file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | matPolyEquiv_eq_x_pow_sub_c | [
{
"state_after": "case a.a.h\nR : Type u\ninst✝⁵ : CommRing R\nn G : Type v\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\nα β : Type v\ninst✝² : DecidableEq α\nM✝ : Matrix n n R\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\nK : Type u_1\nk : ℕ\ninst✝ : Field K\nM : Matrix n n K\nm : ℕ\ni j : n\n⊢ coeff (↑matPolyEquiv (↑(... | [
221,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Algebra/Field/Basic.lean | neg_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.30697\nβ : Type ?u.30700\nK : Type u_1\ninst✝¹ : DivisionMonoid K\ninst✝ : HasDistribNeg K\na✝ b✝ a b : K\n⊢ -b / a = -(b / a)",
"tactic": "rw [neg_eq_neg_one_mul, mul_div_assoc, ← neg_eq_neg_one_mul]"
}
] | [
117,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.not_le_of_gt | [] | [
365,
55
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
360,
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Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow_succ | [
{
"state_after": "β : Type ?u.278866\nA : Type ?u.278869\nG : Type ?u.278872\nM : Type u_1\nR : Type ?u.278878\ninst✝ : LinearOrderedCommGroupWithZero M\na : M\nm n : ℕ\nha : 1 < a\n⊢ 1 * a ^ n < a * a ^ n",
"state_before": "β : Type ?u.278866\nA : Type ?u.278869\nG : Type ?u.278872\nM : Type u_1\nR : Type ... | [
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70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
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Mathlib/Topology/Connected.lean | Subtype.preconnectedSpace | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.71334\nπ : ι → Type ?u.71339\ninst✝ : TopologicalSpace α\ns✝ t u v s : Set α\nh : IsPreconnected s\n⊢ IsPreconnected univ",
"tactic": "rwa [← inducing_subtype_val.isPreconnected_image, image_univ, Subtype.range_val]"
}
] | [
863,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
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Mathlib/Data/Set/Basic.lean | Set.compl_inter | [] | [
1669,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1668,
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Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.submodule_mk | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Data/Nat/Periodic.lean | Function.Periodic.map_mod_nat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : ℕ → α\na : ℕ\nhf : Periodic f a\nn : ℕ\n⊢ f (n % a) = f n",
"tactic": "conv_rhs => rw [← Nat.mod_add_div n a, mul_comm, ← Nat.nsmul_eq_mul, hf.nsmul]"
}
] | [
41,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.find | [] | [
768,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
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Mathlib/Data/PFun.lean | PFun.mem_fix_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.19607\nδ : Type ?u.19610\nε : Type ?u.19613\nι : Type ?u.19616\nf : α →. β ⊕ α\na : α\nb : β\nh : b ∈ fix f a\nh₁ : Acc (fun x y => Sum.inr x ∈ f y) a\nh₂ :\n b ∈\n WellFounded.fixF\n (fun a IH =>\n Part.assert (f a).Dom fun hf =>\n ... | [
305,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.num_mem_deg | [] | [
519,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
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Mathlib/Data/Bool/AllAny.lean | List.any_iff_exists_prop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nl : List α\na : α\n⊢ (any l fun a => decide (p a)) = true ↔ ∃ a, a ∈ l ∧ p a",
"tactic": "simp [any_iff_exists]"
}
] | [
51,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
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Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.isIso_op_iff | [] | [
151,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_natMod | [
{
"state_after": "no goals",
"state_before": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ % ↑n✝ = ↑(Nat.mod n✝¹ n✝)",
"tactic": "aesop"
}
] | [
973,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.set_smul_subset_iff₀ | [] | [
1039,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mul_imI | [] | [
333,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.inr_apply | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Logic/Relation.lean | Relation.transGen_swap | [] | [
504,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
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Mathlib/NumberTheory/PythagoreanTriples.lean | coprime_sq_sub_mul | [
