file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.tendsto_integral_filter_of_dominated_convergence | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF✝ : Type ?u.995907\n𝕜 : Type ?u.995910\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : NormedAddCommGroup F✝\ninst✝² : Norme... | [
1010,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_le_infEdist_add_hausdorffEdist | [
{
"state_after": "ι : Sort ?u.38558\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\nε : ℝ≥0\nεpos : 0 < ε\nh : infEdist x s + hausdorffEdist s t < ⊤\nε0 : ↑ε / 2 ≠ 0\n⊢ infEdist x t ≤ infEdist x s + hausdorffEdist s t + ↑ε",
"state_bef... | [
336,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_le_map_iff_of_injective | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.594358\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.594367\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nhf : Injective ↑f\nH K : Subgroup G\n⊢ map f H ≤ map f K ↔ H ≤ K",
"tactic": "rw [map_le_iff_le_com... | [
3102,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3101,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.smul_boundedBy | [
{
"state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\nc : ℝ≥0∞\nhc : c ≠ ⊤\n⊢ OuterMeasure.ofFunction (c • fun s => ⨆ (_ : Set.Nonempty s), m s) (_ : (c • ⨆ (_ : Set.Nonempty ∅), m ∅) = 0) =\n OuterMeasure.ofFunction (fun s => ⨆ (_ : Set.Nonempty s), (c • m) s) (_ : (⨆ (_ : Set.Nonempty ∅), (c • m) ∅) = 0)",
... | [
902,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Topology/Maps.lean | ClosedEmbedding.comp | [] | [
694,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | measure_Ioc_lt_top | [] | [
4598,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4597,
1
] |
Mathlib/Data/Set/Prod.lean | Set.update_preimage_univ_pi | [] | [
862,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_add_nat | [] | [
378,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.option_elim' | [] | [
230,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.72544\nγ : Type ?u.72547\nι : Sort u_2\nι' : Sort ?u.72553\nf✝ : ι → α\ns t : Set α\nf : ι → α\n⊢ range f = ∅ ↔ IsEmpty ι",
"tactic": "rw [← not_nonempty_iff, ← range_nonempty_iff_nonempty, not_nonempty_iff_eq_empty]"
}
] | [
749,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_add_le | [] | [
342,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.remainder_lt' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nm : ℝ\nm1 : 1 < m\nm0 : 0 < m\nmi : 1 / m < 1\n⊢ (∑' (i : ℕ), 1 / m ^ (i + (n + 1)!)) = ∑' (i : ℕ), (1 / m) ^ i * (1 / m ^ (n + 1)!)",
"tactic": "simp only [pow_add, one_div, mul_inv, inv_pow]"
},
{
"state_after": "no goals",
"state_before... | [
137,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_le_neg_pi_div_two | [] | [
270,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.multiplicative_factorization | [
{
"state_after": "case hp\nβ : Type u_1\ninst✝ : CommMonoid β\nf : ℕ → β\nh_mult : ∀ (x y : ℕ), coprime x y → f (x * y) = f x * f y\nhf : f 1 = 1\n⊢ ∀ (p n : ℕ), Prime p → 0 < n → p ^ n ≠ 0 → f (p ^ n) = Finsupp.prod (factorization (p ^ n)) fun p k => f (p ^ k)\n\ncase h0\nβ : Type u_1\ninst✝ : CommMonoid β\nf ... | [
888,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Functor.preservesMonomorphisms_of_map_exact | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\ninst✝⁴ : Abelian C\nA : Type u₁\nB : Type u₂\ninst✝³ : Category A\ninst✝² : Category B\ninst✝¹ : Abelian A\ninst✝ : Abelian B\nL : A ⥤ B\nh : ∀ ⦃X Y Z : A⦄ {f : X ⟶ Y} {g : Y ⟶ Z}, Exact f g → Exact (L.map f) (L.map g)\nX✝ Y✝ : A\nf : X✝ ⟶ Y✝\nhf : Mono f\nthi... | [
399,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.20627\na a₁ a₂ : α\nb b₁ b₂ : β\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nl : α → β\nu : β → α\ngc : GaloisConnection l u\ns : Set α\n⊢ l (sSup s) = ⨆ (a : α) (_ : a ∈ s), l a",
"t... | [
307,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_image_const_self | [] | [
347,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.diagonal_kronecker | [] | [
338,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.zero_def | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/GradedMulAction.lean | GradedMonoid.mk_smul_mk | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_toOrderIso_inv | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.separation_prod | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\na₁ a₂ : α\nb₁ b₂ : β\n⊢ (a₁, b₁) ≈ (a₂, b₂) → a₁ ≈ a₂ ∧ b₁ ≈ b₂\n\ncase mpr\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : Unif... | [
437,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_option_elim | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.170514\nγ : Type ?u.170517\nι : Sort ?u.170520\nι' : Sort ?u.170523\nκ : ι → Sort ?u.170528\nκ' : ι' → Sort ?u.170533\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b a : α\nf : β → α\n⊢ (⨆ (o : Option β), Option.elim o... | [
1585,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/Topology/Order/Basic.lean | Iio_mem_nhds | [] | [
329,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi | [
