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.coe_two_pi | [
{
"state_after": "no goals",
"state_before": "⊢ 2 * π - 0 = 2 * π * ↑1",
"tactic": "rw [sub_zero, Int.cast_one, mul_one]"
}
] | [
130,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.rat_mul | [] | [
149,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_of_forall_lt | [] | [
617,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/Part.lean | Part.right_dom_of_div_dom | [] | [
768,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.isIntegral_root | [] | [
544,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.image_eq | [
{
"state_after": "case refine'_1\n𝕜 : Type u_3\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_1\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\ns : Set H\n⊢ s ⊆ I.source\n\ncase refine'_2\n𝕜 : Type u_3\ninst✝³ : NontriviallyNo... | [
294,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
11
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.IndexSet.eqId_iff_mono | [
{
"state_after": "case mp\nC : Type ?u.5440\ninst✝ : Category C\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\n⊢ EqId A → Mono (e A)\n\ncase mpr\nC : Type ?u.5440\ninst✝ : Category C\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\n⊢ Mono (e A) → EqId A",
"state_before": "C : Type ?u.5440\ninst✝ : Category C\nΔ : SimplexCa... | [
175,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumCompl_apply_inl | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_of_norm_le_const | [] | [
576,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_norm_iff | [] | [
257,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_one | [
{
"state_after": "n : ℕ\ninst✝ : Fact (1 < n)\n⊢ 1 % n = 1",
"state_before": "n : ℕ\ninst✝ : Fact (1 < n)\n⊢ val 1 = 1",
"tactic": "rw [val_one_eq_one_mod]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\ninst✝ : Fact (1 < n)\n⊢ 1 % n = 1",
"tactic": "exact Nat.mod_eq_of_lt Fact.... | [
594,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_deriv_comp_smul_deriv | [] | [
1450,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_iff_isMin | [] | [
617,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.strictMonoOn_tan | [] | [
990,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_iff_left | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhb : AddLECancellable b\nhba : b ≤ a\n⊢ a < b + c → a - b < c",
"state_b... | [
123,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_eq_tsum_div | [] | [
185,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Cover.lean | Wcovby.snd | [] | [
514,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin_comp | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1830938\nM✝ : Type ?u.1830941\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M✝\ninst✝¹⁸ : Module R M✝\nR₁ : Type ?u.1830977\nM₁ : Type ?u.1830980\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type u_2\nM₂ : Type u_5\nin... | [
423,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.comp_familyOfBFamily' | [] | [
1233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_id_continuousOrderHom | [] | [
306,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.succ_mul_binomial | [
{
"state_after": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : a ≠ b\n⊢ succ (f a + f b) * choose (f a + f b) (f a) = choose (succ (f a) + f b) (succ (f a)) * succ (f a)",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : ... | [
144,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.comp_apply | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Set/Basic.lean | Disjoint.inter_right | [] | [
2969,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2968,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toOpen_germ | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nU : Opens ↑(PrimeSpectrum.Top R)\nx : { x // x ∈ U }\n⊢ toOpen R ⊤ ≫ germ (structureSheaf R).val ((fun x => { val := ↑x, property := (_ : ↑x ∈ ↑⊤) }) x) = toStalk R ↑x",
"state_before": "R : Type u\ninst✝ : CommRing R\nU : Opens ↑(PrimeSpectrum.Top R)\nx : {... | [
450,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_sum | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.5063\ninst✝¹ : Finite α\ninst✝ : Finite β\nthis : Fintype α\n⊢ Nat.card (α ⊕ β) = Nat.card α + Nat.card β",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.5063\ninst✝¹ : Finite α\ninst✝ : Finite β\n⊢ Nat.card (α ⊕ β) = Nat.card α + Nat.card... | [
172,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | RingHom.FinitePresentation.of_finiteType | [] | [
448,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_injective_of_injective | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf✝ : G →g G'\nf' : G' →g G''\nu✝ v✝ u' v' : V\np✝ : Walk G u✝ v✝\nf : G →g G'\nhinj : Injective ↑f\nu v : V\np p' : Walk G u v\nh : Walk.map f p = Walk.map f p'\n⊢ p = p'",
"state_before":... | [
1597,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1581,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isField_of_isIntegral_of_isField' | [
{
"state_after": "R✝ : Type ?u.1647177\nA : Type ?u.1647180\nB : Type ?u.1647183\nS✝ : Type ?u.1647186\nT : Type ?u.1647189\ninst✝¹² : CommRing R✝\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : CommRing S✝\ninst✝⁸ : CommRing T\ninst✝⁷ : Algebra A B\ninst✝⁶ : Algebra R✝ B\nf : R✝ →+* S✝\ng : S✝ →+* T\nins... | [
1159,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.le_sup_toSubalgebra | [] | [
1176,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Std/Data/Array/Lemmas.lean | Array.singleton_def | [] | [
35,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
35,
9
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_inf_principal | [] | [
1242,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.mul_apply | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.isAtom_pure | [] | [
413,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk | [] | [
771,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.bot_factors_iff_zero | [
{
"state_after": "case intro\nC : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nA B : C\nh : A ⟶ ⊥.obj.left\n⊢ h ≫ MonoOver.arrow ⊥ = 0",
"state_before": "C : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Cat... | [
