : SignedMeasure α\ni✝ j✝ : Set α\ns : SignedMeasure α\ni j : Set α\nhi : MeasurableSet i\nhj : MeasurableSet j\nhi' : (∀ ⦃... | [
453,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsRefl.nondegenerate_of_separatingRight | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.576918\nR₂ : Type ?u.576921\nR₃ : Type ?u.576924\nM : Type u_2\nM₁ : Type ?u.576930\nM₂ : Type ?u.576933\nMₗ₁ : Type ?u.576936\nMₗ₁' : Type ?u.576939\nMₗ₂ : Type ?u.576942\nMₗ₂' : Type ?u.576945\nK : Type ?u.576948\nK₁ : Type ?u.576951\nK₂ : Type ?u.576954\nV : Type ... | [
745,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_eq_one | [
{
"state_after": "case hn\nb n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\n⊢ (n + b - 1) / b ≤ 1",
"state_before": "b n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\n⊢ clog b n = 1",
"tactic": "rw [clog_of_two_le (hn.trans h) hn, clog_of_right_le_one]"
},
{
"state_after": "case hn\nb n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\nn_pos : 0 < n\n... | [
292,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.choice_mem | [
{
"state_after": "x : ZFSet\nh : ¬∅ ∈ x\ny : ZFSet\nyx : y ∈ x\n⊢ ↑(map (fun y => Classical.epsilon fun z => z ∈ y) x) ′ ↑y ∈ ↑y",
"state_before": "x : ZFSet\nh : ¬∅ ∈ x\ny : ZFSet\nyx : y ∈ x\n⊢ ↑(choice x) ′ ↑y ∈ ↑y",
"tactic": "delta choice"
},
{
"state_after": "x : ZFSet\nh : ¬∅ ∈ x\ny : ZFS... | [
1822,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1819,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.snd_map_fst | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.358968\nM₆ : Type ?u.358971\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np : Sub... | [
666,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives | [] | [
343,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk | [
{
"state_after": "case a\nR : Type u\ninst✝ : CommRing R\nI J : Ideal R\nh : I ≤ J\nx✝ : R\n⊢ ↑(RingHom.comp (↑(RingEquiv.symm (quotQuotEquivQuotOfLE h))) (Ideal.Quotient.mk J)) x✝ = ↑(quotQuotMk I J) x✝",
"state_before": "R : Type u\ninst✝ : CommRing R\nI J : Ideal R\nh : I ≤ J\n⊢ RingHom.comp (↑(RingEquiv... | [
644,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableAtFilter.inf_of_right | [] | [
419,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.opow_omega | [] | [
446,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/List/Forall2.lean | List.left_unique_forall₂' | [] | [
140,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.mul_left | [] | [
1261,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.isLeftRegular | [] | [
92,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Finset.measurable_range_sup' | [
{
"state_after": "M : Type ?u.1408591\ninst✝³ : MeasurableSpace M\nα : Type u_2\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf✝ g : α → M\nδ : Type u_1\ninst✝² : MeasurableSpace δ\ninst✝¹ : SemilatticeSup α\ninst✝ : MeasurableSup₂ α\nf : ℕ → δ → α\nn : ℕ\nhf : ∀ (k : ℕ), k < Nat.succ n → Measurable (f k... | [
255,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.coe_smul | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Order/Atoms.lean | IsCoatom.of_isCoatom_coe_Ici | [] | [
147,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_sub_of_le | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.130352\nβ : Type ?u.130355\nγ : Type ?u.130358\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\nh : b ≤ a\n⊢ c ≤ a - b ↔ b + c ≤ a",
"tactic": "rw [← add_le_add_iff_left b, Ordinal.add_sub_cancel_of_le h]"
}
] | [
576,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_iff' | [
{