{
"state_after": "case inl\nm n : ℤ\nh : Int.gcd m n = 1\nh1 : m % 2 = 0 ∧ n % 2 = 1\n⊢ Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1\n\ncase inr\nm n : ℤ\nh : Int.gcd m n = 1\nh2 : m % 2 = 1 ∧ n % 2 = 0\n⊢ Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1",
"state_before": "m n : ℤ\nh : Int.gcd m n = 1\nhmn : m % 2 = 0 ∧ ... | [
403,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_restrict_of_subset_le | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.544674\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid M\ninst✝ : PartialOrder M\nv w : VectorMeasure α M\ni : Set α\nh : ∀ ⦃j : Set α⦄, MeasurableSet j → j ⊆ i → ↑v j ≤ ↑w j\nhi : MeasurableSet i\n⊢ restrict v i ≤ r... | [
891,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
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Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_nonneg_of_forall_set_integral_nonneg_of_stronglyMeasurable | [
{
"state_after": "α : Type u_1\nE : Type ?u.69084\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf : α → ℝ\nhfm : StronglyMeasurable f\nhf : Integrable f\nhf_zero : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → 0 ... | [
280,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.evaln_mono | [
{
"state_after": "no goals",
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"tactic": "simp [evaln] at h"
},
{
"state_after": "k k₂ : ℕ\nc : Code\nn x : ℕ\nhl : k + 1 ≤ k₂ + 1\nh : x ∈ evaln (k + 1) c n\nhl' : k ≤ k₂\n⊢ x ∈ evaln (k₂ + 1) c n",... | [
817,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Iio_neBot | [] | [
2412,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2411,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_C | [] | [
384,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/List/Forall2.lean | List.rel_join | [] | [
274,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.refl | [] | [
270,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/List/Indexes.lean | List.foldlIdx_eq_foldlIdxSpec | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nf : ℕ → α → β → α\na : α\nstart : ℕ\n⊢ foldlIdx f a [] start = foldlIdxSpec f a [] start\n\ncase cons\nα : Type u\nβ : Type v\nf : ℕ → α → β → α\nhead✝ : β\ntail✝ : List β\ntail_ih✝ : ∀ (a : α) (start : ℕ), foldlIdx f a tail✝ start = foldlIdxSpec f a tail✝ sta... | [
269,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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] |
Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | CategoryTheory.Free.single_comp_single | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\nC : Type u\ninst✝ : Category C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nr s : R\n⊢ (sum (single f r) fun f' s_1 => sum (single g s) fun g' t => single (f' ≫ g') (s_1 * t)) = single (f ≫ g) (r * s)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\nC : Type u\... | [
310,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | IsAbsoluteValue.map_prod | [] | [
761,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
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Mathlib/Data/Set/Basic.lean | Set.Subset.antisymm | [] | [
372,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_Ioi_atTop | [
{
"state_after": "ι : Type ?u.333628\nι' : Type ?u.333631\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.333640\ninst✝ : SemilatticeSup α\na : α\nf : β → ↑(Ioi a)\nl : Filter β\n⊢ Tendsto (Subtype.val ∘ f) l atTop ↔ Tendsto (fun x => ↑(f x)) l atTop",
"state_before": "ι : Type ?u.333628\nι' : Type ?u.333631\nα : ... | [
1597,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.norm_image_sub_le_of_norm_derivWithin_le | [] | [
654,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.right_le_of_le_left' | [] | [
739,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.self_sub_monomial_natDegree_leadingCoeff | [] | [
81,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/Atoms.lean | Set.isSimpleOrder_Iic_iff_isAtom | [] | [
683,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Algebra/LinearRecurrence.lean | LinearRecurrence.solSpace_rank | [] | [
203,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Star/Pointwise.lean | Set.star_preimage | [] | [
69,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_sInf | [] | [
676,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_ne_top | [
