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/Data/List/Basic.lean | List.take_succ | [
{
"state_after": "case nil\nι : Type ?u.175545\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn✝ n : ℕ\n⊢ take (n + 1) [] = take n [] ++ Option.toList (get? [] n)\n\ncase cons\nι : Type ?u.175545\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn✝ : ℕ\nhd : α\ntl : List α\nhl :... | [
2039,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2034,
1
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Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.pnatCast_eq_natCast | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I))\nn : ℕ+\n⊢ ↑(IsUnit.unit (_ : IsUnit ↑↑n)) = ↑↑n",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I))\nn : ℕ+\n⊢ ↑↑n = ↑↑n",
"tactic": "... | [
221,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.prodIsoProd_hom_fst | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\n⊢ prodFst = BinaryFan.fst (prodBinaryFan X Y)",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\n⊢ (prodIsoProd X Y).hom ≫ prodFst = prod.fst",
"tactic": "simp [← Iso.eq_inv_comp, prodIsoProd]"
},
{
"state_af... | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.desc_inl_inr | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ inl ≫ desc inl inr = inl ≫ 𝟙 (X ⨿ Y)\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ inr ≫ desc inl inr = inr ≫ 𝟙 (X ⨿ Y)",
"state_before": "C : Type u... | [
860,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_one | [] | [
2831,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2830,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_liminf_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73864\nγ : Type ?u.73867\nδ : Type ?u.73870\nι : Type ?u.73873\nR : Type ?u.73876\nR' : Type ?u.73879\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : ℕ → Set α\nh : (∑' (i : ℕ), ↑↑μ (s i)) ≠ ⊤\n⊢ ↑↑μ (liminf s atTop) ≤ 0",
"state_before": "α :... | [
609,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_neg_iff | [
{
"state_after": "x y : ℝ\nh : 0 < x\n⊢ log x < log 1 ↔ x < 1",
"state_before": "x y : ℝ\nh : 0 < x\n⊢ log x < 0 ↔ x < 1",
"tactic": "rw [← log_one]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : 0 < x\n⊢ log x < log 1 ↔ x < 1",
"tactic": "exact log_lt_log_iff h zero_lt_o... | [
181,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.smul_right | [] | [
111,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Analysis/NormedSpace/Ray.lean | SameRay.norm_add | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro\nE : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.239\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nu : E\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nh : SameRay ℝ (a • u) (b • u)\n⊢ ‖a • u + b • u‖ = ‖a • u‖... | [
38,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝ : NormedLinearOrderedField β\n⊢ (∀ (n : ℕ), Tendsto (fun a => ‖k a ^ n * f a‖) l (𝓝 0)) ↔ SuperpolynomialDecay l (fun a => ‖k a‖) fun a => ‖f a‖",
"tactic": "simp [SuperpolynomialDecay]"
}
... | [
328,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_sinh | [] | [
103,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Set/Image.lean | Set.inter_preimage_subset | [] | [
538,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
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Mathlib/Algebra/Order/Group/Abs.lean | abs_eq_sup_inv | [] | [
38,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_idem | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.70425\nα : Type u_1\nβ : Type ?u.70431\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ b ⇨ b ⇨ a = b ⇨ a",
"tactic": "rw [himp_himp, inf_idem]"
}
] | [
401,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Order/WithBot.lean | WithTop.toDual_apply_top | [] | [
673,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.diag_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ X Y : C\nf : X ⟶ Y\ninst✝¹ : HasBinaryProduct X X\ninst✝ : HasBinaryProduct Y Y\n⊢ diag X ≫ map f f = f ≫ diag Y",
"tactic": "simp"
}
] | [
804,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.card_support_trinomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nx y z : R\nhx : x ≠ 0\nhy : y ≠ 0\nhz : z ≠ 0\n⊢ card (support (↑C x * X ^ k + ↑C y * X ^ m + ↑C z * X ^ n)) = 3",
"tactic": "rw [support_trino... | [
225,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.principal_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.44590\nγ : Type ?u.44593\nι : Sort u_2\nι' : Sort ?u.44599\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'\nhl : HasBasis l p s\ns' : Set α\n⊢ HasBasis (𝓟 s' ⊓ l) p fun i => s'... | [
628,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_left_inj' | [] | [
