file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | DifferentiableOn.restrictScalars | [] | [
85,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Algebra/Order/Group/Defs.lean | le_inv_iff_mul_le_one_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ a * b ≤ b⁻¹ * b ↔ a * b ≤ 1",
"tactic": "rw [inv_mul_self]"
}
] | [
240,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Std/Data/String/Lemmas.lean | String.utf8GetAux_add_right_cancel | [
{
"state_after": "case ind\ns : List Char\ni p n : Nat\n⊢ ∀ (c : Char) (cs : List Char) (i : Pos),\n ¬i = { byteIdx := p } →\n utf8GetAux cs { byteIdx := i.byteIdx + csize c + n } { byteIdx := p + n } =\n utf8GetAux cs (i + c) { byteIdx := p } →\n (if { byteIdx := i.byteIdx + n } = { byt... | [
194,
11
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
185,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.pow | [] | [
1641,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
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Mathlib/Algebra/Associated.lean | unit_associated_one | [] | [
425,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_or_finite | [] | [
152,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
11
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Mathlib/Data/Matrix/PEquiv.lean | PEquiv.toMatrix_refl | [
{
"state_after": "case a.h\nk : Type ?u.9804\nl : Type ?u.9807\nm : Type ?u.9810\nn : Type u_1\nα : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Zero α\ninst✝ : One α\ni✝ x✝ : n\n⊢ toMatrix (PEquiv.refl n) i✝ x✝ = OfNat.ofNat 1 i✝ x✝",
"state_before": "k : Type ?u.9804\nl : Type ?u.9807\nm : Type ?u.9810\nn : T... | [
90,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_inv | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
11
] |
Mathlib/LinearAlgebra/TensorProduct/Matrix.lean | Matrix.toLin_kronecker | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nM : Type u_6\nN : Type u_7\nP : Type ?u.79666\nM' : Type u_8\nN' : Type u_9\nι : Type u_2\nκ : Type u_5\nτ : Type ?u.79681\nι' : Type u_1\nκ' : Type u_4\ninst✝¹⁸ : DecidableEq ι\ninst✝¹⁷ : DecidableEq κ\ninst✝¹⁶ : DecidableEq τ\ninst✝¹⁵ : Fintype ι... | [
64,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.le_of_epi | [] | [
516,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_sub' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.980208\nγ : Type ?u.980211\nδ : Type ?u.980214\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhg : AEMeasurable g\nhg_fin : (∫⁻ (a : α), g a ∂μ) ≠ ⊤\nh_le : g ≤ᵐ[μ] f\n⊢ ((∫⁻ (a : α), f a - g a ∂μ) + ∫⁻ (a : α), g a ∂μ) = ∫⁻ (a : α), f a ∂μ",
"state_befo... | [
914,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.zero_iff_nonpos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ smoothTransition x = 0 ↔ x ≤ 0",
"tactic": "simp only [smoothTransition, _root_.div_eq_zero_iff, (pos_denom x).ne', zero_iff_nonpos, or_false]"
}
] | [
190,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
8
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.map_injOn | [
{
"state_after": "α : Type ?u.385070\nβ : Type ?u.385073\nn d k N : ℕ\nx x₁ : Fin n → ℕ\nhx₁ : x₁ ∈ {x | ∀ (i : Fin n), x i < d}\nx₂ : Fin n → ℕ\nhx₂ : x₂ ∈ {x | ∀ (i : Fin n), x i < d}\nh : ↑(map d) x₁ = ↑(map d) x₂\n⊢ x₁ = x₂",
"state_before": "α : Type ?u.385070\nβ : Type ?u.385073\nn d k N : ℕ\nx : Fin ... | [
165,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.coeFn_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1924351\nι : Type ?u.1924354\nE : Type ?u.1924357\nF : Type ?u.1924360\n𝕜 : Type ?u.1924363\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\nG : Type u_2\ninst✝ : Norme... | [
819,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/RingTheory/Artinian.lean | isArtinian_of_le | [] | [
84,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.lt_def | [] | [
935,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.uniformContinuous_equiv_symm | [] | [
457,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.upper_le_upper | [] | [
