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/Topology/MetricSpace/Basic.lean | comap_dist_right_atTop_eq_cocompact | [] | [
2806,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2803,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.fderiv_integral_of_tendsto_ae | [] | [
734,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Std/Data/Array/Lemmas.lean | Array.mapIdx_induction | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nas : Array α\nf : Fin (size as) → α → β\nmotive : Nat → Prop\nh0 : motive 0\np : Fin (size as) → β → Prop\nhs : ∀ (i : Fin (size as)), motive i.val → p i (f i as[i]) ∧ motive (i.val + 1)\nthis :\n ∀ (p : Fin (size as) → β → Prop),\n (∀ (i : Fin (size as)), motiv... | [
201,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
193,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_apply | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.of_edist_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nx✝ y✝ : α\nr : ℝ≥0∞\nh : ∀ (x y : α), edist (f x) (f y) ≤ edist x y\nx y : α\n⊢ edist (f x) (f y) ≤ ↑1... | [
167,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
11
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_comp | [
{
"state_after": "l : Type ?u.22310\nm : Type u_1\nn : Type u_3\no : Type ?u.22319\nl' : Type ?u.22322\nm' : Type u_2\nn' : Type u_4\no' : Type ?u.22331\nm'' : Type u_5\nn'' : Type u_6\nR : Type u_8\nA : Type u_7\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid A\ninst✝ : Module R A\ne₁ : m ≃ m'\ne₂ : n ≃ n'\ne₁' :... | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_bot | [] | [
1673,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1672,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : LinearOrderedRing α\ninst✝² : LinearOrderedAddCommGroup β\ninst✝¹ : Module α β\ninst✝ : OrderedSMul α β\ns : Finset ι\nσ : Perm ι\nf : ι → α\ng : ι → β\nhfg : AntivaryOn f g ↑s\nhσ : {x | ↑σ x ≠ x} ⊆ ↑s\n⊢ ∑ i i... | [
240,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.sub_coeff | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddGroup R\nx y : HahnSeries Γ R\na : Γ\n⊢ coeff (x - y) a = coeff x a - coeff y a",
"tactic": "simp"
}
] | [
474,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_neg | [] | [
597,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.disjoint_iff | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → CanonicallyLinearOrderedAddMonoid (α i)\ninst✝ : DecidableEq ι\nf g : Π₀ (i : ι), α i\n⊢ support f ∩ support g = ∅ ↔ support f ⊓ support g = ⊥",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → CanonicallyLinearOrderedAd... | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
8
] |
Mathlib/Data/Set/Basic.lean | Set.powerset_inter | [] | [
2146,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2145,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : ConcreteCategory C\nJ : Type v\ninst✝² : SmallCategory J\nF : J ⥤ C\ninst✝¹ : PreservesColimit F (forget C)\ninst✝ : IsFiltered J\nD : Cocone F\ni j : J\nhD : IsColimit D\nx : (forget C).obj (F.obj i)\ny : (forget C).obj (F.obj j)\nh : (forget C).map (... | [
285,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.const_inv_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nf g : α → β\nc c₁ c₂ x : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\n⊢ Periodic (fun x => f (a⁻¹ • x)) (a • c)",
"tactic": "simpa only [inv_inv] using h.const_smu... | [
130,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Order/Kleene.lean | add_eq_right_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.20923\nι : Type ?u.20926\nπ : ι → Type ?u.20931\ninst✝ : IdemSemiring α\na b c : α\n⊢ a + b = b ↔ a ≤ b",
"tactic": "simp"
}
] | [
156,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocMod hp a (b - p) = toIocMod hp a b",
"tactic": "simpa only [one_zsmul] using toIocMod_sub_zsmul hp a b 1"
}
] | [
524,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.pi_div_four_le_arcsin | [