86,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_iUnion_congr | [
{
"state_after": "α : Type u_2\nβ : Type ?u.314892\nγ : Type ?u.314895\nδ : Type ?u.314898\nι : Type u_1\nR : Type ?u.314904\nR' : Type ?u.314907\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝ : Countable ι\ns : ι → Set ... | [
1854,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1847,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_iff_left | [] | [
782,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
11
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Mathlib/Algebra/Group/Prod.lean | MonoidHom.coe_fst | [] | [
494,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_right_injective | [] | [
117,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_add_of_sub_lt_left | [
{
"state_after": "case inl\nα : Type ?u.179238\nβ : Type ?u.179241\na c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≠ ⊤ ∨ ⊤ ≠ ⊤\n⊢ a - ⊤ < c → a < ⊤ + c\n\ncase inr\nα : Type ?u.179238\nβ : Type ?u.179241\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≠ ⊤ ∨ b ≠ ⊤\nhb : b ≠ ⊤\n⊢ a - b < c → a < b + c",
"state_before": "α : Type ?u.17... | [
1153,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
11
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_empty | [] | [
73,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Subsemigroup.mem_centralizer_iff | [] | [
182,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.neg_apply | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
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] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.integrable_iff | [] | [
364,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_div_left | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulLeftInvariant μ\ng : G\n⊢ QuasiMeasurePreserving fun h => g * h⁻¹",
"state_before": "G :... | [
454,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.nonempty_of_mem | [] | [
160,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Ioc_eq_integral_Ioo | [] | [
656,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
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Mathlib/Analysis/Convex/Basic.lean | ite_eq_mem_stdSimplex | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.296852\nF : Type ?u.296855\nβ : Type ?u.296858\nι : Type u_2\ninst✝¹ : OrderedSemiring 𝕜\ninst✝ : Fintype ι\ni j : ι\n⊢ 0 ≤ if i = j then 1 else 0",
"state_before": "𝕜 : Type u_1\nE : Type ?u.296852\nF : Type ?u.296855\nβ : Type ?u.296858\nι : Type u_2\ninst✝¹ ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_think_left | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\ns : WSeq α\nt : WSeq β\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) (destruct (think s)) (destruct t) ↔\n Computation.LiftRel (LiftRelO R (LiftRel R)) (destruct s) (destruct t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w... | [
1108,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.comm_sq₂ | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.513561\nW : Type ?u.513564\nV₁ : Type u_1\nV₂ : Type u_4\nV₃ : Type u_6\ninst✝⁷ : SeminormedAddCommGroup V\ninst✝⁶ : SeminormedAddCommGroup W\ninst✝⁵ : SeminormedAddCommGroup V₁\ninst✝⁴ : SeminormedAddCommGroup V₂\ninst✝³ : SeminormedAddCommGroup V₃\... | [
970,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
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] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom | [] | [
366,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | mem_subalgebraOfSubsemiring | [] | [
1481,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
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] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.equiv_iff_mem | [] | [
307,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_principal | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.122... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_iInf | [] | [
529,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Mathlib/Data/Fin/Basic.lean | Fin.is_le' | [] | [
282,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_induction' | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.24742\nK : Type ?u.24745\nM : Type u_1\nM₂ : Type ?u.24751\nV : Type ?u.24754\nS : Type ?u.24757\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 →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝... | [
170,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Data/List/TFAE.lean | List.tfae_nil | [] | [
34,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
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Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.infty_mul | [
{
