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/LinearAlgebra/FiniteDimensional.lean | LinearMap.ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nV₂ : Type v'\ninst✝³ : AddCommGroup V₂\ninst✝² : Module K V₂\ninst✝¹ : FiniteDimensional K V\ninst✝ : FiniteDimensional K V₂\nH : finrank K V = finrank K V₂\nf : V →ₗ[... | [
1059,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | WfDvdMonoid.of_exists_prime_factors | [
{
"state_after": "case refine'_2.intro.intro.intro\nα : Type u_1\ninst✝ : CancelCommMonoidWithZero α\npf : ∀ (a : α), a ≠ 0 → ∃ f, (∀ (b : α), b ∈ f → Prime b) ∧ Multiset.prod f ~ᵤ a\na b : α\nane0 : a ≠ 0\nc : α\nhc : ¬IsUnit c\nb_eq : b = a * c\n⊢ (if h : a = 0 then ⊤\n else ↑(↑Multiset.card (Classical.cho... | [
327,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | generateFrom_prod | [] | [
150,
72
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src/lean/Init/Prelude.lean | Nat.not_succ_le_zero | [] | [
1573,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1571,
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Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.eqToHom_proj | [
{
"state_after": "C : Type u\ninst✝ : Category C\nI : Type u_1\nx : GradedObject I C\ni : I\n⊢ eqToHom (_ : x = x) i = eqToHom (_ : x i = x i)",
"state_before": "C : Type u\ninst✝ : Category C\nI : Type u_1\nx x' : GradedObject I C\nh : x = x'\ni : I\n⊢ eqToHom h i = eqToHom (_ : x i = x' i)",
"tactic":... | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.toFun_eq_coe | [] | [
228,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.mem_cylinder_iff_le_firstDiff | [
{
"state_after": "case mp\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nhne : x ≠ y\ni : ℕ\n⊢ x ∈ cylinder y i → i ≤ firstDiff x y\n\ncase mpr\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nhne : x ≠ y\ni : ℕ\n⊢ i ≤ firstDiff x y → x ∈ cylinder y i",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nhne : x ≠ y\ni... | [
163,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasFDerivWithinAt.rpow_const | [] | [
454,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
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Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimitRecOn_pred | [] | [
395,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
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Mathlib/RingTheory/Int/Basic.lean | Nat.factors_multiset_prod_of_irreducible | [
{
"state_after": "s : Multiset ℕ\nh : ∀ (x : ℕ), x ∈ s → Irreducible x\n⊢ Multiset.Rel (fun x x_1 => Associated x x_1) (normalizedFactors (Multiset.prod s)) s",
"state_before": "s : Multiset ℕ\nh : ∀ (x : ℕ), x ∈ s → Irreducible x\n⊢ normalizedFactors (Multiset.prod s) = s",
"tactic": "rw [← Multiset.re... | [
331,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Data/Set/Lattice.lean | Set.subset_iInter_iff | [] | [
316,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_trim | [] | [
986,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
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Mathlib/Analysis/Normed/Group/InfiniteSum.lean | hasSum_of_subseq_of_summable | [] | [
105,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | Filter.EventuallyEq.iteratedFDerivWithin_eq | [
{
"state_after": "no goals",
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899,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_cos_add_sin_mul_I | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\nhθ : θ ∈ Set.Ioc (-π) π\n⊢ arg (cos ↑θ + sin ↑θ * I) = θ",
"tactic": "rw [← one_mul (_ + _), ← ofReal_one, arg_mul_cos_add_sin_mul_I zero_lt_one hθ]"
}
] | [
118,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_mul_of_dvd_right | [
{
"state_after": "α : Type u_1\ninst✝ : CommSemigroup α\na b c✝ : α\nh : a ∣ b\nc : α\n⊢ a ∣ b * c",
"state_before": "α : Type u_1\ninst✝ : CommSemigroup α\na b c✝ : α\nh : a ∣ b\nc : α\n⊢ a ∣ c * b",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nin... | [
172,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/Algebra/Lie/OfAssociative.lean | AlgHom.to_lieHom_injective | [
{
"state_after": "case H\nA : Type v\ninst✝⁶ : Ring A\nR : Type u\ninst✝⁵ : CommRing R\ninst✝⁴ : Algebra R A\nB : Type w\nC : Type w₁\ninst✝³ : Ring B\ninst✝² : Ring C\ninst✝¹ : Algebra R B\ninst✝ : Algebra R C\nf✝ : A →ₐ[R] B\ng✝ : B →ₐ[R] C\nf g : A →ₐ[R] B\nh : toLieHom f = toLieHom g\na : A\n⊢ ↑f a = ↑g a",... | [
201,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsQF.castLE | [] | [
737,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.coeFn_injective | [] | [
433,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty | [
{
"state_after": "case a\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁷ : Fintype ι\ninst✝¹⁶ : Fintype ι'\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : (i : ι) → NormedAddCommGroup (E... | [
821,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.neBot_inv_iff | [] | [
225,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.neg_mem | [] | [
190,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
11
] |
Mathlib/Data/Real/EReal.lean | EReal.induction₂ | [
{