{
"state_after": "x : ℝ\n⊢ π / 4 ∈ Ioc (-(π / 2)) (π / 2)",
"state_before": "x : ℝ\n⊢ π / 4 ≤ arcsin x ↔ sqrt 2 / 2 ≤ x",
"tactic": "rw [← sin_pi_div_four, le_arcsin_iff_sin_le']"
},
{
"state_after": "x : ℝ\nthis : 0 < π\n⊢ π / 4 ∈ Ioc (-(π / 2)) (π / 2)",
"state_before": "x : ℝ\n⊢ π / 4 ∈ I... | [
277,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Int/GCD.lean | Int.dvd_lcm_right | [
{
"state_after": "i j : ℤ\n⊢ j ∣ ↑(Nat.lcm (natAbs i) (natAbs j))",
"state_before": "i j : ℤ\n⊢ j ∣ ↑(lcm i j)",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "i j : ℤ\n⊢ natAbs j ∣ Nat.lcm (natAbs i) (natAbs j)",
"state_before": "i j : ℤ\n⊢ j ∣ ↑(Nat.lcm (natAbs i) (natAbs j))",
"tactic"... | [
492,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | Commute.lie_eq | [] | [
65,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.IsImage.e_isoExt_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf : X ⟶ Y\nF F' : MonoFactorisation f\nhF : IsImage F\nhF' : IsImage F'\n⊢ F.e ≫ (isoExt hF hF').hom = F'.e",
"tactic": "simp"
}
] | [
229,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_toAddSubmonoid | [] | [
703,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable | [] | [
410,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.det_kronecker | [
{
"state_after": "R : Type u_3\nα : Type ?u.168871\nα' : Type ?u.168874\nβ : Type ?u.168877\nβ' : Type ?u.168880\nγ : Type ?u.168883\nγ' : Type ?u.168886\nl : Type ?u.168889\nm : Type u_1\nn : Type u_2\np : Type ?u.168898\nq : Type ?u.168901\nr : Type ?u.168904\nl' : Type ?u.168907\nm' : Type ?u.168910\nn' : Ty... | [
390,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Continuous.cexp | [] | [
115,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.dest'_eq_dest' | [
{
"state_after": "case refl\nn : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\nx : PFunctor.M (last P)\na₁ : P.A\nf₁ : PFunctor.B (last P) a₁ → PFunctor.M (last P)\nh₁ : PFunctor.M.dest x = { fst := a₁, snd := f₁ }\nf' : Path P x ⟹ α\nh₂ : PFunctor.M.dest x = { fst := a₁, snd := f₁ }\n⊢ dest' P h₁ f' = dest' P h₂ f... | [
233,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Topology/Maps.lean | ClosedEmbedding.continuous | [] | [
656,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.subsingleton_of_rank_adjoin_eq_one | [] | [
765,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.exists_open | [] | [
97,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/NormedSpace/Extend.lean | LinearMap.extendTo𝕜'_apply | [] | [
87,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | one_lt_gold | [
{
"state_after": "⊢ φ * 1 < φ * φ",
"state_before": "⊢ 1 < φ",
"tactic": "refine' lt_of_mul_lt_mul_left _ (le_of_lt gold_pos)"
},
{
"state_after": "no goals",
"state_before": "⊢ φ * 1 < φ * φ",
"tactic": "simp [← sq, gold_pos, zero_lt_one, - div_pow]"
}
] | [
119,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Std/Data/String/Lemmas.lean | String.get_of_valid | [] | [
211,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
210,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_inter_distrib_right | [] | [
1769,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Mathlib/Analysis/Convex/Caratheodory.lean | Caratheodory.mem_convexHull_erase | [
{
"state_after": "𝕜 : Type u_1\nE : Type u\ninst✝³ : LinearOrderedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : DecidableEq E\nt : Finset E\nh : ¬AffineIndependent 𝕜 Subtype.val\nx : E\nm : ∃ w x_1 x_2, centerMass t w id = x\n⊢ ∃ y w x_1 x_2, centerMass (erase t ↑y) w id = x",
"state_be... | [
103,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.ofNat_den | [] | [
166,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
166,
9
] |
Mathlib/Order/Monotone/Basic.lean | Antitone.strictAnti_of_injective | [] | [
422,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_singleton | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.206883\nγ : Type ?u.206886\ninst✝ : DecidableEq α\ns t u v : Finset α\na✝ b a x : α\n⊢ x ∈ erase {a} a ↔ x ∈ ∅",
