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/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.m_pos_part_def | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.hasFDerivAt | [] | [
89,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/Connected.lean | IsConnected.nonempty | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_self | [] | [
188,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | Flow.omegaLimit_image_eq | [
{
"state_after": "no goals",
"state_before": "τ : Type u_1\ninst✝³ : TopologicalSpace τ\ninst✝² : AddCommGroup τ\ninst✝¹ : TopologicalAddGroup τ\nα : Type u_2\ninst✝ : TopologicalSpace α\nf : Filter τ\nϕ : Flow τ α\ns : Set α\nhf : ∀ (t : τ), Tendsto (fun x => x + t) f f\nt : τ\n⊢ ω f ϕ.toFun s = ω f ϕ.toFu... | [
379,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.mem_split_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type ?u.24493\nn : ℕ\nI J : Box ι\ni : ι\nx : ℝ\n⊢ J ∈ split I i x ↔ ↑J = Box.splitLower I i x ∨ ↑J = Box.splitUpper I i x",
"tactic": "simp [split]"
}
] | [
179,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.const_inv | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.1108115\nF : Type u_2\nG : Type ?u.1108121\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nc : F\nhμ : μ ≠ 0\n⊢ snormEssSup (fun x ... | [
284,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/PFun.lean | PFun.compl_dom_subset_core | [] | [
476,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.IsAdjMatrix.apply_ne_one_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.3595\nA : Matrix V V α\ninst✝¹ : MulZeroOneClass α\ninst✝ : Nontrivial α\nh : IsAdjMatrix A\ni j : V\n⊢ ¬A i j = 1 ↔ A i j = 0",
"tactic": "obtain h | h := h.zero_or_one i j <;> simp [h]"
}
] | [
73,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_imJ | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_ne_zero_iff' | [] | [
2019,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2018,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.IsSheafFor.unique_extend | [] | [
566,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_le_inv | [] | [
1492,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
11
] |
Mathlib/Analysis/Convex/Segment.lean | Icc_subset_segment | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type ?u.284099\nF : Type ?u.284102\nG : Type ?u.284105\nι : Type ?u.284108\nπ : ι → Type ?u.284113\ninst✝ : LinearOrderedField 𝕜\nx y z✝ z : 𝕜\nhxz : x ≤ z\nhyz : z ≤ y\n⊢ z ∈ [x-[𝕜]y]",
"state_before": "𝕜 : Type u_1\nE : Type ?u.284099\nF : Type ?u.28410... | [
500,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.Prime.prod_properDivisors | [
{
"state_after": "no goals",
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"tactic": "simp [h.properDivisors]"
}
] | [
382,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.inv_eq_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nf✝ g✝ : X ≅ Y\nX✝ Y✝ : C\nf g : X✝ ≅ Y✝\nh : f.hom = g.hom\n⊢ f.inv = g.inv",
"tactic": "rw [ext h]"
}
] | [
239,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Std/Data/Int/DivMod.lean | Int.zero_fdiv | [
{
"state_after": "no goals",
"state_before": "b : Int\n⊢ fdiv 0 b = 0",
"tactic": "cases b <;> rfl"
}
] | [
39,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
39,
9
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.not_mem_affineSpan_diff | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Nontrivial k\np : ι → P\nha : AffineIndependent k p\ni : ι\ns : Set ι\n⊢ ¬p i ∈ affineSpan k (p '' (s \\ {i})... | [
466,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.map_pre' | [
{
"state_after": "case w\nJ : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF✝ : J ⥤ C\ninst✝¹ : HasLimitsOfShape J C\nG : J ⥤ C\nα✝ : F✝ ⟶ G\ninst✝ : HasLimitsOfShape K C\nF : J ⥤ C\nE₁ E₂ : K ⥤ J\nα : E₁ ⟶ E₂\nj✝ : K\n⊢ pre F E₂ ≫ π (E₂ ⋙ F) j✝ = (pre F E₁ ≫ ... | [
552,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.mem_range_self | [] | [
668,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_zero | [] | [
88,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.ι_of_eq | [] | [
867,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.IsPrime.mul_mem_pow | [
{
"state_after": "case zero\nR : Type u_1\nA : Type ?u.1174042\nK : Type ?u.1174045\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : IsDomain R\ninst✝ : IsDedekindDomain R\nI : Ideal R\nhI : IsPrime I\na b : R\nh : a * b ∈ I ^ Nat.zero\n⊢ a ∈ I ∨ b ∈ I ^ Nat.zero\n\ncas... | [
1223,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1214,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.nextCoeff_map | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nf : R →+* S\nhf : Injective ↑f\np : R[X]\n⊢ (if natDegree (map f p) = 0 then 0 else coeff (map f p) (natDegree (map f p) - 1)) =\n ↑f (if natDegree p = 0 then 0 else coeff p (natDegree p - 1))",
... | [
349,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_sub_nat_mul_two_pi | [] | [