"state_after": "case inl\nP : EReal → EReal → Prop\ntop_top : P ⊤ ⊤\ntop_pos : ∀ (x : ℝ), 0 < x → P ⊤ ↑x\ntop_zero : P ⊤ 0\ntop_neg : ∀ (x : ℝ), x < 0 → P ⊤ ↑x\ntop_bot : P ⊤ ⊥\npos_top : ∀ (x : ℝ), 0 < x → P ↑x ⊤\npos_bot : ∀ (x : ℝ), 0 < x → P ↑x ⊥\nzero_top : P 0 ⊤\ncoe_coe : ∀ (x y : ℝ), P ↑x ↑y\nzero_bot... | [
200,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
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Mathlib/Order/Filter/Basic.lean | Filter.nontrivial_iff_nonempty | [] | [
780,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.400038\nγ : Type ?u.400041\nδ : Type ?u.400044\nι : Type ?u.400047\nR : Type u_1\nR' : Type ?u.400053\nm0 : MeasurableSpace α\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ni... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.zero_testAgainstNN | [
{
"state_after": "case h\nΩ : Type u_1\ninst✝⁵ : MeasurableSpace Ω\nR : Type ?u.53954\ninst✝⁴ : SMul R ℝ≥0\ninst✝³ : SMul R ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : TopologicalSpace Ω\nx✝ : Ω →ᵇ ℝ≥0\n⊢ testAgainstNN 0 x✝ = OfNat.ofNat 0 x✝",
"state_before": "Ω : T... | [
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54
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369,
1
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Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_one | [] | [
235,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
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Mathlib/Topology/ContinuousOn.lean | ContinuousOn.comp | [] | [
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52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
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Std/Data/Int/DivMod.lean | Int.zero_ediv | [
{
"state_after": "no goals",
"state_before": "a✝ : Nat\n⊢ ofNat (0 / a✝) = 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "a✝ : Nat\n⊢ -ofNat (0 / succ a✝) = 0",
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}
] | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_union | [] | [
2039,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2037,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_pos | [] | [
223,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp'_supports | [
{
"state_after": "case zero'\nS : Finset Λ'\nk : Cont'\nH : codeSupp Code.zero' k ⊆ S\n⊢ Supports (codeSupp' Code.zero' k) S\n\ncase succ\nS : Finset Λ'\nk : Cont'\nH : codeSupp Code.succ k ⊆ S\n⊢ Supports (codeSupp' Code.succ k) S\n\ncase tail\nS : Finset Λ'\nk : Cont'\nH : codeSupp Code.tail k ⊆ S\n⊢ Supports... | [
2038,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2001,
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Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.cycles_eq_top | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\ni : ι\nh : ¬ComplexShape.Rel c i (ComplexShape.next c i)\n⊢ ⊤ ≤ cycles C i",
"state_before": "ι : Type u_1\nV : Type u\ninst✝² : Category V\nins... | [
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Mathlib/Algebra/Star/Subalgebra.lean | Subalgebra.star_adjoin_comm | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.414752\nR : Type u_2\nA : Type u_1\nB : Type ?u.414761\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRin... | [
380,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Card.lean | Finset.exists_ne_of_one_lt_card | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.58840\ns t : Finset α\nf : α → β\nn : ℕ\nhs : 1 < card s\na x : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≠ y\n⊢ ∃ b, b ∈ s ∧ b ≠ a",
"state_before": "α : Type u_1\nβ : Type ?u.58840\ns t : Finset α\nf : α → β\nn : ℕ\nhs : 1 < card s\... | [
593,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.card_typein_lt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.230049\nγ : Type ?u.230052\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nx : α\nh : ord (#α) = type r\n⊢ typein r x < type r",
"state_before": "α : Type u_1\nβ : Type ?u.230049\nγ : Type ?u.230052\nr✝ : α → α → ... | [
1453,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_self_atTop | [] | [
886,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.map | [] | [
851,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
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] |
Mathlib/Data/Finset/Sigma.lean | Finset.sigma_mono | [] | [
75,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | contDiffOn_homeomorphUnitBall_symm | [
{
"state_after": "case h\nn : ℕ∞\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nf : E → E\nh : ∀ (y : E) (hy : y ∈ ball 0 1), f y = ↑(Homeomorph.symm homeomorphUnitBall) { val := y, property := hy }\ny : E\nhy : y ∈ ball 0 1\n⊢ ContDiffAt ℝ n f y",
"state_before": "n : ℕ∞\nE : ... | [
388,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Order/BoundedOrder.lean | monotone_le | [] | [
565,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioc_union_Ico | [] | [
1624,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1623,
1