{
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321,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_lt_isLUB_of_ne | [] | [
1105,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
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Mathlib/CategoryTheory/Simple.lean | CategoryTheory.subobject_simple_iff_isAtom | [] | [
267,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sSameSide_lineMap_left | [] | [
738,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
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Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.rec_computable | [
{
"state_after": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nc : α → Code\nhc : Computable c\nz : α → σ\nhz : Computable z\ns : α → σ\nhs : Computable s\nl : α → σ\nhl : Computable l\nr : α → σ\nhr : Computable r\npr : α → Code × Code × σ × σ → σ\nhpr : Computable₂ pr\nco : α → C... | [
604,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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Mathlib/Order/LocallyFinite.lean | Ioo_ofDual | [
{
"state_after": "α : Type u_1\nβ : Type ?u.115891\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na✝ b✝ : α\na b : αᵒᵈ\n⊢ Ioo (↑ofDual a) (↑ofDual b) = Ioo b a",
"state_before": "α : Type u_1\nβ : Type ?u.115891\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder ... | [
880,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
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Mathlib/Computability/Reduce.lean | ManyOneDegree.le_refl | [
{
"state_after": "case h\nα : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : Type v\ninst✝³ : Primcodable β\ninst✝² : Inhabited β\nγ : Type w\ninst✝¹ : Primcodable γ\ninst✝ : Inhabited γ\np✝ : Set ℕ\n⊢ of p✝ ≤ of p✝",
"state_before": "α : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : ... | [
444,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
9
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Mathlib/Data/Set/Function.lean | Function.Semiconj.mapsTo_image | [] | [
1619,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1618,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_equiv_symm_one | [] | [
938,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_product_right | [] | [
683,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_pi | [
{
"state_after": "⊢ ↑0 = 0",
"state_before": "⊢ sin ↑π = 0",
"tactic": "rw [← ofReal_sin, Real.sin_pi]"
},
{
"state_after": "no goals",
"state_before": "⊢ ↑0 = 0",
"tactic": "simp"
}
] | [
1122,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.sSup_def | [
{
"state_after": "M : Type u_1\nN : Type ?u.30817\nP : Type ?u.30820\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nc : Con M\nS : Set (Con M)\n⊢ (conGen fun x y => ∃ c, c ∈ S ∧ ↑c x y) = conGen (⨆ (a : Con M) (_ : a ∈ S), ↑a)",
"state_before": "M : Type u_1\nN : Type ?u.30817\nP : Type ?u.30820\ninst✝² : ... | [
606,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Topology/Perfect.lean | Perfect.splitting | [
{
"state_after": "case intro\nα : Type u_1\ninst✝¹ : TopologicalSpace α\nC : Set α\ninst✝ : T25Space α\nhC : Perfect C\ny : α\nyC : y ∈ C\n⊢ ∃ C₀ C₁, (Perfect C₀ ∧ Set.Nonempty C₀ ∧ C₀ ⊆ C) ∧ (Perfect C₁ ∧ Set.Nonempty C₁ ∧ C₁ ⊆ C) ∧ Disjoint C₀ C₁",
"state_before": "α : Type u_1\ninst✝¹ : TopologicalSpace ... | [
160,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Order/Monotone/Basic.lean | Function.const_mono | [] | [
1197,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_σ_self' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ δ X (↑Fin.castSucc i) ≫ σ X i = 𝟙 (X.obj [n])",
"state_before": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nH : j = ↑Fin.castSucc i\n⊢ δ X j ≫ σ X i ... | [
538,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Topology/Filter.lean | ContinuousWithinAt.nhds | [] | [
236,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
18
] |
Mathlib/Data/List/Rdrop.lean | List.rdropWhile_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\n⊢ rdropWhile p [x] = if p x = true then [] else [x]",
"tactic": "rw [← nil_append [x], rdropWhile_concat, rdropWhile_nil]"
}
] | [
124,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mul_cancel_right_coe_nonZeroDivisors | [] | [
74,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_singleton_one | [] | [
226,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_nonempty | [] | [