1248,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.paste_vert | [] | [
723,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_fst_prod | [] | [
932,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.support_formPerm_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.746484\ninst✝¹ : DecidableEq α\nl : List α\nx✝ : α\ninst✝ : Fintype α\nx : α\nhx : x ∈ support (formPerm l)\n⊢ x ∈ toFinset l",
"state_before": "α : Type u_1\nβ : Type ?u.746484\ninst✝¹ : DecidableEq α\nl : List α\nx : α\ninst✝ : Fintype α\n⊢ support (formPerm l) ... | [
208,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_zero_eq_zero | [] | [
107,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.zmodEquivZpowers_symm_apply_zpow' | [] | [
726,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | MulOpposite.map_unop_nhds | [] | [
73,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Antitone.map_limsInf_of_continuousAt | [] | [
371,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.ihom.coev_naturality | [] | [
128,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Order/Concept.lean | Concept.strictAnti_snd | [] | [
263,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Order/Hom/Basic.lean | Equiv.toOrderIso_toEquiv | [] | [
1134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.foldr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl m r : List Char\nf : Char → α → α\ninit : α\n⊢ Substring.foldr f init\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l },\n stopPos := { byteIdx := utf8Len l + utf8Len m } } =\n List.foldr f init m",
"tact... | [
926,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
925,
1
] |
Mathlib/Order/Monotone/Basic.lean | antitone_toDual_comp_iff | [] | [
157,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.lt_succ_self | [] | [
294,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
294,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.indicator_eq_of_affineCombination_eq | [] | [
274,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_of_tendsto | [] | [
1464,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.exists_lt_of_prod_lt' | [
{
"state_after": "ι : Type u_2\nα : Type ?u.143423\nβ : Type ?u.143426\nM : Type u_1\nN : Type ?u.143432\nG : Type ?u.143435\nk : Type ?u.143438\nR : Type ?u.143441\ninst✝ : LinearOrderedCancelCommMonoid M\nf g : ι → M\ns t : Finset ι\nHle : ∀ (i : ι), i ∈ s → g i ≤ f i\n⊢ ∏ i in s, g i ≤ ∏ i in s, f i",
"s... | [
555,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.toRelIsoLT_ofRelIsoLT | [
{
"state_after": "case h\nF : Type ?u.91547\nα✝ : Type ?u.91550\nβ✝ : Type ?u.91553\nγ : Type ?u.91556\nδ : Type ?u.91559\ninst✝⁴ : Preorder α✝\ninst✝³ : Preorder β✝\ninst✝² : Preorder γ\nα : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\ne : (fun x x_1 => x < x_1) ≃r fun x x_1 => x < ... | [
1059,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | ContinuousOn.tendstoUniformly | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝⁴ : UniformSpace α\ninst✝³ : UniformSpace β\ninst✝² : LocallyCompactSpace α\ninst✝¹ : CompactSpace β\ninst✝ : UniformSpace γ\nf : α → β → γ\nx : α\nU : Set α\nhxU : U ∈ 𝓝 x\nh : ContinuousOn (↿f) (U ×ˢ univ)\nK : Set α\nhx... | [
255,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_int_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝ : Ring R\np q r : R[X]\nn : ℤ\nx : R\n⊢ eval x ↑n = ↑n",
"tactic": "simp only [← C_eq_int_cast, eval_C]"
}
] | [
1246,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.mul_mem_center | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : Semigroup M\na b : M\nha : a ∈ center M\nhb : b ∈ center M\ng : M\n⊢ g * (a * b) = a * b * g",
"tactic": "rw [mul_assoc, ← hb g, ← mul_assoc, ha g, mul_assoc]"
}
] | [
66,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_eq_one_iff_pos | [] | [
1288,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1287,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.foldrM_eq_reverse_foldlM_data | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝ : Monad m\nf : α → β → m β\ninit : β\narr : Array α\nthis : arr = #[] ∨ 0 < size arr\n⊢ foldrM f init arr (size arr) = List.foldlM (fun x y => f y x) init (List.reverse arr.data)",
"state_before": "m : Type u_1 → Type u_2\nα : Type... | [
64,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_div | [
{
"state_after": "α : Type u_1\ninst✝ : DivisionRing α\nx✝³ x✝² : α\nx✝¹ : ℤ\nx✝ : ℕ\nh : IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝",
"state_before": "α : Type u_1\ninst✝ : DivisionRing α\nx✝³ x✝² : α\nx✝¹ : ℤ\nx✝ : ℕ\nh : IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsRat (x✝³ / x✝²) x✝¹ x✝",
"tactic":... | [
557,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_indicator | [] | [
522,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
src/lean/Init/Core.lean | Iff.comm | [] | [
675,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