353,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.im_imI | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_comp_perm_mul_eq_sum_mul_iff | [] | [
488,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_comp_toAlgHom | [] | [
1629,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Iic | [] | [
470,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.center_eq_top | [] | [
499,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_pair | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.141744\nγ : Type ?u.141747\nι : Sort ?u.141750\nι' : Sort ?u.141753\nκ : ι → Sort ?u.141758\nκ' : ι' → Sort ?u.141763\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b✝ : α\nf : β → α\na b : β\n⊢ (⨆ (x : β) (_ : x ∈ {a, ... | [
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35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/Order/Bounds/Basic.lean | Set.Nonempty.bddBelow_upperBounds | [] | [
270,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Module.lean | ContinuousLinearEquiv.hasSum' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_5\nR : Type u_1\nR₂ : Type u_2\nM : Type u_3\nM₂ : Type u_4\ninst✝⁹ : Semiring R\ninst✝⁸ : Semiring R₂\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\ninst✝⁵ : AddCommMonoid M₂\ninst✝⁴ : Module R₂ M₂\ninst✝³ : TopologicalSpace M\ninst✝² : TopologicalS... | [
80,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
11
] |
Mathlib/SetTheory/Lists.lean | Lists'.of_toList | [
{
"state_after": "α : Type u_1\nb : Bool\nh : true = b\nl : Lists' α b\n⊢ Lists' α b",
"state_before": "α : Type u_1\nb : Bool\nh : true = b\nl : Lists' α b\n⊢ Lists' α true",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nb : Bool\nh : true = b\nl : Lists'... | [
122,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | Measurable.im | [] | [
56,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.blunt_iff_not_pointed | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.62541\nG : Type ?u.62544\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\nS✝ S : ConvexCone 𝕜 E\n⊢ Blunt S ↔ ¬Pointed S",
"tactic": "rw [pointed_iff_not_blunt, Classical.not_not]"
}
] | [
360,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn | [] | [
280,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.bit0_re | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.coe_mk | [] | [
73,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_fun | [
{
"state_after": "L : Language\nM : Type u_3\nN : Type u_4\nP : Type ?u.308452\nQ : Type ?u.308455\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nφ : M ↪ₑ[L] N\nn : ℕ\nf : Functions L n\nx : Fin n → M\nh :\n Formula.Realize (Formula.graph f) (↑φ ∘ Fin.cons (funM... | [
146,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/MvPolynomial/Polynomial.lean | MvPolynomial.polynomial_eval_eval₂ | [
{
"state_after": "case h_C\nR : Type u_1\nS : Type u_2\nσ : Type u_3\nx : S\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : R →+* Polynomial S\ng : σ → Polynomial S\np : MvPolynomial σ R\n⊢ ∀ (a : R),\n Polynomial.eval x (eval₂ f g (↑C a)) =\n eval₂ (RingHom.comp (Polynomial.evalRingHom x) f) (fun... | [
29,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
20,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.half_lt_self | [
{
"state_after": "case intro\nα : Type ?u.326127\nβ : Type ?u.326130\nb c d : ℝ≥0∞\nr p q a : ℝ≥0\nhz : ↑a ≠ 0\n⊢ ↑a / 2 < ↑a",
"state_before": "α : Type ?u.326127\nβ : Type ?u.326130\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhz : a ≠ 0\nht : a ≠ ⊤\n⊢ a / 2 < a",
"tactic": "lift a to ℝ≥0 using ht"
},
{
"sta... | [
1755,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1751,
11
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_zero | [
{
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113,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.eqOn_closedBall_of_isMaxOn_norm | [] | [
330,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
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Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_sub | [
{
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874,
84
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874,
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Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_right | [
{
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"tactic": "ac_r... | [
474,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_same_apply | [
{
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550,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atBot_mul_neg_const | [] | [
1236,
43
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1234,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.union_ae_eq_univ_of_ae_eq_univ_left | [
{
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513,
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Mathlib/GroupTheory/Abelianization.lean | Abelianization.hom_ext | [] | [
169,
77
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168,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.independent | [
{
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2172,
49
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2157,
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.piCongrRight_refl | [] | [
662,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.one_add_of_omega_le | [
{
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"tactic": "rw [← Ordinal.add_sub_cancel_of_le h, ← add_assoc, one_add_omega]"
}
] | [
632,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Function.lean | Function.Semiconj.mapsTo_preimage | [
{
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"tacti... | [
1665,
89
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1664,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two | [
{
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511,
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505,
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Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | lt_iff_exists_mul | [
{
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300,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
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Mathlib/Init/Algebra/Order.lean | lt_of_le_of_ne | [] | [