"state_before": "α : Type u_1\nβ : Type ?u.206883\nγ : Type ?u.206886\ninst✝ : DecidableEq α\ns t u v : Finset α\na✝ b a : α\n⊢ erase {a} a = ∅... | [
1876,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1874,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.isCauSeq_norm | [] | [
797,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coe_inj | [] | [
130,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_eq_lim_of_equiv | [] | [
359,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/CategoryTheory/Abelian/Generator.lean | CategoryTheory.Abelian.has_projective_separator | [
{
"state_after": "case intro.intro\nC : Type u\ninst✝³ : Category C\ninst✝² : Abelian C\ninst✝¹ : HasColimits C\ninst✝ : EnoughProjectives C\nG : C\nhG : IsCoseparator G\nT : Cᵒᵖ\nhT₁ : Injective T\nhT₂ : IsCoseparator T\n⊢ ∃ G, Projective G ∧ IsSeparator G",
"state_before": "C : Type u\ninst✝³ : Category C... | [
61,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Topology/Basic.lean | mapClusterPt_of_comp | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\na : α\ns s₁ s₂ t : Set α\np✝ p₁ p₂ : α → Prop\ninst✝¹ : TopologicalSpace α\nι : Type u_1\nδ : Type u_2\nF : Filter ι\nφ : δ → ι\np : Filter δ\nx : α\nu : ι → α\ninst✝ : NeBot p\nh : Tendsto φ p F\nH : Tendsto (u ∘ φ) p (𝓝 x)\nthis : map (u ∘ φ) p ≤ map u F... | [
1164,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_subtype | [] | [
908,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_powerset_insert | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nb : β\nf✝ g : α → β\ninst✝¹ : DecidableEq α\ninst✝ : CommMonoid β\ns : Finset α\nx : α\nh : ¬x ∈ s\nf : Finset α → β\n⊢ ∀ (x_1 : Finset α), x_1 ∈ powerset s → ∀ (y : Finset α), y ∈ powerset s → insert x x_1 = insert x y → x_1 = y\... | [
257,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.ext_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.8146\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv w : VectorMeasure α M\n⊢ v = w → ∀ (i : Set α), MeasurableSet i → ↑v i = ↑w i\n\ncase mpr\nα : Type u_1\nβ : Type ?u.8146\nm : MeasurableSpace α\nM : Type u_2\n... | [
138,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Finset.tsum_subtype | [] | [
590,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.ext | [] | [
211,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.mul_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : MulZeroClass α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nhb : 0 ≤ b\n⊢ 0 ≤ a * b",
"tactic": "simpa only [mul_zero] using mul_le_mul_of_nonneg_left hb ha"
}
] | [
376,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.eq_liftOfRightInverse | [
{
"state_after": "G : Type ?u.666706\nG' : Type ?u.666709\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.666718\ninst✝³ : AddGroup A\nG₁ : Type u_1\nG₂ : Type u_2\nG₃ : Type u_3\ninst✝² : Group G₁\ninst✝¹ : Group G₂\ninst✝ : Group G₃\nf : G₁ →* G₂\nf_inv : G₂ → G₁\nhf : Function.RightInverse f_inv ↑f\ng : G₁... | [
3375,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3371,
1
] |
Mathlib/Logic/Relation.lean | Relation.iff_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11101\nγ : Type ?u.11104\nδ : Type ?u.11107\nr✝ : α → β → Prop\np : β → γ → Prop\nq : γ → δ → Prop\nr : Prop → α → Prop\nthis : (fun x x_1 => x ↔ x_1) = fun x x_1 => x = x_1\n⊢ (fun x x_1 => x ↔ x_1) ∘r r = r",
"tactic": "rw [this, ... | [
151,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLUB.csSup_eq | [] | [
533,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_mul_int_iff | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nm : ℤ\nn : ℕ\nx : ℝ\n⊢ Irrational (x * ↑m) ↔ m ≠ 0 ∧ Irrational x",
"tactic": "rw [← cast_coe_int, irrational_mul_rat_iff, Int.cast_ne_zero]"
}
] | [