{
"state_after": "θ ψ : Angle\nh : 2 • θ + 2 • ψ = ↑π\n⊢ tan ψ = (tan θ)⁻¹",
"state_before": "θ ψ : Angle\nh : 2 • θ + 2 • ψ = ↑π\n⊢ tan ψ = (tan θ)⁻¹",
"tactic": "simp_rw [two_zsmul, ← two_nsmul] at h"
},
{
"state_after": "no goals",
"state_before": "θ ψ : Angle\nh : 2 • θ + 2 • ψ = ↑π\n⊢ t... | [
846,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.abs_abv_sub_le_abv_sub | [
{
"state_after": "R : Type u_2\nS : Type u_1\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommRing S\nabv : AbsoluteValue R S\na b : R\n⊢ ↑abv b - ↑abv a ≤ ↑abv (b - a)",
"state_before": "R : Type u_2\nS : Type u_1\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommRing S\nabv : AbsoluteValue R S\na b : R\n⊢ ↑abv b - ↑ab... | [
275,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.algebraMap_mem | [] | [
134,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_sub_int | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nm : ℤ\nh : Irrational (x - ↑m)\n⊢ Irrational (x - ↑↑m)",
"tactic": "rwa [Rat.cast_coe_int]"
}
] | [
304,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | OrderIso.tendsto_atBot_iff | [] | [
438,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_le_iff | [] | [
237,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Std/Data/List/Lemmas.lean | List.length_replaceF | [
{
"state_after": "case cons\nα✝ : Type u_1\nf : α✝ → Option α✝\nhead✝ : α✝\ntail✝ : List α✝\ntail_ih✝ : length (replaceF f tail✝) = length tail✝\n⊢ length\n (match f head✝ with\n | none => head✝ :: replaceF f tail✝\n | some a => a :: tail✝) =\n succ (length tail✝)",
"state_before": "α✝ : T... | [
1346,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1345,
9
] |
Mathlib/Order/SuccPred/Basic.lean | Pred.rec_linear | [] | [
1462,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_mk | [] | [
606,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | one_memℓp_infty | [
{
"state_after": "case intro\nα : Type ?u.628429\nE : α → Type ?u.628434\np q : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\nI : Type u_1\nB : I → Type u_2\ninst✝¹ : (i : I) → NormedRing (B i)\ninst✝ : ∀ (i : I), NormOneClass (B i)\ni : I\n⊢ (fun i => ‖OfNat.ofNat 1 i‖) i ≤ 1",
"state_before": "α : Ty... | [
867,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Topology/Basic.lean | ClusterPt.of_inf_right | [] | [
1137,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.empty_not_mem | [] | [
169,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_one | [] | [
382,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_reindex | [] | [
186,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.hom_ext | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Mul β\nf g : FreeSemigroup α →ₙ* β\nh : ↑f ∘ of = ↑g ∘ of\nx✝ : FreeSemigroup α\nx : α\ny : FreeSemigroup α\nhx : ↑f (of x) = ↑g (of x)\nhy : ↑f y = ↑g y\n⊢ ↑f (of x * y) = ↑g (of x * y)",
"tactic": "simp only [map_mul, *]"
... | [
519,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.ext | [] | [
116,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.toFunBilinear_apply_eq_sum | [
{
"state_after": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na : A\np : R[X]\n⊢ (Finset.sum (support p) fun x => a • (↑(algebraMap R A[X]) (coeff p x) * X ^ x)) =\n Finset.sum (support p) fun x => ↑(monomial x) (a * ↑(algebraMap R A) (coeff p x))",
"sta... | [
66,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_equiv_eq_trans | [] | [
908,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.polar_closedBall | [
{
"state_after": "𝕜✝ : Type ?u.142772\ninst✝⁵ : NontriviallyNormedField 𝕜✝\nE✝ : Type ?u.142778\ninst✝⁴ : SeminormedAddCommGroup E✝\ninst✝³ : NormedSpace 𝕜✝ E✝\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nr : ℝ\nhr : 0 < r\n⊢ polar 𝕜 (closedBall ... | [
274,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.out_embedding | [
{
"state_after": "α β : Type u\nc c' : Cardinal\n⊢ c ≤ c' ↔ ?m.14386\n\nα β : Type u\nc c' : Cardinal\n⊢ ?m.14386 ↔ Nonempty (Quotient.out c ↪ Quotient.out c')\n\nα β : Type u\nc c' : Cardinal\n⊢ Prop",
"state_before": "α β : Type u\nc c' : Cardinal\n⊢ c ≤ c' ↔ Nonempty (Quotient.out c ↪ Quotient.out c')",
... | [
300,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/Finite/Card.lean | Set.card_union_le | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.6896\nγ : Type ?u.6899\ns t : Set α\nh : Finite ↑(s ∪ t)\n⊢ Nat.card ↑(s ∪ t) ≤ Nat.card ↑s + Nat.card ↑t\n\ncase inr\nα : Type u_1\nβ : Type ?u.6896\nγ : Type ?u.6899\ns t : Set α\nh : Infinite ↑(s ∪ t)\n⊢ Nat.card ↑(s ∪ t) ≤ Nat.card ↑s + Nat.card ↑t",
... | [
205,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.cons_val | [] | [
850,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_aux | [
{
"state_after": "a b : ℝ\nn : ℕ\ncontinuous_sin_pow : ∀ (k : ℕ), Continuous fun x => sin x ^ k\n⊢ (∫ (x : ℝ) in a..b, sin x ^ (n + 2)) =\n (sin a ^ (n + 1) * cos a - sin b ^ (n + 1) * cos b + (↑n + 1) * ∫ (x : ℝ) in a..b, sin x ^ n) -\n (↑n + 1) * ∫ (x : ℝ) in a..b, sin x ^ (n + 2)",
"state_before"... | [