1143,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.preimage_coe_inter_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\n⊢ val ⁻¹' (t ∩ s) = val ⁻¹' t",
"tactic": "rw [preimage_coe_eq_preimage_coe_iff, inter_assoc, inter_self]"
}
] | [
1448,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.tendsto_integral_cos_pow_mul_div | [
{
"state_after": "f : ℝ → ℂ\nhf : ContinuousOn f (Icc 0 (π / 2))\n⊢ Tendsto (fun n => (∫ (t : ℝ) in Icc 0 (π / 2), cos t ^ n)⁻¹ • ∫ (t : ℝ) in Icc 0 (π / 2), cos t ^ n • f t) atTop\n (𝓝 (f 0))",
"state_before": "f : ℝ → ℂ\nhf : ContinuousOn f (Icc 0 (π / 2))\n⊢ Tendsto (fun n => (∫ (x : ℝ) in 0 ..π / 2,... | [
302,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_mk_fin | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\n⊢ lift (#Fin n) = ↑n",
"tactic": "simp"
}
] | [
1316,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.divInt_ne_zero_of_ne_zero | [] | [
448,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.ofStream_cons | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\na : α\ns : Stream' α\n⊢ ↑↑(a :: s) = ↑(cons a ↑s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : Stream' α\n⊢ ↑(a :: s) = cons a ↑s",
"tactic": "apply Subtype.eq"
},
{
"state_after": "case a\nα : Type u\nβ : Type v\... | [
815,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_int_mod_four | [
{
"state_after": "n : ℤ\n⊢ ↑χ₄ ↑(n % ↑4) = ↑χ₄ ↑(n % 4)",
"state_before": "n : ℤ\n⊢ ↑χ₄ ↑n = ↑χ₄ ↑(n % 4)",
"tactic": "rw [← ZMod.int_cast_mod n 4]"
},
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ ↑χ₄ ↑(n % ↑4) = ↑χ₄ ↑(n % 4)",
"tactic": "norm_cast"
}
] | [
65,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.141980\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinear... | [
227,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Std/Data/List/Lemmas.lean | List.sublist_cons | [] | [
339,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
339,
9
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_induction' | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.648999\nP : Type ?u.649002\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\ns✝ s : Set M\np : (x : M) → x ∈ LowerAdjoint.toFun (closure L) s → Prop\nHs : ∀ (x : M) (h : x ∈ s), p x (_ : x ∈ ↑(LowerAdjoint.toFun ... | [
698,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | Metric.Bounded.right_of_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns : Set α\nt : Set β\nh : Bounded (s ×ˢ t)\nhs : Set.Nonempty s\n⊢ Bounded t",
"tactic": "simpa only [snd_image_prod hs t] using (@LipschitzWith.prod_s... | [
484,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.eq_bot_iff | [
{
"state_after": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\n⊢ K ≤ ⊥ ↔ ∀ (x : L), x ∈ K → x = 0",
"state_before": "R : Type u\nL : Type... | [
567,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.neg_normalize | [
{
"state_after": "n : Int\nd : Nat\nz : d ≠ 0\n⊢ -mk' (Int.div n ↑(Nat.gcd (Int.natAbs n) d)) (d / Nat.gcd (Int.natAbs n) d) =\n mk' (-Int.div n ↑(Nat.gcd (Int.natAbs n) d)) (d / Nat.gcd (Int.natAbs n) d)",
"state_before": "n : Int\nd : Nat\nz : d ≠ 0\n⊢ -normalize n d = normalize (-n) d",
"tactic": ... | [
210,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
209,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_pure | [] | [
288,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.mk_normalize | [] | [
131,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Convex/Basic.lean | MonotoneOn.convex_gt | [] | [
357,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Std/Data/Option/Lemmas.lean | Option.elim_none | [] | [
193,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
193,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_bot_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ relindex ⊥ H = Nat.card { x // x ∈ H }",
"tactic": "rw [relindex, bot_subgroupOf, index_bot]"
}
] | [
256,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_diff_of_mem | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nh : a ∈ t\nx✝ : α\n⊢ x✝ ∈ insert a s \\ t ↔ x✝ ∈ s \\ t",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nh : a ∈ t\n⊢ insert a s \\ t = s ... | [
1973,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1971,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.sSup_N | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.HasZeroObject.from_zero_ext | [] | [