619,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Analysis/Complex/Circle.lean | expMapCircle_add | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(↑expMapCircle (x + y)) = ↑(↑expMapCircle x * ↑expMapCircle y)",
"tactic": "simp only [expMapCircle_apply, Submonoid.coe_mul, ofReal_add, add_mul, Complex.exp_add]"
}
] | [
137,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div' | [
{
"state_after": "α : Type u_2\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : IsLocal... | [
878,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.toSubmonoid_injective | [] | [
237,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Topology/Order.lean | coinduced_compose | [] | [
487,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.balance1_toList | [
{
"state_after": "α : Type u_1\nl : RBNode α\nv : α\nr : RBNode α\n⊢ toList\n (match l, v, r with\n | node red (node red a x b) y c, z, d => node red (node black a x b) y (node black c z d)\n | node red a x (node red b y c), z, d => node red (node black a x b) y (node black c z d)\n | a, x, ... | [
421,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
419,
9
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Mathlib/Data/Int/Interval.lean | Int.Ioo_eq_finset_map | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.basis_singleton_iff | [
{
"state_after": "case mp\nι✝ : Type ?u.616874\nι' : Type ?u.616877\nR✝ : Type ?u.616880\nR₂ : Type ?u.616883\nK : Type ?u.616886\nM✝ : Type ?u.616889\nM' : Type ?u.616892\nM'' : Type ?u.616895\nV : Type u\nV' : Type ?u.616900\ninst✝¹⁰ : Semiring R✝\ninst✝⁹ : AddCommMonoid M✝\ninst✝⁸ : Module R✝ M✝\ninst✝⁷ : Ad... | [
854,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_sub_zsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIocMod hp a (b - m • p) = toIocMod hp a b",
"tactic": "rw [sub_eq_add_neg, ← neg_smul, toIocMod_add_zsmul]"
}
] | [
463,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.map_mrange | [
{
"state_after": "no goals",
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1064,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_one | [] | [
156,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Std/Data/List/Lemmas.lean | List.eq_or_mem_of_mem_insert | [] | [
914,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
913,
1
] |
Mathlib/MeasureTheory/Integral/Layercake.lean | MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul | [
{
"state_after": "α : Type u_1\ninst✝¹ : MeasurableSpace α\nf : α → ℝ\ng : ℝ → ℝ\ns : Set α\nμ : Measure α\ninst✝ : SigmaFinite μ\nf_nn : 0 ≤ f\nf_mble : Measurable f\ng_intble : ∀ (t : ℝ), t > 0 → IntervalIntegrable g volume 0 t\ng_nn : ∀ᵐ (t : ℝ) ∂Measure.restrict volume (Ioi 0), 0 ≤ g t\nex_G : ∃ G, Measurab... | [
207,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_neg' | [] | [
1355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/Algebra/Group/Conj.lean | conj_mul | [] | [
107,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.append_right_nil | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα✝ : Fin (n + 1) → Type u\nx : α✝ 0\nq : (i : Fin (n + 1)) → α✝ i\np : (i : Fin n) → α✝ (succ i)\ni : Fin n\ny : α✝ (succ i)\nz : α✝ 0\nα : Type ?u.31388\nu : Fin m → α\nv : Fin n → α\nhv : n = 0\n⊢ m + n = m",
"tactic": "rw [hv, add_zero]"
},
{... | [
313,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.univ_pi_Ioo_ae_eq_Icc | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.4246959\nα : ι → Type u_1\ninst✝⁴ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝³ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝² : ∀ (i : ι), SigmaFinite (μ i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : ∀ (i : ι), NoAtoms (μ i)\nf g... | [
521,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.quotient_map' | [] | [
1178,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
15
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_of_mul_dvd_mul_right | [
{
"state_after": "k m n : Nat\nkpos : 0 < k\nH : k * m ∣ k * n\n⊢ m ∣ n",