674,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_eq_add_neg | [] | [
94,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
94,
11
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.C_neg | [] | [
72,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | TensorProduct.LieModule.coe_linearMap_map | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.contractNth_apply_of_lt | [] | [
964,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.vanishingIdeal_iUnion | [
{
"state_after": "case h.e'_3\nR : Type u_3\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nγ : Sort u_1\nt : γ → Set (ProjectiveSpectrum 𝒜)\n⊢ HomogeneousIdeal.toIdeal (⨅ (i : γ), vanishingIdeal (t i)) =\n ⨅ (i : γ), Homog... | [
276,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotoneOn_toDual_comp_iff | [] | [
172,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.coe_comp | [] | [
1096,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Data/List/Basic.lean | List.zipLeft_nil_left | [] | [
4181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4180,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | isLUB_of_tendsto_atBot | [] | [
295,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.linearIndependent_X | [] | [
124,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cotrident.π_ofπ | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_map_ret | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ ∀ {s t : WSeq α},\n (fun s1 s2 => join (map ret s2) = s1) s t →\n Computation.LiftRel (LiftRelO (fun x x_1 => x = x_1) fun s1 s2 => join (map ret s2) = s1) (destruct s)\n (destruct t)",
"state_before": "α : Type u\nβ : Type v... | [
1704,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1690,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_of_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b : α\nh : a = b\n⊢ a ∣ b",
"tactic": "rw [h]"
}
] | [
133,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.norm_of_mem_sphere | [
{
"state_after": "α : Type ?u.30416\nβ : Type ?u.30419\nn d k N : ℕ\nx✝ x : Fin n → ℕ\nhx : x ∈ sphere n d k\n⊢ Real.sqrt (∑ i : Fin n, ‖↑(PiLp.equiv 2 fun a => ℝ).symm (Nat.cast ∘ x) i‖ ^ 2) = Real.sqrt ↑k",
"state_before": "α : Type ?u.30416\nβ : Type ?u.30419\nn d k N : ℕ\nx✝ x : Fin n → ℕ\nhx : x ∈ sphe... | [
109,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.equicontinuousAt_iff_right | [] | [
50,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/RingTheory/Polynomial/Quotient.lean | MvPolynomial.eval₂_C_mk_eq_zero | [
{
"state_after": "R : Type u_1\nσ : Type u_2\ninst✝ : CommRing R\nr : R\nI : Ideal R\na : MvPolynomial σ R\nha : a ∈ Ideal.map C I\n⊢ ↑(eval₂Hom (RingHom.comp C (Ideal.Quotient.mk I)) X) (Finset.sum (support a) fun v => ↑(monomial v) (coeff v a)) = 0",
"state_before": "R : Type u_1\nσ : Type u_2\ninst✝ : Co... | [
215,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.vertices_eq | [
{
"state_after": "case h\n𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.39096\ninst✝² : OrderedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nK : SimplicialComplex 𝕜 E\ns t : Finset E\nx✝ x : E\n⊢ x ∈ vertices K ↔ x ∈ ⋃ (k : Finset E) (_ : k ∈ K.faces), ↑k",
"state_before": "𝕜 : Type u_2\nE : Type u_1\... | [
161,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.formPerm_reverse | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\ns s' : Cycle α\na✝ : List α\nh : Nodup (Quot.mk Setoid.r a✝)\n⊢ formPerm (reverse (Quot.mk Setoid.r a✝)) (_ : Nodup (reverse (Quot.mk Setoid.r a✝))) =\n (formPerm (Quot.mk Setoid.r a✝) h)⁻¹",
"state_before": "α : Type u_1\ninst✝ : DecidableEq... | [
192,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
8
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.Pairwise.mono' | [] | [
75,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_uIoc_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.586\nγ : Type ?u.589\nδ : Type ?u.592\nι : Type ?u.595\nR : Type ?u.598\nR' : Type ?u.601\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\ninst✝ : LinearOrder α\na b : α\nP : α → Prop\n⊢ (∀ᵐ (x : α) ∂μ, x ∈ Ι a b → P x) ↔... | [
125,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.extendWith_zero | [
{
"state_after": "case h.none\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.663995\nα : Option ι → Type v\ninst✝¹ : DecidableEq ι\ninst✝ : (i : Option ι) → Zero (α i)\nx : α none\n⊢ ↑(extendWith x 0) none = ↑(single none x) none\n\ncase h.some\nι :... | [
1662,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/Data/Sum/Order.lean | WithTop.orderIsoSumLexPUnit_toLex | [] | [
789,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_mul | [] | [
106,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.join_apply | [] | [
115,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.leftLim_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : ConditionallyCompleteLinearOrder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\nh : x ≤ y\nthis : TopologicalSpace α := Preorder.topology α\n⊢ leftLim f x ≤ f y",
