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/Order/Category/LatCat.lean | latCat_dual_comp_forget_to_partOrdCat | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_def | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure | [] | [
922,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.one_right | [] | [
90,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mrangeRestrict_mker | [
{
"state_after": "case h\nM : Type u_1\nN : Type u_2\nP : Type ?u.138500\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.138521\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.138545\nmc : MonoidHomClass F M N\nf : M →* N\nx : M\n⊢ x ∈ mke... | [
1204,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.decompId_p_toKaroubi | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝ : Category C\nX : C\n⊢ decompId_p ((toKaroubi C).obj X) = 𝟙 (mk ((toKaroubi C).obj X).X (𝟙 ((toKaroubi C).obj X).X))",
"tactic": "rfl"
}
] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mk'_X_1 | [] | [
771,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_subset | [] | [
1780,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1779,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Ideal.rank_eq | [
{
"state_after": "case intro\nK : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.427665\nR✝ : Type u\ninst✝¹⁰ : Ring R✝\ninst✝⁹ : StrongRankCondition R✝\nM : Type v\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R✝ M\nR : Type u_1\nS : Type u_2\... | [
900,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_inter_of_neg | [] | [
1769,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_of_mul_eq_mul_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nha : a ≠ 0\nh : b * a = c * a\n⊢ (b - c) * a = 0",
"tactic": "rwa [Int.sub_mul, Int.sub_eq_zero]"
}
] | [
1311,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1309,
11
] |
Mathlib/Data/Prod/Basic.lean | Prod.Lex.trans | [] | [
268,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_empty | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nE : Type u_1\nF : Type ?u.5996\nι : Type u_3\nι' : Type ?u.6002\nα : Type ?u.6005\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst... | [
52,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.natCast_lt | [
{
"state_after": "α β : Type u\nm n : ℕ\n⊢ ↑m ≤ ↑n ∧ ¬↑n ≤ ↑m ↔ ¬n ≤ m",
"state_before": "α β : Type u\nm n : ℕ\n⊢ ↑m < ↑n ↔ m < n",
"tactic": "rw [lt_iff_le_not_le, ← not_le]"
},
{
"state_after": "α β : Type u\nm n : ℕ\n⊢ m < n → m ≤ n",
"state_before": "α β : Type u\nm n : ℕ\n⊢ ↑m ≤ ↑n ∧ ¬... | [
1361,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_le_lift | [
{
"state_after": "no goals",
"state_before": "c : Cardinal\n⊢ 𝔠 ≤ lift c ↔ 𝔠 ≤ c",
"tactic": "rw [← lift_continuum.{u,v}, lift_le]"
}
] | [
52,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Std/Data/List/Lemmas.lean | List.sublist.erase | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ eraseP (fun b => decide (a = b)) l₁ <+ eraseP (fun b => decide (a = b)) l₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ List.erase l₁ a <+ List.erase l₂ a",
"ta... | [
1080,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1079,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_left_right | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime x (y + x * z)",
"state_before": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime x (x * z + y)",
"tactic": "rw [add_comm]"
},
{
"state_after": "no goals",
"state_be... | [
315,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_two | [
{
"state_after": "⊢ cos (choose exists_cos_eq_zero) = 0",
"state_before": "⊢ cos (π / 2) = 0",
"tactic": "rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]"
},
{
"state_after": "no goals",
"state_before": "⊢ cos (choose exists_cos_eq_zero) = 0",
"tactic": "exact (Classical.choose_spec... | [
140,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.aestronglyMeasurable | [] | [
216,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj | [
{
"state_after": "ι : Sort ?u.101434\n𝕜 : Type ?u.101437\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nh : ¬Adj G a b\nhn : a ≠ b\n⊢ ∀ (x : Sym2 V), x ∈ incidenceSet G a → ¬x ∈ incidenceSet G b",
"state_before": "ι : Sort ?u.101434\n𝕜 : Type ?u.10... | [
872,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_inj | [] | [
76,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.Finite.wellFoundedOn | [] | [
494,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
11
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.commute_sub_nat | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ↑f fun x => x - ↑n",
"tactic": "simpa only [sub_eq_add_neg] using\n (f.commute_add_nat n).inverses_right (Equiv.addRight _).right_inv (Equiv.addRight _).left_inv"
}
] | [
344,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nv w : V\nh : IsMatching M\nhv : v ∈ M.verts\nhw : w ∈ M.verts\nha : Adj M v w\n⊢ toEdge h { val := v, property := hv } = toEdge h { val := w, property := hw }",
"tactic": "rw [h.toEdge_eq_of_adj hv ha, h.toEd... | [
83,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Finset/Pi.lean | Finset.mem_pi | [] | [
54,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Rel.lean | Rel.comp_assoc | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\nr✝ : Rel α β\nδ : Type u_1\nr : Rel α β\ns : Rel β γ\nt : Rel γ δ\n⊢ (fun x z => ∃ y, (∃ y_1, r x y_1 ∧ s y_1 y) ∧ t y z) = fun x z => ∃ y, r x y ∧ ∃ y_1, s y y_1 ∧ t y_1 z",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\nr✝ : Rel α β\n... | [
103,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_right_of_left_le' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.537715\nα : Type ?u.537718\nβ : Type u_3\nι : Type ?u.537724\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : LinearOrderedCancelAddCommMonoid β\ninst✝² : SMul 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul 𝕜 ... | [
733,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.not_lt | [] | [
52,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
51,
19
] |
Mathlib/Data/List/Sigma.lean | List.kerase_kerase | [
{