"state_after": "α : Type ?u.560431\nE : α → Type ?u.560436\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nI : Type u_1\nB : I → Type u_2\ninst✝ : (i : I) → NonUnitalNormedRing (B i)\nf g : (i : I) → B i\nhf : Memℓp f ⊤\nhg : Memℓp g ⊤\n⊢ BddAbove (Set.range fun i => ‖(f * g) i‖)",
"state_before... | [
792,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
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Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.mem_nhds_iff_symm | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.60190\ninst✝ : UniformSpace α\nx : α\ns : Set α\n⊢ (∃ V, V ∈ 𝓤 α ∧ ball x V ⊆ s) ↔ ∃ V, V ∈ 𝓤 α ∧ SymmetricRel V ∧ ball x V ⊆ s",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.60190\ninst✝ ... | [
758,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isOpen_iff | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nU : Set (PrimeSpectrum R)\n⊢ IsOpen U ↔ ∃ s, zeroLocus s = Uᶜ",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nU : Set (PrimeSpectrum R)\n⊢ IsOpen U ↔ ∃ s, Uᶜ = zeroLocus s",
"tactic": "... | [
418,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.coeHom_apply | [] | [
117,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convex_closedBall | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.23609\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\na : E\nr : ℝ\n⊢ Convex ℝ (closedBall a r)",
"tactic": "simpa only [Metric.closedBall, sep_univ] using (convexOn_univ_dist a).convex_le r"
}
] | [
70,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_eq_zero_of_isempty | [
{
"state_after": "V : Type u\nG✝ : SimpleGraph V\nα : Type v\nC : Coloring G✝ α\nG : SimpleGraph V\ninst✝ : IsEmpty V\n⊢ chromaticNumber G ≤ 0",
"state_before": "V : Type u\nG✝ : SimpleGraph V\nα : Type v\nC : Coloring G✝ α\nG : SimpleGraph V\ninst✝ : IsEmpty V\n⊢ chromaticNumber G = 0",
"tactic": "rw [... | [
294,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_cancel' | [
{
"state_after": "n m : Nat\nH : n ∣ m\nthis : m % n + n * (m / n) = m\n⊢ n * (m / n) = m",
"state_before": "n m : Nat\nH : n ∣ m\n⊢ n * (m / n) = m",
"tactic": "have := mod_add_div m n"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\nH : n ∣ m\nthis : m % n + n * (m / n) = m\n⊢ ... | [
734,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
732,
11
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_apply_right | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a < a + p ∧ ∃ z, a + p = a + p + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α... | [
231,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/Order/Basic.lean | TFAE_mem_nhdsWithin_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na b : α\nh : a < b\ns : Set α\n⊢ TFAE\n [s ∈ 𝓝[Iio b] b, s ∈ 𝓝[Ico a b] b, s ∈ 𝓝[Ioo a b] b, ∃ l, l ∈ Ico a b ∧ Ioo l b ⊆ s, ∃ l, l ∈ Iio b ∧ ... | [
1685,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | HasFTaylorSeriesUpToOn.continuousLinearMap_comp | [] | [
208,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.refl | [
{
"state_after": "no goals",
"state_before": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ : BoundedFormula L α n\nM : ModelType T\nv : α → ↑M\nxs : Fin n → ↑M\n⊢ BoundedFormula.Realize (φ ⇔ φ) v xs",
"tactic": "rw [BoundedFormula.realize_iff]"
}
] | [
423,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Topology/Constructions.lean | prod_mem_nhds_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.38336\nδ : Type ?u.38339\nε : Type ?u.38342\nζ : Type ?u.38345\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
572,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mod_eq_sub_mul_div | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\ninst✝¹ : EuclideanDomain R✝\nR : Type u_1\ninst✝ : EuclideanDomain R\na b : R\n⊢ b * (a / b) + a % b - b * (a / b) = a - b * (a / b)",
"tactic": "rw [div_add_mod]"
}
] | [
145,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Lp.lean | MeasureTheory.Lp.finStronglyMeasurable | [] | [
77,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_one_div_eq_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0\nz : ℝ\nhz : z ≠ 0\n⊢ x ^ (1 / z) = y ↔ x = y ^ z",
"tactic": "rw [← rpow_eq_rpow_iff hz, rpow_self_rpow_inv hz]"
}
] | [
263,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.iSup_Prop | [
{
"state_after": "case h.e'_5.h\nα✝ : Type ?u.1402885\nβ : Type ?u.1402888\nγ : Type ?u.1402891\nγ₂ : Type ?u.1402894\nδ : Type u_2\nι : Sort y\ns t u : Set α✝\ninst✝¹¹ : TopologicalSpace α✝\ninst✝¹⁰ : MeasurableSpace α✝\ninst✝⁹ : BorelSpace α✝\ninst✝⁸ : TopologicalSpace β\ninst✝⁷ : MeasurableSpace β\ninst✝⁶ : ... | [