"state_before": "k m n : Nat\nkpos : 0 < k\nH : m * k ∣ n * k\n⊢ m ∣ n",
"tactic": "rw [Nat.mul_comm m k, Nat.mul_comm n k] at H"
},
{
"state_after": "no goals",
"state_before": "k m n : Nat\nkpos : 0 < k\nH : k * m ∣ ... | [
753,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
752,
11
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_ne_zero_iff | [] | [
197,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots | [
{
"state_after": "case pos\nM : Type ?u.3642802\nN : Type ?u.3642805\nG : Type ?u.3642808\nR : Type u_1\nS : Type ?u.3642814\nF : Type ?u.3642817\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k\ninst✝ : IsDomain R\nζ ... | [
935,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_biUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi✝ πi₁ πi₂ πi : (J : Box ι) → Prepartition J\n⊢ Prepartition.iUnion (biUnion π πi) = ⋃ (J : Box ι) (_ : J ∈ π), Prepartition.iUnion (πi J)",
"tactic": "simp [Prepartition.iUnion]"
}
] | [
345,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.of_mem_span_of_iff | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : CommMonoid M\ninst✝ : Nontrivial R\nm : M\nS : Set M\nh : ↑(of R M) m ∈ span R (↑(of R M) '' S)\n⊢ m ∈ S",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : CommMonoid M\ninst✝ : Nontrivial R\nm : M\nS : Set... | [
559,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.getVert_zero | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nw : Walk G u v\n⊢ getVert w 0 = u",
"tactic": "cases w <;> rfl"
}
] | [
217,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.lift_def | [] | [
1979,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1977,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.getLast_digit_ne_zero | [
{
"state_after": "case zero\nn m : ℕ\nhm : m ≠ 0\n⊢ List.getLast (digits zero m) (_ : digits zero m ≠ []) ≠ 0\n\ncase succ.zero\nn m : ℕ\nhm : m ≠ 0\n⊢ List.getLast (digits (succ zero) m) (_ : digits (succ zero) m ≠ []) ≠ 0\n\ncase succ.succ\nn m : ℕ\nhm : m ≠ 0\nb : ℕ\n⊢ List.getLast (digits (succ (succ b)) m)... | [
367,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_zero' | [
{
"state_after": "case inl\nα : Type u_1\nE : Type ?u.915301\nF : Type u_2\nG : Type ?u.915307\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhq0_ne : q ≠ 0\nhμ : μ ≠ 0\nhq0 : 0 ≤ q\n⊢ snorm' 0 q μ = 0\n\nc... | [
194,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_conj | [] | [
1007,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin'_stdBasis | [] | [
189,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.mem_leftTransversals_iff_existsUnique_inv_mul_mem | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\n⊢ (∀ (g : G), ∃! x, ↑x.fst * ↑x.snd = g) ↔ ∀ (g : G), ∃! s, (↑s)⁻¹ * g ∈ T",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\n⊢ S ∈ leftTransversals T ↔ ∀ (g : G), ∃! s, (↑s)⁻¹ * g ∈ T",
"tactic... | [
222,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.tendsto_toReal | [
{
"state_after": "case intro\nα : Type ?u.4599\ninst✝ : TopologicalSpace α\na : ℝ\nha : ↑a ≠ ⊤\nh'a : ↑a ≠ ⊥\n⊢ Tendsto toReal (𝓝 ↑a) (𝓝 (toReal ↑a))",
"state_before": "α : Type ?u.4599\ninst✝ : TopologicalSpace α\na : EReal\nha : a ≠ ⊤\nh'a : a ≠ ⊥\n⊢ Tendsto toReal (𝓝 a) (𝓝 (toReal a))",
"tactic":... | [
92,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.induction | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.314614\nγ : Type ?u.314617\nι : Type ?u.314620\nM : Type u_2\nM' : Type ?u.314626\nN : Type ?u.314629\nP : Type ?u.314632\nG : Type ?u.314635\nH : Type ?u.314638\nR : Type ?u.314641\nS : Type ?u.314644\ninst✝ : AddZeroClass M\np : (α →₀... | [
1096,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.map_id_id | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ map (𝟙 X) (𝟙 Y) ≫ fst = 𝟙 (X ⨯ Y) ≫ fst\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ map (𝟙 X) (𝟙 Y) ≫ snd = 𝟙 (X ⨯ Y) ≫ snd",
"state_before": "C : ... | [