"state_before": "α ... | [
110,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk | [] | [
734,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.17675\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\nm : Fin n → 𝕜\n⊢ ↑(iteratedFDerivWithin 𝕜 n f s x) m ... | [
109,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.mem_smul_pointwise_iff_exists | [] | [
83,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_eq_iff | [] | [
1764,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1759,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_dirac' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.1479555\n𝕜 : Type ?u.1479558\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : Nor... | [
1591,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictDerivAt.csin | [] | [
209,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_rat_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : LinearOrderedField R\na b : ℍ[R]\nq : ℚ\n⊢ ↑(↑normSq ↑q) = ↑q ^ 2",
"tactic": "rw [← coe_rat_cast, normSq_coe, coe_pow]"
}
] | [
1407,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.sum_repr_mul_repr_mul | [
{
"state_after": "R : Type ?u.810929\nM : Type ?u.810932\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M\ninst✝¹⁶ : Module R M\nR₁ : Type ?u.810968\nM₁ : Type ?u.810971\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_3\ninst✝¹² : CommSemiring R₂\ninst✝¹¹ : AddC... | [
845,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
src/lean/Init/Core.lean | Decidable.em | [] | [
735,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
734,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.eventually_nhds_iff | [] | [
950,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.hasBasis_compactConvergenceUniformity_of_compact | [] | [
432,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.coe_liftRight | [] | [
254,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/RingTheory/Ideal/Prod.lean | Ideal.isPrime_ideal_prod_top | [
{
"state_after": "case ne_top'\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ J' : Ideal S\nI : Ideal R\nh : IsPrime I\n⊢ prod I ⊤ ≠ ⊤\n\ncase mem_or_mem'\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ J' : Ideal S\nI : Ideal R\nh : IsPrime I\n⊢ ∀ {x y... | [
141,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.IsRegular.inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : HeytingAlgebra α\na b : α\nha : IsRegular a\nhb : IsRegular b\n⊢ IsRegular (a ⊓ b)",
"tactic": "rw [IsRegular, compl_compl_inf_distrib, ha.eq, hb.eq]"
}
] | [
70,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_top | [] | [
1881,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.addLECancellable_iff_ne | [
{
"state_after": "case mp\nα : Type ?u.165330\nβ : Type ?u.165333\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ AddLECancellable a → a ≠ ⊤\n\ncase mpr\nα : Type ?u.165330\nβ : Type ?u.165333\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ a ≠ ⊤ → AddLECancellable a",
"state_before": "α : Type ?u.165330\nβ : Type ?u... | [
1060,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_coe | [] | [
1999,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1998,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_zero' | [
{
"state_after": "R : Type ?u.826028\nR' : Type ?u.826031\n𝕜 : Type u_2\n𝕜₂ : Type ?u.826037\n𝕜₃ : Type ?u.826040\n𝕝 : Type ?u.826043\nE : Type u_1\nE₂ : Type ?u.826049\nE₃ : Type ?u.826052\nF : Type ?u.826055\nG : Type ?u.826058\nι : Type ?u.826061\ninst✝² : SeminormedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst... | [
687,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/RingTheory/Finiteness.lean | Ideal.fg_ker_comp | [
{
"state_after": "R✝ : Type ?u.349218\nM : Type ?u.349221\ninst✝⁵ : Semiring R✝\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R✝ M\nR : Type u_1\nS : Type u_2\nA : Type u_3\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing A\nf : R →+* S\ng : S →+* A\nhf : FG (RingHom.ker f)\nhg : FG (RingHom.ker g)\nhsu... | [
494,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Init/Algebra/Order.lean | Decidable.lt_or_eq_of_le | [] | [
217,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/List/Sigma.lean | List.mem_dlookup | [
{
"state_after": "case intro\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : NodupKeys l\nh : { fst := a, snd := b } ∈ l\nb' : β { fst := a, snd := b }.fst\nh' : dlookup { fst := a, snd := b }.fst l = some b'\n⊢ b ∈ dlookup a l",
"state... | [
220,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.coe_zero | [] | [
756,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.toMeasure_apply | [] | [
671,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasLimit_of_comp_equivalence | [] | [
261,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
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