1242,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/Data/Set/Finite.lean | Set.exists_max_image | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : LinearOrder β\ns : Set α\nf : α → β\nh1 : Set.Finite s\nx : α\nhx : x ∈ s\n⊢ ∃ a, a ∈ s ∧ ∀ (b : α), b ∈ s → f b ≤ f a",
"tactic": "simpa only [exists_prop, Finite.mem_toFinset] using\n h1.toFinset.exi... | [
1454,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Algebra/DualQuaternion.lean | Quaternion.imK_snd_dualNumberEquiv | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_one | [
{
"state_after": "case h.h\nm k : ℕ\n⊢ hyperoperation 1 m k = m + k",
"state_before": "⊢ hyperoperation 1 = fun x x_1 => x + x_1",
"tactic": "ext (m k)"
},
{
"state_after": "case h.h.zero\nm : ℕ\n⊢ hyperoperation 1 m Nat.zero = m + Nat.zero\n\ncase h.h.succ\nm bn : ℕ\nbih : hyperoperation 1 m bn... | [
70,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/List/AList.lean | AList.mem_lookup_iff | [] | [
175,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.symm_map_nhdsWithin_image | [
{
"state_after": "no goals",
"state_before": "𝕜 : 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\nx : H\ns : Set H\n⊢ map (↑(ModelWithCorners.symm I)) (𝓝[↑I '' s] ↑... | [
318,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.singleton_vsub | [] | [
655,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean | is_bot_adic_iff | [
{
"state_after": "R : Type ?u.334870\ninst✝⁵ : CommRing R\ninst✝⁴ : TopologicalSpace R\ninst✝³ : TopologicalRing R\nA : Type u_1\ninst✝² : CommRing A\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalRing A\n⊢ ((∀ (n : ℕ), IsOpen ↑(⊥ ^ n)) ∧ ∀ (s : Set A), s ∈ 𝓝 0 → ∃ n, ↑(⊥ ^ n) ⊆ s) ↔ DiscreteTopology A",
... | [
223,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_neg | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_image_homothety | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1956140\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
394,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.mem_bind | [
{
"state_after": "α : Type u_1\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\nQ : (i : α) → i ∈ P.parts → Finpartition i\n⊢ (∃ a_1, a_1 ∈ attach P.parts ∧ b ∈ (Q ↑a_1 (_ : ↑a_1 ∈ P.parts)).parts) ↔ ∃ A hA, b ∈ (Q A hA).parts",
"state_before": "α : Type... | [
394,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.rat_cast_imK | [] | [
1366,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.tanh_eq_sinh_div_cosh | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(tanh x) = ↑(sinh x / cosh x)",
"tactic": "simp [tanh_eq_sinh_div_cosh]"
}
] | [
1391,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
8
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_coe | [] | [
1130,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_Ico_le_of_lt_one | [
{
"state_after": "case inl\nα : Type u\ninst✝ : LinearOrderedField α\nx : α\nhx : 0 ≤ x\nh'x : x < 1\nm n : ℕ\nhmn : m ≤ n\n⊢ ∑ i in Ico m n, x ^ i ≤ x ^ m / (1 - x)\n\ncase inr\nα : Type u\ninst✝ : LinearOrderedField α\nx : α\nhx : 0 ≤ x\nh'x : x < 1\nm n : ℕ\nhmn : n < m\n⊢ ∑ i in Ico m n, x ^ i ≤ x ^ m / (1 ... | [
375,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Std/Data/String/Lemmas.lean | String.anyAux_of_valid | [
{
"state_after": "p : Char → Bool\nl r : List Char\n⊢ (if h : { byteIdx := utf8Len l } < { byteIdx := utf8Len l + utf8Len [] } then\n if p (get { data := l ++ [] ++ r } { byteIdx := utf8Len l }) = true then true\n else\n let_fun this :=\n (_ :\n { byteIdx := utf8Len l + utf8... | [
715,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
707,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero | [
{
"state_after": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.101515\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.102031\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.102994\ninst✝² : Semiring S\nM : Type ... | [
138,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.id_comp | [] | [
802,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_eq_zero | [] | [
2421,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2420,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mul_def | [] | [
698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.preimage_mk_closure | [] | [
499,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.toLin'_apply | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.hsum_smul | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : Semiring R\nα : Type u_3\nx : HahnSeries Γ R\ns : SummableFamily Γ R α\ng : Γ\n⊢ coeff (hsum (x • s)) g = coeff (x * hsum s) g",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCancelAddCo... | [
1637,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1608,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_mul_top_of_neg | [] | [