201,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/Data/List/Chain.lean | List.chain'_append_cons_cons | [
{
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}
] | [
224,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_mem_iff | [
{
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531,
91
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528,
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Mathlib/GroupTheory/Complement.lean | Subgroup.mem_transferSet | [] | [
620,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
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Mathlib/Data/TypeVec.lean | TypeVec.subtypeVal_diagSub | [
{
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"state_before": "n : ℕ\nα : TypeVec n\n⊢ subtypeVal (repeatEq α) ⊚ diagSub = prod.diag",
"tactic": "ext i x"
},
{
"state_after": "case a.h.fz\nn : ℕ\nα✝ : TypeVec n\... | [
790,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
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Mathlib/Data/ENat/Basic.lean | ENat.succ_def | [
{
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}
] | [
185,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Mathlib/Algebra/GroupWithZero/Power.lean | zpow_ne_zero | [] | [
181,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.reClm_coe | [] | [
890,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.singleMapHomologicalComplex_hom_app_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁶ : Category V\ninst✝⁵ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh✝ k : D ⟶ E\ni✝ : ι\ninst✝⁴ : HasZeroObject V\nW : Type u_3\ninst✝³ : Category W\ninst✝² : Preadditive W\ninst✝¹ : HasZeroObj... | [
324,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.inj | [] | [
184,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_injective | [] | [
686,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
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Mathlib/Data/List/Sigma.lean | List.kerase_sublist | [] | [
419,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_ne_top | [
{
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"tactic": "simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]"
}
] | [
83,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/CategoryTheory/FullSubcategory.lean | CategoryTheory.fullSubcategoryInclusion_map_lift_map | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.nhds_mkOfNhds_filterBasis | [
{
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150,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit0_ne_one | [] | [
98,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
11
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_apply | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.sub_eq_add' | [] | [
80,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.subset_maximalAtlas | [] | [
916,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.homOfElement_eq_iff | [
{
"state_after": "no goals",
"state_before": "X : Type u\nx y : X\n⊢ x = y → homOfElement x = homOfElement y",
"tactic": "aesop"
}
] | [
236,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Dynamics/Flow.lean | IsFwInvariant.isInvariant | [] | [
71,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.map_add | [
{
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301,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
11
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | Measurable.lintegral_prod_right' | [
{
"state_after": "α : Type u_2\nα' : Type ?u.3342539\nβ : Type u_1\nβ' : Type ?u.3342545\nγ : Type ?u.3342548\nE : Type ?u.3342551\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : MeasureTheory.Measure α\nν ν' :... | [
261,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Algebra/CharP/Basic.lean | CharP.neg_one_pow_char | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\np : ℕ\ninst✝¹ : CharP R p\ninst✝ : Fact (Nat.Prime p)\n⊢ (-1) ^ p + 1 = 0",
"state_before": "R : Type u_1\ninst✝² : CommRing R\np : ℕ\ninst✝¹ : CharP R p\ninst✝ : Fact (Nat.Prime p)\n⊢ (-1) ^ p = -1",
"tactic": "rw [eq_neg_iff_add_eq_zero]"
},
{
... | [
315,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.trans | [] | [
154,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UniformIntegrable.aeStronglyMeasurable | [] | [
83,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_id | [] | [
630,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.of_neg | [] | [
288,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.omega_zero | [] | [
948,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt.mul | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\na b : ℤ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ padicValNat p (Int.natAbs (a * b)) = padicValNat p (Int.natAbs a) + padicValNat p (Int.natAbs b)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na b : ℤ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ padicValInt p (a * b) = padicValInt p a ... | [
533,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.append_castAdd_aux | [
{
"state_after": "case mk\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nα : Type u_1\nm n : ℕ\na : Fin (Nat.succ m) → α\nb : Fin (Nat.succ n) → α\nval✝ : ℕ\nisLt✝ : val✝ < m\n⊢ Matrix.vecAppend (_ : Nat.succ (m + n) = m + Nat.succ n) (a ∘ ↑Fin.castSucc) b\n (↑Fin.castSucc (↑(Fin.castAdd n... | [
462,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Data/Set/Function.lean | StrictAntiOn.strictAnti | [] | [
332,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_smul | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx✝ : S\ng : R →+* S\np : R[X]\nx : S\ns : R\nA : natDegree p < Nat.succ (natDegree p)\n⊢ eval₂ g x (s • p) = ↑g s * eval₂ g x p",
"state_before": "R : Type... | [
119,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_iInf_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.62085\nγ : Type ?u.62088\nι : Sort u_2\nι' : Sort ?u.62094\nl l' : Filter α\np : ι → Prop\ns✝ : ι → Set α\nt✝ : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\ns : ι → Set α\nh : Directed (fun x x_1 => x ≥ x_1) s\ninst✝ : Nonemp... | [
764,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
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