103,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.minimalPeriod_dvd | [] | [
401,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.comp_assoc | [] | [
699,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjoint_comp | [
{
"state_after": "case h\n𝕜 : Type u_1\nE : Type u_4\nF : Type u_2\nG : Type u_3\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : Complete... | [
145,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/Instances/Rat.lean | Int.uniformEmbedding_coe_rat | [
{
"state_after": "no goals",
"state_before": "⊢ Pairwise fun x y => 1 ≤ dist ↑x ↑y",
"tactic": "simpa using Int.pairwise_one_le_dist"
}
] | [
80,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.le_cons | [
{
"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\ninst✝ : (i : Fin (n + 1)) → Preorder (α i)\nx : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\nj : Fin ... | [
255,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.rfl | [] | [
72,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_eq_zero_iff | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.2324170\nG : Type ?u.2324173\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → E\nhf : AEStronglyMeasurable f μ\nh0 : p ≠ 0\nh_top : ... | [
743,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_det_of_right_inverse | [] | [
227,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_Ioo_atBot | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf✝ : α → β\nf : β → ↑(Ioo a b)\n⊢ Tendsto (Subtype.val ∘ f) l (𝓝[Ioi a] a) ↔ Tendsto (fun x => ↑(f x)) l (𝓝[Ioi a] a)... | [
2566,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2564,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | RingHom.iterate_map_smul | [] | [
152,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.multinomial_univ_three | [
{
"state_after": "α : Type ?u.20128\ns : Finset α\nf : α → ℕ\na✝ b✝ : α\nn a b c : ℕ\n⊢ (Matrix.vecCons a ![b, c] 0 + Matrix.vecCons a ![b, c] 1 + Matrix.vecCons a ![b, c] 2)! /\n ((Matrix.vecCons a ![b, c] 0)! * (Matrix.vecCons a ![b, c] 1)! * (Matrix.vecCons a ![b, c] 2)!) =\n (a + b + c)! / (a ! * b ... | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_one | [] | [
66,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Finsupp/BigOperators.lean | List.support_sum_subset | [
{
"state_after": "case nil\nι : Type u_2\nM : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : AddMonoid M\n⊢ (sum []).support ⊆ foldr ((fun x x_1 => x ⊔ x_1) ∘ Finsupp.support) ∅ []\n\ncase cons\nι : Type u_2\nM : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : AddMonoid M\nhd : ι →₀ M\ntl : List (ι →₀ M)\nIH : (sum tl).su... | [
47,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_comp_perm_smul_le_sum_smul | [] | [
272,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_symm_coe | [] | [
726,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.pure_traverse | [
{
"state_after": "t : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng : α → F β\nh : β → G γ\nf : β → γ\nx✝ : t β\nx : t α\nthis : traverse... | [
97,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.sum_split_boxes | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nM✝ : Type ?u.34450\nn : ℕ\nI✝ J : Box ι\ni✝ : ι\nx✝ : ℝ\nM : Type u_1\ninst✝ : AddCommMonoid M\nI : Box ι\ni : ι\nx : ℝ\nf : Box ι → M\n⊢ ∑ J in (split I i x).boxes, f J = Option.elim' 0 f (Box.splitLower I i x) + Option.elim' 0 f (Box.splitUpper I... | [
200,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.gcd_content_eq_of_dvd_sub | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\na : R\np q : R[X]\nh : ↑C a ∣ p - q\n⊢ gcd a (Finset.gcd (Finset.range (Nat.succ (max (natDegree p) (natDegree q)))) (coeff p)) = gcd a (content q)",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ni... | [
348,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_subset_of_subset | [] | [
1099,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/Data/Nat/Factorial/Cast.lean | Nat.cast_descFactorial_two | [
{