911,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/NumberTheory/Fermat4.lean | Int.coprime_of_sq_sum' | [
{
"state_after": "r s : ℤ\nh : IsCoprime r s\n⊢ IsCoprime (r ^ 2 + s ^ 2) s",
"state_before": "r s : ℤ\nh : IsCoprime r s\n⊢ IsCoprime (r ^ 2 + s ^ 2) (r * s)",
"tactic": "apply IsCoprime.mul_right (Int.coprime_of_sq_sum (isCoprime_comm.mp h))"
},
{
"state_after": "r s : ℤ\nh : IsCoprime r s\n⊢ ... | [
167,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_one_comm | [
{
"state_after": "k : Type u₁\nG : Type u₂\nR : Type ?u.844334\ninst✝¹ : CommSemiring k\ninst✝ : MulOneClass G\nr : k\nf : MonoidAlgebra k G\nx✝ : G\n⊢ ↑(single 1 r * f) x✝ = ↑(f * single 1 r) x✝",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.844334\ninst✝¹ : CommSemiring k\ninst✝ : MulOneClass G\... | [
742,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.mem_rangeS | [] | [
608,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Order/Compare.lean | cmp_toDual | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_inj | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17832\nδ : Type ?u.17835\nι : Sort ?u.17838\ns : Set α\nt : Set β\nf : Filter α\ng : Filter β\nf₁ f₂ : Filter α\ng₁ g₂ : Filter β\ninst✝¹ : NeBot f₁\ninst✝ : NeBot g₁\nh : f₁ ×ˢ g₁ = f₂ ×ˢ g₂\n⊢ f₁ = f₂ ∧ g₁ = g₂",
"state_before": "α : Type u_1\nβ : ... | [
295,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_neg_one | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\n⊢ x ^ (-1) = x⁻¹",
"tactic": "simp [rpow_neg]"
}
] | [
96,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.nonempty_sInter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.140766\nγ : Type ?u.140769\nι : Sort ?u.140772\nι' : Sort ?u.140775\nι₂ : Sort ?u.140778\nκ : ι → Sort ?u.140783\nκ₁ : ι → Sort ?u.140788\nκ₂ : ι → Sort ?u.140793\nκ' : ι' → Sort ?u.140798\nc : Set (Set α)\n⊢ Set.Nonempty (⋂₀ c) ↔ ∃ a, ... | [
1234,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/Data/List/Sigma.lean | List.lookupAll_cons_ne | [] | [
271,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_mul | [] | [
2464,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2460,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_expand | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q : ℕ\nf : R[X]\nr : R\n⊢ ↑(expand R p) (↑(expand R q) (↑C r)) = ↑(expand R (p * q)) (↑C r)",
"tactic": "simp_rw [expand_C]"
},
{
"state_after": "no goals",
"state_before"... | [
73,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_one | [] | [
1469,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_dvd_lcm_mul_left_right | [] | [
857,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.tendsto_lp_of_tendsto_pi | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type ?u.1002373\nl : Filter ι\ninst✝ : NeBot l\n_i : Fact (1 ≤ p)\nF : ℕ → { x // x ∈ lp E p }\nhF : CauchySeq F\nf : { x // x ∈ lp E p }\nhf : Tendsto (id fun i => ↑(F i)) atTop (𝓝 ↑f)\n⊢ ∀ (i : ℝ), ... | [
1201,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn ν k : ℕ\nw : k < n - ν\n⊢ eval 1 ((↑derivative^[k]) (bernsteinPolynomial R n ν)) = 0",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν k : ℕ\n⊢ k < n - ν → eval 1 ((↑derivative^[k]) (bernsteinPolynomial R n ν)) = 0",
"tactic": "intro w"
},
... | [
225,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.equivQuotient_symm_proj_apply | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.natDegree_divByMonic | [
{
"state_after": "R✝ : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R✝\nn : ℕ\ninst✝¹ : CommRing R✝\np q : R✝[X]\nR : Type u\ninst✝ : CommRing R\nf g : R[X]\nhg : Monic g\n✝ : Nontrivial R\n⊢ natDegree (f /ₘ g) = natDegree f - natDegree g",
"state_before": "R✝ : Type u\nS : Type v\nT : Type w\nA : Type... | [
333,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Orthonormal.exists_orthonormalBasis_extension | [
{
"state_after": "case intro.intro.intro\nι : Type ?u.1609152\nι' : Type ?u.1609155\n𝕜 : Type u_1\ninst✝¹⁰ : IsROrC 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.1609184\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type ?u.1609202\ninst... | [
782,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit1_lt_bit0_iff | [] | [
740,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_bit | [
{
"state_after": "b : Bool\nn : ℕ\nh : bit b n ≠ 0\n⊢ binaryRec 0 (fun x x => succ) (bit b n) = succ (binaryRec 0 (fun x x => succ) n)",
"state_before": "b : Bool\nn : ℕ\nh : bit b n ≠ 0\n⊢ size (bit b n) = succ (size n)",
"tactic": "rw [size]"
},
{
"state_after": "b : Bool\nn : ℕ\nh : bit b n ≠... | [
85,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
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