264,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.multiset_prod_le | [
{
"state_after": "R : Type u\nι : Type ?u.344408\ninst✝ : CommSemiring R\nI J K L : Ideal R\ns : Multiset (Ideal R)\nP : Ideal R\nhp : IsPrime P\nhne : s ≠ 0\n⊢ Multiset.prod s ≤ P → ∃ I, I ∈ s ∧ I ≤ P",
"state_before": "R : Type u\nι : Type ?u.344408\ninst✝ : CommSemiring R\nI J K L : Ideal R\ns : Multiset... | [
1055,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/LinearAlgebra/BilinearForm/TensorProduct.lean | BilinForm.tensorDistribEquiv_apply | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.ne_iff_eq_neg | [] | [
357,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.coe_smul | [] | [
661,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.diag_mono | [] | [
345,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_one_add | [
{
"state_after": "no goals",
"state_before": "a b : Ordinal\n⊢ a ^ (1 + b) = a * a ^ b",
"tactic": "rw [opow_add, opow_one]"
}
] | [
211,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.filter_eq_iInf | [
{
"state_after": "case refine'_1\n𝕜 : Type u_1\n𝕜₂ : Type ?u.89095\n𝕝 : Type ?u.89098\n𝕝₂ : Type ?u.89101\nE : Type u_2\nF : Type ?u.89107\nG : Type ?u.89110\nι : Type u_3\nι' : Type ?u.89116\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np✝ : SeminormFamily 𝕜 E ι\ninst✝ : Nonempt... | [
208,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.map_think | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : Stream' (Option α)\nal : ∀ ⦃n : ℕ⦄ ⦃a : α⦄, s n = some a → s (n + 1) = some a\n⊢ ↑(map f (think { val := s, property := al })) = ↑(think (map f { val := s, property := al }))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf... | [
702,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Topology/Constructions.lean | map_fst_nhdsWithin | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.52987\nδ : Type ?u.52990\nε : Type ?u.52993\nζ : Type ?u.52996\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\nx : α × β\ns : Set α\... | [
699,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Std/Data/List/Lemmas.lean | List.length_range | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ length (range n) = n",
"tactic": "simp only [range_eq_range', length_range']"
}
] | [
1901,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1900,
9
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.div_eq_bot_iff | [] | [
465,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.unit_of_val_units | [] | [
738,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/NumberTheory/FermatPsp.lean | FermatPsp.coprime_of_fermatPsp | [
{
"state_after": "case intro.intro\nn b : ℕ\nh₁ : 1 ≤ b\nhp : ProbablePrime n b\nleft✝ : ¬Nat.Prime n\nhn₂ : 1 < n\n⊢ Nat.coprime n b",
"state_before": "n b : ℕ\nh : FermatPsp n b\nh₁ : 1 ≤ b\n⊢ Nat.coprime n b",
"tactic": "rcases h with ⟨hp, _, hn₂⟩"
},
{
"state_after": "no goals",
"state_b... | [
127,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.coe_copy | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_embedding | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.266753\nι' : Type ?u.266756\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ne : β → γ\nl : Filter α\nhm : ∀ (b₁ b₂ : β), e b₁ ≤ e b₂ ↔ b₁ ≤ b₂\nhu : ∀ (c : γ), ∃ b, c ≤ e b\n⊢ Tendsto (e ∘ f) l atTop ↔ T... | [
1348,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_empty | [] | [
1085,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/Data/Set/Function.lean | Set.InvOn.symm | [] | [
1182,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.prodComm_symm | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Homeomorph.toMeasurableEquiv_coe | [] | [
926,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.QInfty_f_naturality | [] | [
101,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_def' | [
{
"state_after": "case mk\nα : Type ?u.23052\nβ : Type ?u.23055\nγ : Type ?u.23058\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nα✝ : Type u_1\nr✝ : α✝ → α✝ → Prop\nwo✝ : IsWellOrder α✝ r✝\n⊢ Quotient.mk isEquivalent { α := α✝, r := r✝, wo := wo✝ } = type { α := α✝, r := r✝, wo := wo✝ }.r",
"state_... | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | eq_of_uniformity | [] | [
149,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
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