"state_after": "case pos\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nl : List (Sigma β)\nh : a = a'\n⊢ kerase a (kerase a' l) = kerase a' (kerase a l)\n\ncase neg\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nl : List (Sig... | [
473,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.map_lift | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Combinatorics/Quiver/Arborescence.lean | Quiver.shortest_path_spec | [] | [
114,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Algebra/Order/Ring/Canonical.lean | mul_tsub | [] | [
152,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_cases | [
{
"state_after": "ι : Type ?u.10756409\n𝕜 : Type ?u.10756412\nE : Type u_1\nF : Type ?u.10756418\nA : Type ?u.10756421\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na✝ b✝ : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\na b : ℝ\n⊢ ((if a ≤ b then 1 else -1) • ∫ (x... | [
504,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GeneralLinearGroup.toLinear_apply | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Opposite.lean | Opposite.unop_eq_iff_eq_op | [] | [
110,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_cons | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ Seq.join\n ((fun o =>\n match o with\n | none => Seq1.ret none\n | some s => (none, s)) <$>\n cons s S) =\n Seq.cons none\n (append s\n (Seq.join\n ((fun o =>\n ... | [
770,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Icc | [] | [
3352,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3351,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_univ | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.43744\nδ : Type ?u.43747\nε : Type ?u.43750\nι : Type ?u.43753\nf : α →. β\nx✝ : α\n⊢ x✝ ∈ preimage f Set.univ ↔ x✝ ∈ Dom f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.43744\nδ : Type ?u.43747\nε : Type ?u.43750\nι : Type ?u.43... | [
454,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_iff_nthLe | [] | [
340,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv | [
{
"state_after": "J : 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\nt : ColimitCocone F\nj : J\n⊢ t.cocone.ι.app j ≫ IsColimit.desc t.isColimit (cocone F) = ι F j",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : T... | [
833,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.mem_gradeBy_iff | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nι : Type u_3\nR : Type u_1\ninst✝¹ : DecidableEq M\ninst✝ : CommSemiring R\nf : M → ι\ni : ι\na : AddMonoidAlgebra R M\n⊢ a ∈ gradeBy R f i ↔ ↑a.support ⊆ f ⁻¹' {i}",
"tactic": "rfl"
}
] | [
66,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.225603\nf g : α → β\nc c₁ c₂ x : α\ninst✝² : Add α\ninst✝¹ : DivisionMonoid β\ninst✝ : HasDistribNeg β\nhf : Antiperiodic f c\nhg : Antiperiodic g c\n⊢ Periodic (f / g) c",
"tactic": "simp_all [neg_div_neg_eq]"
}
] | [
541,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Order/Iterate.lean | Monotone.le_iterate_of_le | [] | [
115,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_self | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu✝ v a✝ b u a : α\n⊢ (if Disjoint u a ∧ u ≤ a then (a ⊔ u) \\ u else a) = a",
"state_before": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\nin... | [
133,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.const_add_term | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommMonoid α\nk : α\nn : ℕ\nx a a' : α\nh : k + a = a'\n⊢ k + term n x a = term n x a'",
"tactic": "simp [h.symm, term, add_comm, add_assoc]"
}
] | [
128,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_ne_zero_of_eq_degree | [] | [
438,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.indicatorConstLp_disjoint_union | [
{
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801,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.hasFDerivWithinAt | [] | [
117,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_midpoint_right | [] | [
200,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_copy | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ici_of_neg | [] | [
575,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/Topology/Separation.lean | lim_nhdsWithin | [] | [
1084,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
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Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_one | [] | [
134,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.natDegree_mul | [
{
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176,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.unop | [] | [
1351,
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1350,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.AbsolutelyContinuous.prod | [
{
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.card_quotient_rightRel | [] | [
448,
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446,
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Mathlib/Data/Matrix/Reflection.lean | Matrix.exists_iff | [
{
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87,
42
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_empty | [] | [
194,
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193,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.le_generate | [] | [
422,
25
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421,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_normal | [
{
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488,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
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Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.rpow_arith_mean_le_arith_mean_rpow | [
{
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142,
63
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138,
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Mathlib/Algebra/CharZero/Lemmas.lean | nat_mul_inj | [
{
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114,
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112,
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Mathlib/LinearAlgebra/Dimension.lean | LinearEquiv.lift_rank_eq | [
{
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196,