729,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.snd | [] | [
828,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioc_mem_nhdsWithin_Ioi' | [] | [
414,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_ne_zero | [] | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_C_of_natDegree_eq_zero | [] | [
1121,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/Algebra/Group/Pi.lean | Function.update_mul | [] | [
624,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Filter.EventuallyEq.isEquivalent | [] | [
344,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_I_re | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (z * I).re = -z.im",
"tactic": "simp"
}
] | [
338,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_exp_div_pow_atTop | [
{
"state_after": "α : Type ?u.26645\nx y z : ℝ\nl : Filter α\nn : ℕ\nC : ℝ\nhC₁ : 1 ≤ C\n⊢ ∃ ia, True ∧ ∀ (x : ℝ), x ∈ Set.Ioi ia → exp x / x ^ n ∈ Set.Ici C",
"state_before": "α : Type ?u.26645\nx y z : ℝ\nl : Filter α\nn : ℕ\n⊢ Tendsto (fun x => exp x / x ^ n) atTop atTop",
"tactic": "refine' (atTop_b... | [
236,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_of_mem_C | [
{
"state_after": "case zero\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nhx✝ : x ∈ c✝.C\nc : CU X\nhx : x ∈ c.C\n⊢ approx Nat.zero c x = 0\n\ncase succ\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nhx✝ : x ∈ c✝.C\nn : ℕ\nihn : ∀ (c :... | [
146,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.neg | [
{
"state_after": "case intro\np q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nC : ℝ\nhC : ∃ᶠ (n : ℕ) in atTop, ∃ m, x ≠ ↑m / ↑n ∧ abs (x - ↑m / ↑n) < C / ↑n ^ p\n⊢ LiouvilleWith p (-x)",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\n⊢ LiouvilleWith p (-x)",
"tactic": "rcases h with ⟨C, hC⟩... | [
255,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
11
] |
Mathlib/Data/Finsupp/Antidiagonal.lean | Finsupp.antidiagonal_filter_fst_eq | [
{
"state_after": "case a.mk\nα : Type u\nf g : α →₀ ℕ\nD : (p : (α →₀ ℕ) × (α →₀ ℕ)) → Decidable (p.fst = g)\na b : α →₀ ℕ\n⊢ (a, b) ∈ Finset.filter (fun p => p.fst = g) (antidiagonal f) ↔ (a, b) ∈ if g ≤ f then {(g, f - g)} else ∅",
"state_before": "α : Type u\nf g : α →₀ ℕ\nD : (p : (α →₀ ℕ) × (α →₀ ℕ)) →... | [
72,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Logic/Equiv/List.lean | Encodable.encode_list_nil | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Order/Bounds/Basic.lean | image2_upperBounds_upperBounds_subset_upperBounds_image2 | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Antitone (f a)\na : α\nb : β\nha : a ∈ lowerBoun... | [
1470,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1467,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_sup | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\nB : Type ?u.722967\nS✝ : Type ?u.722970\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S✝\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S✝\nS T : Subalgebra R A\n⊢ Algebra.IsIntegral R { x //... | [
585,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_add | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ exp (x + y) = exp x * exp y",
"tactic": "simp [exp_add, exp]"
}
] | [
1137,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
8
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_eq_iInter_cthickening | [
{
"state_after": "ι : Sort ?u.144673\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns t : Set α\nx : α\nE : Set α\n⊢ cthickening 0 E = ⋂ (δ : ℝ) (_ : 0 < δ), cthickening δ E",
"state_before": "ι : Sort ?u.144673\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns t : Set α\nx ... | [
1363,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDerivWithin_neg_apply | [
{
"state_after": "case zero\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst... | [
1305,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
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