"state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ncg : KernelFork g\nhg : IsLimit cg\ncf : CokernelCofork f\nhf : IsColimit cf\n⊢ Exact f g → f ≫ g = 0 ∧ Fork.ι cg ≫ Cofork.π cf = 0\n\ncase mpr\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX... | [
97,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_zero | [] | [
219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_mono | [] | [
545,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_take | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.128087\nδ : Type ?u.128090\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nx✝² : List α\nx✝¹ : List β\nx✝ : Forall₂ R x✝² x✝¹\n⊢ Forall₂ R (take 0 x✝²) (take 0 x✝¹)",
"tactic": "simp only [Forall₂.nil, take]"... | [
216,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.exists_measurable_le_lintegral_eq | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.77053\nγ : Type ?u.77056\nδ : Type ?u.77059\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nh₀ : (∫⁻ (a : α), f a ∂μ) = 0\n⊢ ∃ g, Measurable g ∧ g ≤ f ∧ (∫⁻ (a : α), f a ∂μ) = ∫⁻ (a : α), g a ∂μ\n\ncase inr\nα : Type u_1\nβ : Type ?u.77053\nγ : Type ?... | [
219,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.compStarAlgHom'_id | [] | [
1033,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_has_biproduct | [] | [
780,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | HasDerivWithinAt.inner | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.53238\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : NormedSpace ℝ E\nG : Type ?u.53367\ninst✝¹ : NormedAddComm... | [
118,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.le_sum_card_inter | [
{
"state_after": "ι : Type ?u.106343\nα : Type u_1\nβ : Type ?u.106349\nM : Type ?u.106352\nN : Type ?u.106355\nG : Type ?u.106358\nk : Type ?u.106361\nR : Type ?u.106364\ninst✝ : DecidableEq α\ns : Finset α\nB : Finset (Finset α)\nn : ℕ\nh : ∀ (a : α), a ∈ s → n ≤ card (filter ((fun x x_1 => x ∈ x_1) a) B)\n⊢ ... | [
343,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_union | [] | [
335,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | IsPrimitiveRoot.norm'_eq_one | [] | [
108,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | MonoidHom.ext_int | [
{
"state_after": "case h.ofNat\nF : Type ?u.48754\nι : Type ?u.48757\nα : Type ?u.48760\nβ : Type ?u.48763\nM : Type u_1\ninst✝ : Monoid M\nf g : ℤ →* M\nh_neg_one : ↑f (-1) = ↑g (-1)\nh_nat : comp f ↑ofNatHom = comp g ↑ofNatHom\nx : ℕ\n⊢ ↑f (ofNat x) = ↑g (ofNat x)\n\ncase h.negSucc\nF : Type ?u.48754\nι : Typ... | [
277,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_comp | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\ns : WSeq α\n⊢ Seq.map (Option.map (g ∘ f)) s = Seq.map (Option.map g) (Seq.map (Option.map f) s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\ns : WSeq α\n⊢ map (g ∘ f) s = map g (map f s)",
"tacti... | [
1429,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1426,
1
] |
Mathlib/Topology/SubsetProperties.lean | not_compactSpace_iff | [] | [
782,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.IsEquiv.ne_zero | [
{
"state_after": "K : Type ?u.3011502\nF : Type ?u.3011505\nR : Type u_1\ninst✝⁴ : DivisionRing K\nΓ₀ : Type u_2\nΓ'₀ : Type u_3\nΓ''₀ : Type ?u.3011520\ninst✝³ : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\ninst✝ : LinearOrderedCommMonoidWithZero Γ'₀\nv v₁... | [
410,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.image_subtype | [
{
"state_after": "ι : Type u'\nι' : Type ?u.632452\nR : Type u_2\nK : Type ?u.632458\nM : Type u_1\nM' : Type u_3\nM'' : Type ?u.632467\nV : Type u\nV' : Type ?u.632472\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹ : Module... | [
978,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_eq_toMatrix' | [] | [