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Mathlib/GroupTheory/Nilpotent.lean | upperCentralSeries_mono | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ ∀ (n : ℕ), upperCentralSeries G n ≤ upperCentralSeries G (n + 1)",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ Monotone (upperCentralSeries G)",
"tactic": "refine' monotone_nat_... | [
217,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.norm_eq_one_of_pow_eq_one | [] | [
205,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sInfGen_def | [] | [
1145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeft_apply | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.continuous_abs | [] | [
176,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Nat/Choose/Bounds.lean | Nat.pow_le_choose | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedSemifield α\nr n : ℕ\n⊢ ↑((n + 1 - r) ^ r) ≤ ↑r ! * ↑(choose n r)\n\nα : Type u_1\ninst✝ : LinearOrderedSemifield α\nr n : ℕ\n⊢ 0 < ↑r !",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedSemifield α\nr n : ℕ\n⊢ ↑((n + 1 - r) ^ r) / ↑r ! ≤ ↑(choose n r... | [
48,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_sup | [] | [
64,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arctan_tan | [] | [
137,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_lt_add_iff_right | [] | [
789,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
788,
11
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_eq | [] | [
1617,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1615,
1
] |
Mathlib/Data/List/Dedup.lean | List.sum_map_count_dedup_eq_length | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : DecidableEq α\nl : List α\n⊢ sum (map (fun x => count x l) (dedup l)) = length l",
"tactic": "simpa using sum_map_count_dedup_filter_eq_countp (fun _ => True) l"
}
] | [
140,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_induction_on | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.37815\nG : Type ?u.37818\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN P : Submodule R M\np : M → Prop\nx : M\nH : x ∈ I • N\nHb : ∀ (r : R), r ∈ I → ∀ (n : M), n ∈ N → p (r • n)\nH1 : ∀ (x y : M), p x → p y → p (x ... | [
123,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.of_mul_left | [] | [
387,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_blockDiag' | [] | [
280,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.agree_iff_agree' | [
{
"state_after": "case mp\nF : PFunctor\nX : Type ?u.17090\nf : X → Obj F X\nn : ℕ\nx y : M F\nh : Agree (MIntl.approx x n) (MIntl.approx y (n + 1))\n⊢ Agree' n x y\n\ncase mpr\nF : PFunctor\nX : Type ?u.17090\nf : X → Obj F X\nn : ℕ\nx y : M F\nh : Agree' n x y\n⊢ Agree (MIntl.approx x n) (MIntl.approx y (n + ... | [
435,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.changeOriginSeries_summable_aux₃ | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.1521843\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... | [
1233,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/Order/Lattice.lean | sup_assoc | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d x : α\n⊢ (a ≤ x ∧ b ≤ x) ∧ c ≤ x ↔ a ≤ x ∧ b ≤ x ∧ c ≤ x",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d x : α\n⊢ a ⊔ b ⊔ c ≤ x ↔ a ⊔ (b ⊔ c) ≤ x",
"tactic": "simp only [sup_le_iff]"
},
{
"st... | [
255,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_singleton | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\ns : Finset ι\nι₂ : Type ?u.480542\ns₂ : Finset ι₂\np : ι → P\ni : ι\n⊢ centroid k {i} p = p i",
"tactic": ... | [
859,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | AddSubmonoid.closure_singleton_eq | [] | [
594,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_iff_comap | [] | [
2878,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2876,
1
] |
Mathlib/RingTheory/Valuation/Quotient.lean | Valuation.onQuot_comap_eq | [] | [
52,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Part.lean | Part.getOrElse_of_dom | [] | [
273,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_def | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr_trans | [] | [
534,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
9
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.of_null_right | [] | [
151,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/PathConnected.lean | Joined.mem_pathComponent | [] | [
948,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_one | [] | [
565,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
11
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | MulPosMono.toMulPosReflectLT | [] | [
316,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_reverse | [] | [
1133,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/Data/Set/Image.lean | Set.subset_image_union | [] | [
547,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | mod_mem_iff | [] | [
201,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_eq_span_iff | [] | [
233,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.toAddSubmonoid_strictMono | [] | [
257,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.prod_span | [] | [
612,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.length_ndinsert_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α\na : α\ns : Multiset α\nh : a ∈ s\n⊢ ↑card (ndinsert a s) = ↑card s",