646,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_exp_nhds_0_nhds_1 | [
{
"state_after": "case h.e'_5.h.e'_3\nα : Type ?u.22193\nx y z : ℝ\nl : Filter α\n⊢ 1 = exp 0",
"state_before": "α : Type ?u.22193\nx y z : ℝ\nl : Filter α\n⊢ Tendsto exp (𝓝 0) (𝓝 1)",
"tactic": "convert continuous_exp.tendsto 0"
},
{
"state_after": "no goals",
"state_before": "case h.e'_5... | [
192,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.comap_apply | [] | [
254,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.self_cast_int_mul | [] | [
1184,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable | [
{
"state_after": "case hc\nE : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nR : ℝ\nc w : ℂ\nf : ℂ → E\ns : Set ℂ\nhs : Set.Countable s\nhw : w ∈ ball c R\nhc : ContinuousOn f (closedBall c R)\nhd : ∀ (x : ℂ), x ∈ ball c R \\ s → DifferentiableAt ℂ f x\n⊢ 2 * ↑π * I ≠... | [
508,
36
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502,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pos_of_pos_of_lt_pi_div_two | [
{
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"state_before": "x : ℝ\nh0x : 0 < x\nhxp : x < π / 2\n⊢ 0 < tan x",
"tactic": "rw [tan_eq_sin_div_cos]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nh0x : 0 < x\nhxp : x < π / 2\n⊢ 0 < sin x / cos x",
... | [
941,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_comp_apply | [
{
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1072,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.nat_rawCast_2 | [] | [
116,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Data/Set/Countable.lean | Set.Countable.insert | [] | [
232,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Data/List/Lattice.lean | List.mem_bagInter | [
{
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"tactic": "simp only [nil_bagInter, not_mem_nil, false_and_iff]"
},
{
"state_after": "case pos\nα : Type u... | [
244,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Order/Chain.lean | succChain_spec | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7670\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\nh : ∃ t, IsChain r s ∧ SuperChain r s t\nthis : IsChain r s ∧ SuperChain r s (choose h)\n⊢ SuperChain r s (SuccChain r s)",
"state_before": "α : Type u_1\nβ : Type ?u.7670\nr : α → α → Prop\nc c₁ c₂ c₃ s... | [
169,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_inv' | [] | [
522,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
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Mathlib/Order/Hom/Lattice.lean | InfHom.symm_dual_comp | [] | [
1434,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_bit0 | [] | [
363,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Geometry/Manifold/Instances/Real.lean | EuclideanQuadrant.ext | [] | [
87,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.one_def | [] | [
704,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
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Mathlib/Topology/Basic.lean | IsClosed.mem_iff_closure_subset | [] | [
455,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Mathlib/Topology/Order/Basic.lean | map_coe_atTop_of_Ioo_subset | [
{
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2476,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2469,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_top | [] | [
876,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
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Mathlib/Topology/MetricSpace/Basic.lean | exists_lt_subset_ball | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousOn.inv₀ | [] | [
140,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Algebra/GroupPower/Lemmas.lean | MulOpposite.unop_zpow | [] | [
1272,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
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Mathlib/Data/Int/Interval.lean | Int.card_Icc | [
{
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"state_before": "a b : ℤ\n⊢ card (Icc a b) = toNat (b + 1 - a)",
"tactic": "change (Finset.map _ _).card = _"
},
{
"state_after": "no g... | [
109,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_prodMap | [
{
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2871,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/FunctorCategory.lean | CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom | [
{
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316,
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310,
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Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_injective | [
{
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"tactic": "... | [
2613,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2610,
1
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Std/Data/List/Lemmas.lean | List.erase_comm | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\nab : ¬a = b\n⊢ List.erase (List.erase l a) b = List.erase (List.erase l b) a",
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1100,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1087,