538,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/GroupTheory/GroupAction/BigOperators.lean | Multiset.smul_sum | [] | [
52,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.zmodeq_ofDigits_digits | [
{
"state_after": "n✝ b b' : ℕ\nc : ℤ\nh : ↑b' ≡ c [ZMOD ↑b]\nn : ℕ\n⊢ ofDigits (↑b') (digits b' n) ≡ ofDigits c (digits b' n) [ZMOD ↑b]",
"state_before": "n✝ b b' : ℕ\nc : ℤ\nh : ↑b' ≡ c [ZMOD ↑b]\nn : ℕ\n⊢ ↑(ofDigits b' (digits b' n)) ≡ ofDigits c (digits b' n) [ZMOD ↑b]",
"tactic": "rw [coe_int_ofDigi... | [
566,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_le_iff_le_sin | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : x ∈ Icc (-1) 1\nhy : y ∈ Icc (-(π / 2)) (π / 2)\n⊢ arcsin x ≤ y ↔ x ≤ sin y",
"tactic": "rw [← arcsin_sin' hy, strictMonoOn_arcsin.le_iff_le hx (sin_mem_Icc _), arcsin_sin' hy]"
}
] | [
150,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_sum_apply | [] | [
2030,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2029,
1
] |
Mathlib/Logic/Basic.lean | and_forall_ne | [] | [
758,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivWithinAt.rpow | [
{
"state_after": "case h.e'_7\nf g : ℝ → ℝ\nf' g' x y p : ℝ\ns : Set ℝ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\nh : 0 < f x\n⊢ f' * g x * f x ^ (g x - 1) + g' * f x ^ g x * Real.log (f x) =\n ↑((g x * f x ^ (g x - 1)) • ContinuousLinearMap.smulRight 1 f' +\n (f x ^ g x * Real... | [
570,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_one' | [] | [
245,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_comm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.104303\nι : Type ?u.104306\nκ : Type ?u.104309\nα : Type u_1\nβ : Type ?u.104315\nr : α → α → Prop\ninst✝ : DecidableRel r\ns✝ s₁ s₂ t✝ t₁ t₂ : Finset α\na b : α\nhr : Symmetric r\ns t : Finset α\n⊢ edgeDensity r s t = edgeDensity r t s",
"tacti... | [
288,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_punit | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.113572\nR : Type u\ninst✝⁷ : Ring R\nM : Type v\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM' : Type v'\ninst✝⁴ : AddCommGroup M'\ninst✝³ : Module R M'\nM₁ : Type v\ni... | [
284,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.exists_prime | [] | [
118,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_le_count_of_factors_le | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b p : Associates α\nhb : b ≠ 0\nhp : Irreducible p\nh : factors a ≤ factors b\nh... | [
1518,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.second_continuant_aux_eq | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝ : DivisionRing K\ngp : Pair K\nzeroth_s_eq : Stream'.Seq.get? g.s 0 = some gp\n⊢ continuantsAux g 2 = { a := gp.b * g.h + gp.a, b := gp.b }",
"tactic": "simp [zeroth_s_eq, continuantsAux, nextCon... | [
153,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.insert_setBlack | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nv : α\nt : RBNode α\n⊢ setBlack\n (match isRed t with\n | red => setBlack (ins cmp v t)\n | black => ins cmp v t) =\n setBlack (ins cmp v t)",
"state_before": "α : Type u_1\ncmp : α → α → Ordering\nv : α\nt : RBNode α\n⊢ setBlack (ins... | [
90,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
88,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.cancel_right | [] | [
352,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.elim_update_right | [
{
"state_after": "case h\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type ?u.38887\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → γ\ng : β → γ\ni : β\nc : γ\nx : α ⊕ β\n⊢ Sum.elim f (update g i c) x = update (Sum.elim f g) (inr i) c x",
"state_before": "α : Type u\nα' : Typ... | [