"state_after": "S : Type u_1\ninst✝ : Ring S\na b : ℕ\n⊢ Polynomial.eval (↑(a - (2 - 1))) (pochhammer S 2) = ↑a * (↑a - 1)",
"state_before": "S : Type u_1\ninst✝ : Ring S\na b : ℕ\n⊢ ↑(descFactorial a 2) = ↑a * (↑a - 1)",
"tactic": "rw [cast_descFactorial]"
},
{
"state_after": "case zero\nS : ... | [
71,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.le_of_not_le_of_le | [] | [
169,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegrable_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.231038\n𝕜 : Type ?u.231041\nE : Type u_1\nF : Type ?u.231047\nA : Type ?u.231050\ninst✝ : NormedAddCommGroup E\nf : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\n⊢ IntervalIntegrable f μ a b ↔ IntegrableOn f (Ι a b)",
"tactic": "rw [uIoc_eq_union... | [
85,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cos_pow_aux | [
{
"state_after": "a b : ℝ\nn : ℕ\ncontinuous_cos_pow : ∀ (k : ℕ), Continuous fun x => cos x ^ k\n⊢ (∫ (x : ℝ) in a..b, cos x ^ (n + 2)) =\n (cos b ^ (n + 1) * sin b - cos a ^ (n + 1) * sin a + (↑n + 1) * ∫ (x : ℝ) in a..b, cos x ^ n) -\n (↑n + 1) * ∫ (x : ℝ) in a..b, cos x ^ (n + 2)",
"state_before"... | [
727,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | Complex.isTheta_exp_arg_mul_im | [
{
"state_after": "case intro\nα : Type u_1\nl : Filter α\nf g : α → ℂ\nb : ℝ\nhb : ∀ᶠ (x : ℝ) in Filter.map (fun x => Abs.abs (g x).im) l, (fun x x_1 => x ≤ x_1) x b\n⊢ (fun x => Real.exp (arg (f x) * (g x).im)) =Θ[l] fun x => 1",
"state_before": "α : Type u_1\nl : Filter α\nf g : α → ℂ\nhl : IsBoundedUnder... | [
167,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.mem_iff_eq_smul_annIdealGenerator | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nA : Type u_2\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\np : 𝕜[X]\na : A\n⊢ p ∈ annIdeal 𝕜 a ↔ ∃ s, p = s • annIdealGenerator 𝕜 a",
"tactic": "simp_rw [@eq_comm _ p, ← mem_span_singleton, ← span_singleton_annIdealGenerator 𝕜... | [
123,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.ccos | [] | [
185,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedComponent_subset | [] | [
47,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Algebra/Associated.lean | Associates.forall_associated | [] | [
763,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_coe | [] | [
455,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.to_ofPNatMultiset | [
{
"state_after": "v : Multiset ℕ+\nh : ∀ (p : ℕ+), p ∈ v → PNat.Prime p\n⊢ Multiset.map Coe.coe (Multiset.pmap (fun p hp => { val := ↑p, property := hp }) v h) = v",
"state_before": "v : Multiset ℕ+\nh : ∀ (p : ℕ+), p ∈ v → PNat.Prime p\n⊢ toPNatMultiset (ofPNatMultiset v h) = v",
"tactic": "dsimp [ofPN... | [
184,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Trident.ofCone_π | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝ : Category C\nX Y : C\nf : J → (X ⟶ Y)\nF : WalkingParallelFamily J ⥤ C\nt : Cone F\nj : WalkingParallelFamily J\n⊢ F.obj j = (parallelFamily fun j => F.map (line j)).obj j",
"tactic": "cases j <;> aesop_cat"
}
] | [
503,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isLittleO_pow_exp_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.185497\nx y z : ℝ\nl : Filter α\nn : ℕ\n⊢ (fun x => x ^ n) =o[atTop] exp",
"tactic": "simpa [isLittleO_iff_tendsto fun x hx => ((exp_pos x).ne' hx).elim] using\n tendsto_div_pow_mul_exp_add_atTop 1 0 n zero_ne_one"
}
] | [
362,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.continuousOn_prod_circle_transform_function | [
{
"state_after": "E : Type ?u.57155\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR✝ : ℝ\nz✝ w : ℂ\nR r : ℝ\nhr : r < R\nz : ℂ\n⊢ ContinuousOn (fun w => (1 / (circleMap z R w.snd - w.fst)) ^ 2) (closedBall z r ×ˢ univ)",
"state_before": "E : Type ?u.57155\ninst✝¹ : NormedAddCommGroup E\ninst✝ : N... | [
113,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.sphere_zero_subset | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.3289\nβ : Type ?u.3292\nn d k N : ℕ\nx✝ x : Fin n → ℕ\n⊢ x ∈ sphere n d 0 → x ∈ 0",