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Mathlib/Data/List/Rotate.lean | List.IsRotated.refl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl✝ l' l : List α\n⊢ rotate l 0 = l",
"tactic": "simp"
}
] | [
441,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.algebraMap_apply | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.derivation_C_mul' | [
{
"state_after": "σ : Type u_2\nR : Type u_1\nA : Type u_3\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Module R A\ninst✝ : Module (MvPolynomial σ R) A\nD : Derivation R (MvPolynomial σ R) A\na : R\nf : MvPolynomial σ R\nthis : ↑C a • ↑D f = ↑D (↑C a * f)\n⊢ ↑C a • ↑D f = a • ↑D f",
"state_b... | [
79,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.IsTransitive.sUnion' | [
{
"state_after": "case intro.intro\nx y✝ z✝ : ZFSet\nH : ∀ (y : ZFSet), y ∈ x → IsTransitive y\ny : ZFSet\nhy : y ∈ ⋃₀ x\nz : ZFSet\nhz : z ∈ y\nw : ZFSet\nhw : w ∈ x\nhw' : y ∈ w\n⊢ z ∈ ⋃₀ x",
"state_before": "x y✝ z✝ : ZFSet\nH : ∀ (y : ZFSet), y ∈ x → IsTransitive y\ny : ZFSet\nhy : y ∈ ⋃₀ x\nz : ZFSet\n... | [
77,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.exists_mem_eq_inf' | [] | [
1127,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.map | [
{
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222,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Data/Setoid/Basic.lean | Setoid.ker_lift_injective | [] | [
313,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.ae_eq_mk | [] | [
1859,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1858,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.append_nil | [] | [
790,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.strictAntiOn_natAbs | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ natAbs b < natAbs a",
"tactic": "simpa [Int.natAbs_neg] using\n natAbs_lt_natAbs_of_nonneg_of_lt (Right.nonneg_neg_iff.mpr hb) (neg_lt_neg_iff.mpr hab)"
}
] | [
94,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_add_right | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_zsmul] using toIocMod_add_zsmul hp a b 1"
}
] | [
484,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.mem_notConvergentSeq_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nι : Type u_1\nm : MeasurableSpace α\ninst✝¹ : MetricSpace β\nμ : Measure α\nn : ℕ\ni j : ι\ns : Set α\nε : ℝ\nf : ι → α → β\ng : α → β\ninst✝ : Preorder ι\nx : α\n⊢ (∃ i i_1, x ∈ {x | 1 / (↑n + 1) < dist (f i x) (g x)}) ↔ ∃ k x_1, 1 / (↑n + 1) < dist (f k x) (g x)",... | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_cond_eq_right | [
{
"state_after": "no goals",
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"tactic": "simp [@eq_comm _ a]... | [
841,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Algebra/Category/ModuleCat/Kernels.lean | ModuleCat.hasCokernels_moduleCat | [] | [
82,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Computability/Reduce.lean | oneOneEquiv_refl | [] | [
185,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Topology/Order/Basic.lean | closure_Iic | [] | [
164,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_apply_fintype | [] | [
324,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_dite | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.60200\ninst✝² : Fintype α\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : CommMonoid β\nf : (a : α) → p a → β\ng : (a : α) → ¬p a → β\n⊢ (∏ x : { x // x ∈ filter (fun x => p x) univ }, f ↑x (_ : p ↑x)) *\n ∏ x : { x // x ∈ filter (fun x => ¬p x) un... | [
278,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
8
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_singleton_one | [] | [
291,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.mono' | [] | [
1237,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
11
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.uniformEmbedding_of_bound | [] | [
175,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.eq_of_subset_of_ncard_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.49880\ns t : Set α\na b x y : α\nf : α → β\nh : s ⊆ t\nh' : ncard t ≤ ncard s\nht : autoParam (Set.Finite t) _auto✝\nhtfin : Fintype ↑t\n⊢ s = t",
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324,
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314,
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Mathlib/Data/Vector/Basic.lean | Vector.nth_eq_nthLe | [
{
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"state_before": "n : ℕ\nα : Type ?u.12116\nv : Vector α n\ni : Fin n\n⊢ ↑i < List.length (toList v)",
"tactic": "rw [toList_length]"
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{
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.mul_meas_ge_le_pow_snorm' | [
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Mathlib/Analysis/Seminorm.lean | Seminorm.mem_ball_zero | [
{
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_interval_sub_left | [] | [
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_sum_iff | [] | [
1000,
10
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998,
1
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