"tactic": "simp [h]"
}
] | [
78,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.pow_factors | [
{
"state_after": "case zero\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\na : Associates α\n⊢ factors (a ^ Nat.zero) = Nat.zero • fa... | [
1801,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1796,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactConvNhd_nhd_basis | [
{
"state_after": "case intro.intro\nα : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nhV : V ∈ 𝓤 β\nV' : Set (β × β)\nh₁ : V' ∈ 𝓤 β\nh₂ : V' ○ V' ⊆ V\n⊢ ∃ V', V' ∈ 𝓤 β ∧ V' ⊆ V ∧ ∀ (g : C(α, β)), g ∈ compactConvNhd K V' f → compactConvNhd ... | [
127,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.evalFrom_nil | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/CategoryTheory/Types.lean | Equiv.toIso_inv | [] | [
330,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_toFinset | [] | [
220,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.isMin_iterate_pred_of_eq_of_lt | [] | [
659,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_pos | [] | [
2080,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2079,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antivary.antivaryOn | [] | [
66,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
11
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conj_apply | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) ⁻¹' Ioo b c = Ioo (b + a) (c + a)",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
212,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | deriv_sq_norm_ne_zero | [] | [
115,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
9
] |
Mathlib/Data/Bool/Count.lean | List.Chain'.count_false_le_count_true_add_one | [] | [
95,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.trans_symm_eq_iff_forall_isSome | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\n⊢ (∀ (x : α), x ∈ {a | isSome (↑f a) = true}) ↔ ∀ (a : α), isSome (↑f a) = true",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\n⊢ PEquiv.trans f (PEquiv.symm f) = PEquiv.refl α ↔ ∀ (a : α), isSome (↑... | [
290,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_toReal_iff | [
{
"state_after": "case intro\nα : Type ?u.305098\nβ : Type ?u.305101\nγ : Type ?u.305104\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx✝ y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Type u_1\nfi : Filter ι\nx : ℝ≥0∞\nhx : x ≠ ⊤\nf : ι → ℝ≥0\n⊢ Tendsto (fun n => ENNReal.toReal ((fun i => ↑(f i)) n)) fi (𝓝 (ENNReal.toReal x)) ↔ Tends... | [
1069,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.iSup_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.429228\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.429237\nι : Type ?u.429240\nκ : Type ?u.429243\ninst✝ : CompleteLattice β\na : α\ns : α → β\n⊢ (⨆ (x : α) (_ : x ∈ {a}), s x) = s a",
"tactic": "simp"
}
] | [
1932,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1932,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.mem | [
{
"state_after": "case cons_mem\nα : Type u_1\nl : List α\nx : α\nl' : List α\na✝ : x ∈ l'\n⊢ x ∈ x :: l'\n\ncase cons_duplicate\nα : Type u_1\nl : List α\nx y : α\nl' : List α\na✝ : x ∈+ l'\nhm : x ∈ l'\n⊢ x ∈ y :: l'",
"state_before": "α : Type u_1\nl : List α\nx : α\nh : x ∈+ l\n⊢ x ∈ l",
"tactic": "... | [
53,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubgroup_iUnion | [] | [
152,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.strictMono_of_injective | [] | [
418,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Order/Antisymmetrization.lean | acc_antisymmetrization_iff | [] | [
164,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.bot_or_nontrivial | [
{
"state_after": "case pos\nG : Type u_1\nG' : Type ?u.174621\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.174630\ninst✝ : AddGroup A\nH✝ K H : Subgroup G\nh : ∀ (x : G), x ∈ H → x = 1\n⊢ H = ⊥ ∨ Nontrivial { x // x ∈ H }\n\ncase neg\nG : Type u_1\nG' : Type ?u.174621\ninst✝² : Group G\ninst✝¹ : Group G'\n... | [
949,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_addEquiv_lpBcf_symm | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.bddAbove_mul | [
{
"state_after": "case intro.intro\nF : Type ?u.160142\nα : Type u_1\nβ : Type ?u.160148\nγ : Type ?u.160151\ninst✝ : OrderedCommMonoid α\nA B : Set α\nbA : α\nhbA : bA ∈ upperBounds A\nbB : α\nhbB : bB ∈ upperBounds B\n⊢ BddAbove (A * B)",
"state_before": "F : Type ?u.160142\nα : Type u_1\nβ : Type ?u.1601... | [
1334,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
] |
Mathlib/Algebra/ContinuedFractions/ContinuantsRecurrence.lean | GeneralizedContinuedFraction.denominators_recurrence | [
{
"state_after": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝ : DivisionRing K\ngp : Pair K\nppredB predB : K\nsucc_nth_s_eq : Stream'.Seq.get? g.s (n + 1) = some gp\nnth_denom_eq : denominators g n = ppredB\nsucc_nth_denom_eq : denominators g (n + 1) = predB\n⊢ ∃ conts, continuants g n = con... | [
75,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
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