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192,
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Ico.infinite | [] | [
56,
39
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_compl_le | [] | [
399,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/Algebra/Lie/OfAssociative.lean | LieSubmodule.coe_map_toEndomorphism_le | [
{
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269,
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266,
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Mathlib/Data/Nat/Totient.lean | Nat.totient_le | [] | [
66,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | PiLp.inner_apply | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Topology/Sheaves/Functors.lean | TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone | [
{
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62,
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Mathlib/Topology/Order.lean | coinduced_le_iff_le_induced | [] | [
411,
75
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409,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.trans_refl | [] | [
564,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
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Mathlib/Logic/Basic.lean | congr_fun₃ | [] | [
598,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
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Mathlib/GroupTheory/Archimedean.lean | Int.subgroup_cyclic | [
{
"state_after": "no goals",
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}
] | [
103,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.eventually_mul_div_cancel | [] | [
1916,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toLp_eq_toLp | [] | [
550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.preimage_ball | [] | [
247,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Std/Data/List/Lemmas.lean | List.filterMap_map | [
{
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1188,
52
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1186,
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Mathlib/Order/LiminfLimsup.lean | Filter.limsInf_eq_iSup_sInf | [] | [
681,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_pow | [
{
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414,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
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Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean | CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding | [
{
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166,
10
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150,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isNoetherian_zero | [
{
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1558,
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1554,
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Mathlib/Init/Data/List/Lemmas.lean | List.length_mapAccumr₂ | [] | [
80,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/Order/BooleanAlgebra.lean | sdiff_compl | [
{
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"tactic": "rw [sdiff_eq, compl_compl]"
}
] | [
699,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
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Mathlib/Data/List/Sigma.lean | List.kerase_cons_ne | [
{
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] | [
410,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_eq_of_sub_zsmul_mem_Ico | [] | [
57,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_smul | [
{
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1553,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.toStream_toList | [
{
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395,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
394,
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Mathlib/Analysis/Normed/Field/Basic.lean | NormOneClass.nontrivial | [
{
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}
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151,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_image | [] | [
275,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.incl_range | [] | [
1111,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
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Mathlib/Order/OmegaCompletePartialOrder.lean | CompleteLattice.sSup_continuous | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝¹ : OmegaCompletePartialOrde... | [
484,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_eq_card_dsupport | [] | [
396,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.dvd_add_self_left | [] | [
112,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
11
] |
Mathlib/Order/BoundedOrder.lean | OrderDual.ofDual_bot | [] | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_le_himp | [] | [
799,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.eq_of_bot_eq_bot_of_top_eq_top_of_length_eq_zero | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nhb : bot s₁ = bot s₂\nht : top s₁ = top s₂\nhs₁0 : s₁.length = 0\nthis : ∀ (x : X), x ∈ s₁ ↔ x = top s₁\n⊢ s₁ = s₂",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns... | [
744,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_piFinSuccAboveEquiv | [
{
"state_after": "ι : Type ?u.5778373\nι' : Type ?u.5778376\nα✝ : ι → Type ?u.5778381\ninst✝¹ : Fintype ι\nm✝ : (i : ι) → OuterMeasure (α✝ i)\nn : ℕ\nα : Fin (n + 1) → Type u\nm : (i : Fin (n + 1)) → MeasurableSpace (α i)\nμ : (i : Fin (n + 1)) → Measure (α i)\ninst✝ : ∀ (i : Fin (n + 1)), SigmaFinite (μ i)\ni ... | [
766,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.colex_le_of_subset | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nh : A ⊆ B\n⊢ toColex ∅ ≤ toColex (B \\ A)",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nh : A ⊆ B\n⊢ toColex A ≤ toColex B",
"tactic": "rw [← sdiff_le_sdiff_iff_le, sdiff_eq_empty_iff_subset.2 h]"
},
{
... | [
366,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Init/CcLemmas.lean | eq_true_of_not_eq_false | [] | [
116,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
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