"tactic": "simp [sphere, Function.funext_iff]"
}
] | [
94,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_le_pow_card | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.93681\nα : Type ?u.93684\nM : Type u_1\nN : Type ?u.93690\nP : Type ?u.93693\nM₀ : Type ?u.93696\nG : Type ?u.93699\nR : Type ?u.93702\ninst✝⁵ : Monoid M\ninst✝⁴ : Monoid N\ninst✝³ : Monoid P\nl✝ l₁ l₂ : List M\na : M\ninst✝² : Preorder M\ninst✝¹ : C... | [
340,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.symmetric | [] | [
50,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.blsub_nadd_of_mono | [
{
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270,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineMap.affineIndependent_iff | [] | [
395,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Topology/Separation.lean | Filter.coclosedCompact_eq_cocompact | [
{
"state_after": "no goals",
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"tactic": "simp only [coclosedCompact, cocompact, iInf_and',\n and_iff_... | [
1272,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
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Mathlib/Topology/SubsetProperties.lean | irreducibleComponents_eq_maximals_closed | [
{
"state_after": "case h\nα✝ : Type u\nβ : Type v\nι : Type ?u.184350\nπ : ι → Type ?u.184355\ninst✝² : TopologicalSpace α✝\ninst✝¹ : TopologicalSpace β\ns✝ t : Set α✝\nα : Type u_1\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ s ∈ irreducibleComponents α ↔ s ∈ maximals (fun x x_1 => x ≤ x_1) {s | IsClosed s ∧ IsIr... | [
1781,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1772,
1
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Mathlib/Dynamics/Flow.lean | IsInvariant.isFwInvariant | [] | [
65,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.uniformContinuous_toFun | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.103188\nι : Type ?u.103191\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\nh : ⋃₀ 𝔖 = univ\n⊢ ∀ (i : α), UniformContinuous fun x => ↑(toFun 𝔖) x i",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1... | [
866,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
11
] |
Mathlib/Data/List/Basic.lean | List.dropLast_cons_cons | [] | [
693,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.pointwise_smul_le_pointwise_smul_iff | [] | [
509,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | Differentiable.restrictScalars | [] | [
89,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.mem_bipartiteAbove | [] | [
80,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.tail? | [
{
"state_after": "α : Type u_1\ns : Heap α\nle : α → α → Bool\ntl : Heap α\nhwf : WF le s\n⊢ Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl → WF le tl",
"state_before": "α : Type u_1\ns : Heap α\nle : α → α → Bool\ntl : Heap α\nhwf : WF le s\n⊢ Heap.tail? le s = some tl → WF le tl",
"tactic... | [
261,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
257,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_tri_right' | [
{
"state_after": "n m : ℕ\n⊢ n ≤ m + dist m n",
"state_before": "n m : ℕ\n⊢ n ≤ m + dist n m",
"tactic": "rw [dist_comm]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ n ≤ m + dist m n",
"tactic": "apply dist_tri_right"
}
] | [
67,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.localization_comap_range | [
{
"state_after": "case h\nR : Type u\nS : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing S\nS' : Type ?u.255999\ninst✝² : CommRing S'\nf : R →+* S\ninst✝¹ : Algebra R S\nM : Submonoid R\ninst✝ : IsLocalization M S\nx : PrimeSpectrum R\n⊢ x ∈ Set.range ↑(comap (algebraMap R S)) ↔ x ∈ {p | Disjoint ↑M ↑p.asIdeal}... | [
693,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π | [
{
"state_after": "J K : Type v\ninst✝⁵ : SmallCategory J\ninst✝⁴ : SmallCategory K\nC : Type u\ninst✝³ : Category C\nF : J ⥤ K ⥤ C\nG : J × K ⥤ C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimit G\ninst✝ : HasLimit (curry.obj G ⋙ lim)\nj : J\nk : K\n⊢ (limitIsoLimitCurryCompLim G).hom ≫ (limitIsoLimitCurryComp... | [