654,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | symmetric_symmetrizeRel | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.16844\nV : Set (α × α)\n⊢ SymmetricRel (symmetrizeRel V)",
"tactic": "simp [SymmetricRel, symmetrizeRel, preimage_inter, inter_comm, ← preimage_comp]"
}
] | [
218,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.tail_ofFn | [
{
"state_after": "case e_a\nn✝ : ℕ\nα : Type u_1\nn : ℕ\nf : Fin (Nat.succ n) → α\n⊢ get (tail (ofFn f)) = fun i => f (Fin.succ i)",
"state_before": "n✝ : ℕ\nα : Type u_1\nn : ℕ\nf : Fin (Nat.succ n) → α\n⊢ ofFn (get (tail (ofFn f))) = ofFn fun i => f (Fin.succ i)",
"tactic": "congr"
},
{
"state... | [
197,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.finset_card_const_le_le_of_tsum_le | [
{
"state_after": "α : Type ?u.303162\nβ : Type ?u.303165\nγ : Type ?u.303168\na✝ b c✝ d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε✝ ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf g : α → ℝ≥0∞\nι : Type u_1\na : ι → ℝ≥0∞\nc : ℝ≥0∞\nc_ne_top : c ≠ ⊤\ntsum_le_c : (∑' (i : ι), a i) ≤ c\nε : ℝ≥0∞\nε_ne_zero : ε ≠ 0\nhf : Set.Finite {i | ε ≤ a i}\... | [
1060,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos 0 = 1",
"tactic": "simp [cos]"
}
] | [
853,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translationNumber | [
{
"state_after": "f g : CircleDeg1Lift\nx : ℝ\n⊢ Tendsto (fun n => (↑(f ^ n) x - x) / ↑n) atTop\n (𝓝 (τ (↑(↑translate (↑Multiplicative.ofAdd x))⁻¹ * f * ↑(↑translate (↑Multiplicative.ofAdd x)))))",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\n⊢ Tendsto (fun n => (↑(f ^ n) x - x) / ↑n) atTop (𝓝 (τ f))"... | [
798,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.bind_inf_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.299000\nι : Sort x\nf : Filter α\ng : α → Filter β\ns✝ s : Set β\n⊢ (s ∈ bind f fun x => g x ⊓ 𝓟 s✝) ↔ s ∈ bind f g ⊓ 𝓟 s✝",
"tactic": "simp only [mem_bind, mem_inf_principal]"
}
] | [
2763,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2761,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittAdd_zero | [
{
"state_after": "case a\np : ℕ\nR : Type ?u.56659\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(map (Int.castRingHom ℚ)) (wittAdd p 0) = ↑(map (Int.castRingHom ℚ)) (X (0, 0) + X (1, 0))",
"state_before": "p : ℕ\nR : Type ?u.56659\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ wittAdd p 0 = X (0, 0) + ... | [
269,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.AEStronglyMeasurable.prod_mk_left | [
{
"state_after": "case h\nα : Type u_3\nα' : Type ?u.2388487\nβ : Type u_2\nβ' : Type ?u.2388493\nγ✝ : Type ?u.2388496\nE : Type ?u.2388499\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ✝\nμ μ' : Measure α\nν ν' : Mea... | [
212,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_mono | [] | [
196,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finsupp/Antidiagonal.lean | Finsupp.antidiagonal_zero | [
{
"state_after": "α : Type u\n⊢ Multiset.toFinset\n (Multiset.map (Prod.map ↑Multiset.toFinsupp ↑Multiset.toFinsupp) (Multiset.antidiagonal (↑toMultiset 0))) =\n {(0, 0)}",
"state_before": "α : Type u\n⊢ antidiagonal 0 = {(0, 0)}",
"tactic": "rw [antidiagonal, antidiagonal', Multiset.toFinsupp_s... | [
92,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.div_mul_div_comm | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : DivisionMonoid G\na b c d : G\nhbd : Commute b d\nhbc : Commute b⁻¹ c\n⊢ a / b * (c / d) = a * c / (b * d)",
"tactic": "simp_rw [div_eq_mul_inv, mul_inv_rev, hbd.inv_inv.symm.eq, hbc.mul_mul_mul_comm]"
}
] | [
329,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
11
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.