291,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.radical_le_jacobson | [] | [
247,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_one_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.24420\nι : Type ?u.24423\nM : Type u_1\nN : Type ?u.24429\ninst✝¹ : One M\ninst✝ : One N\ns✝ t : Set α\nf g : α → M\na : α\ns : Set M\n⊢ mulIndicator t 1 ⁻¹' s ∈ {univ, ∅}",
"tactic": "classical\n rw [mulIndicator_one', preimage_on... | [
303,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | DifferentiableAt.zpow | [] | [
164,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | centroid_mem_affineSpan_of_cast_card_ne_zero | [] | [
1214,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | Filter.EventuallyEq.deriv | [] | [
621,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
11
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.subsingleton_of_subsingleton | [
{
"state_after": "case allEq\nM : Type u_1\nN : Type ?u.12549\nA : Type ?u.12552\ninst✝² : Mul M\ns : Set M\ninst✝¹ : Add A\nt : Set A\nS : Subsemigroup M\ninst✝ : Subsingleton (Subsemigroup M)\n⊢ ∀ (a b : M), a = b",
"state_before": "M : Type u_1\nN : Type ?u.12549\nA : Type ?u.12552\ninst✝² : Mul M\ns : S... | [
287,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.pair_fst_snd | [] | [
114,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_le_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.105167\nι : Type ?u.105170\ninst✝ : CompleteLattice α\nf : Filter β\nu : β → α\n⊢ IsCoboundedUnder (fun x x_1 => x ≤ x_1) f u",
"tactic": "isBoundedDefault"
}
] | [
686,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ext | [
{
"state_after": "no goals",
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563,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
11
] |
Mathlib/Algebra/Order/Group/Defs.lean | LinearOrderedCommGroup.mul_lt_mul_left' | [] | [
1116,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.equiv_symm_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝¹² : AddCommMonoid M\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Algebra R S\ninst✝⁷ : Module R M\ninst✝⁶ : Module R N\ninst✝⁵ : Module S N\ninst✝⁴ : IsScalarTower R S ... | [
259,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Squarefree.lean | isRadical_iff_squarefree_or_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : GCDMonoid R\n⊢ IsRadical 0",
"state_before": "R : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : GCDMonoid R\nx : R\n⊢ x = 0 → IsRadical x",
"tactic": "rintro rfl"
},
{
"state_after": "R : Type u_1\ninst✝¹ : Can... | [
221,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.eq_X_sub_C_of_algebraMap_inj | [
{
"state_after": "A : Type u_1\nB : Type u_2\nB' : Type ?u.66784\ninst✝² : CommRing A\ninst✝¹ : Ring B\ninst✝ : Algebra A B\nx : B\na : A\nhf : Injective ↑(algebraMap A B)\n✝ : Nontrivial A\n⊢ minpoly A (↑(algebraMap A B) a) = X - ↑C a",
"state_before": "A : Type u_1\nB : Type u_2\nB' : Type ?u.66784\ninst✝... | [
213,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/List/AList.lean | AList.mem_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na a' : α\ns : AList β\n⊢ a' ∈ erase a s ↔ a' ≠ a ∧ a' ∈ s",
"tactic": "rw [mem_keys, keys_erase, s.keys_nodup.mem_erase_iff, ← mem_keys]"
}
] | [
236,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.param_zpow_mul | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : LinearOrderedField β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\nhf : ∀ (z : ℤ), Tendsto (fun a => k a ^ z * f a) l (𝓝 0)\nz : ℤ\n⊢ ∀ (z_1 : ℤ), Tendsto (fun a => k a ^ z_1 * (k a ^ z * f a... | [
264,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.mem_compactConvergence_nhd_filter | [
{
"state_after": "case mp\nα : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nY : Set C(α, β)\n⊢ Y ∈ FilterBasis.filter (compactConvergenceFilterBasis f) → ∃ K V _hK _hV, compactConvNhd K V f ⊆ Y\n\ncase mpr\nα : Type u₁\nβ : Type u₂\ninst✝¹ :... | [
166,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.centralizer_subset | [] | [
123,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/UpperLower/Basic.lean | lowerClosure_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.163100\nγ : Type ?u.163103\nι : Sort ?u.163106\nκ : ι → Sort ?u.163111\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\nx : α\nS : Set (Set α)\n⊢ lowerClosure (⋃₀ S) = ⨆ (s : Set α) (_ : s ∈ S), lowerClosure s",
"tactic": "sim... | [
1459,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_biUnion | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.520534\ninst✝¹ : DecidableEq β\ns✝ s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\ns : Finset α\nf : α → Finset β\np : β → Prop\ninst✝ : DecidablePred p\nb : β\n⊢ b ∈ filter p (Finset.biUnion s f) ↔ b ∈ Finset.biUnion s fun a => filter p (f a)",
"s... | [
3645,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3637,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.continuousAt_sign | [] | [
1039,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Topology/Connected.lean | connectedComponentIn_eq_image | [] | [
588,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.subset_normalizer | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.59591\nA : Type ?u.59594\na a₁ a₂ b c : G\ninst✝ : Group G\ns : Set G\nhs : IsSubgroup s\ng : G\nhg : g ∈ s\nn : G\n⊢ n ∈ s ↔ g * n * g⁻¹ ∈ s",
"tactic": "rw [IsSubgroup.mul_mem_cancel_right hs ((IsSubgroup.inv_mem_iff hs).2 hg),\n ... | [
319,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_biUnion_null_iff | [] | [
286,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.smul | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.119421\nα : Type u_2\nβ : Type ?u.119427\nE : Type ?u.119430\ninst✝⁹ : Group G\ninst✝⁸ : Group H\ninst✝⁷ : MulAction G α\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MulAction H β\ninst✝⁴ : MeasurableSpace β\ninst✝³ : NormedAddCommGroup E\ns t... | [
213,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.Prime.factors_pow | [
{
"state_after": "p : ℕ\nhp : Prime p\nn : ℕ\n⊢ replicate n p = factors (p ^ n)",
"state_before": "p : ℕ\nhp : Prime p\nn : ℕ\n⊢ factors (p ^ n) = replicate n p",
"tactic": "symm"
},
{
"state_after": "p : ℕ\nhp : Prime p\nn : ℕ\n⊢ replicate n p ~ factors (p ^ n)",
"state_before": "p : ℕ\nhp ... | [
190,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_think | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ head (think s) = Computation.think (head s)",
"tactic": "simp [head]"
}
] | [
666,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | PosMulMono.toPosMulStrictMono | [] | [
987,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_inverse | [] | [
533,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.desc_extend | [
{
"state_after": "case w\nJ : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F : J ⥤ C\ninst✝ : HasColimit F\nc : Cocone F\nX : C\nf : c.pt ⟶ X\nj✝ : J\n⊢ ι F j✝ ≫ desc F (Cocone.extend c f) = ι F j✝ ≫ desc F c ≫ f",
"state_before": "J : Type u₁\ninst✝³ :... | [
874,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_eq_sum_map_with_index_aux | [
{
"state_after": "n b : ℕ\nl : List ℕ\n⊢ List.zipWith ((fun i a => a * b ^ i) ∘ succ) (List.range (List.length l)) l =\n List.zipWith (fun i a => b * (a * b ^ i)) (List.range (List.length l)) l",
"state_before": "n b : ℕ\nl : List ℕ\n⊢ List.sum (List.zipWith ((fun i a => a * b ^ i) ∘ succ) (List.range (L... | [
177,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_mul | [
{
"state_after": "case mk.mk\nα : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * nb = ↑k * nc\nh₂ : da * db = k * dc\n⊢ IsRat (↑na * ⅟↑da * (↑nb * ⅟↑db)) nc dc",
"state_before": "α : Type u_1\ninst✝ : Ring α\nf : α → α → α\na b : α\nna nb nc ... | [
378,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.groupoid_of_isDetecting_empty | [] | [
241,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
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