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/Ring/Defs.lean | mul_max_of_nonneg | [] | [
969,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.proj_out | [] | [
467,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_of_lt_mul_of_le_one_of_nonneg_left | [] | [
920,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_pos_right | [
{
"state_after": "n m : Nat\nh : 0 < n\n⊢ 0 < n + m",
"state_before": "n m : Nat\nh : 0 < n\n⊢ 0 < m + n",
"tactic": "rw [Nat.add_comm]"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\nh : 0 < n\n⊢ 0 < n + m",
"tactic": "exact add_pos_left h m"
}
] | [
100,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
98,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_neg | [] | [
427,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_period | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.81127\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddGroup α\nh1 : Periodic f c₁\nh2 : Periodic f c₂\nx : α\n⊢ f (x + (c₁ - c₂)) = f x",
"tactic": "rw [sub_eq_add_neg, ← add_assoc, h2.neg, h1]"
}
] | [
179,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.coe_ndinter | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Topology/Algebra/Field.lean | Subfield.le_topologicalClosure | [] | [
66,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.mem_symmetricSubalgebra | [] | [
98,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.coprod_cofinite | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3352\nα : Type u_1\nβ : Type u_2\nl : Filter α\ns : Set (α × β)\n⊢ sᶜ ∈ Filter.coprod cofinite cofinite ↔ sᶜ ∈ cofinite",
"tactic": "simp only [compl_mem_coprod, mem_cofinite, compl_compl, finite_image_fst_and_snd_iff]"
}
] | [
120,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.mul_left₀ | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nF : Type ?u.95828\nα : Type u_1\nβ : Type ?u.95834\n𝕜 : Type ?u.95837\nE : Type ?u.95840\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NoZeroDivisors α\ns : Set α\na : α\nhs : MulSalemSpencer s\nha : a ≠ 0\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\... | [
241,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_inf | [] | [
141,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.bicomp_mono | [] | [
374,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.preimage_symm_proj_inter | [
{
"state_after": "case h.mk\nι : Type ?u.9734\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.9745\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne : Pretrivialization F proj\nx✝ : Z\ns : Set B\nx : B\ny : F\n⊢ (x, y) ∈ ↑(LocalEquiv.symm e.toLocalEquiv) ⁻¹' (proj ⁻¹' s) ∩ e.b... | [
198,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.of_s_head | [
{
"state_after": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nh : fract v ≠ 0\n⊢ Stream'.Seq.get? (of v).s 0 = some { a := 1, b := ↑⌊(fract v)⁻¹⌋ }",
"state_before": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nh : fract v ≠ 0\n⊢ Stream... | [
280,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_f | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_left_lineMap | [] | [
114,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/CompleteLattice.lean | toDual_iInf | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | gold_mul_goldConj | [
{
"state_after": "⊢ (1 + sqrt 5) * (1 - sqrt 5) = -(2 * 2)",
"state_before": "⊢ φ * ψ = -1",
"tactic": "field_simp"
},
{
"state_after": "⊢ 1 ^ 2 - sqrt 5 ^ 2 = -(2 * 2)",
"state_before": "⊢ (1 + sqrt 5) * (1 - sqrt 5) = -(2 * 2)",
"tactic": "rw [← sq_sub_sq]"
},
{
"state_after": ... | [
66,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | Subalgebra.star_mono | [] | [
371,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_equiv_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ (-x ≈ 0) ↔ (x ≈ 0)",
"tactic": "rw [neg_equiv_iff, neg_zero]"
}
] | [
1396,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1396,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_ofReal | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ ↑abs ↑r = Abs.abs r",
"tactic": "simp [Complex.abs, normSq_ofReal, Real.sqrt_mul_self_eq_abs]"
}
] | [
955,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.stabilizer_quotient | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ inst✝² : Group α\ninst✝¹ : MulAction α β\nx : β\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\nx✝ : G\n⊢ x✝ ∈ stabilizer G ↑1 ↔ x✝ ∈ H",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ inst✝² : Group α\ninst✝¹ : MulAction α β\... | [
232,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | RingEquiv.localRing | [] | [
543,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_le_iSup_lift | [
{
"state_after": "α β ι : Type u\nf : ι → Cardinal\n⊢ sum f ≤ sum fun x => iSup f",
"state_before": "α β ι : Type u\nf : ι → Cardinal\n⊢ sum f ≤ lift (#ι) * iSup f",
"tactic": "rw [← (iSup f).lift_id, ← lift_umax, lift_umax.{max u v, u}, ← sum_const]"
},
{
"state_after": "no goals",
"state_b... | [
994,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.out_empty_iff_eq_zero | [] | [
272,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLUB.ciSup_set_eq | [] | [
542,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.toBlocks_fromBlocks₁₁ | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prodAssoc_prod | [
{
"state_after": "α : Type u_2\nα' : Type ?u.4458428\nβ : Type u_3\nβ' : Type ?u.4458434\nγ : Type u_1\nE : Type ?u.4458440\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MeasurableSpace α'\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : MeasurableSpace β'\ninst✝⁴ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Measu... | [
536,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_inter_of_mem | [] | [
1583,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1582,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.int_coe_zmod_eq_iff | [
{
"state_after": "case mp\np : ℕ\nn : ℤ\nz : ZMod p\ninst✝ : NeZero p\n⊢ ↑n = z → ∃ k, n = ↑(val z) + ↑p * k\n\ncase mpr\np : ℕ\nn : ℤ\nz : ZMod p\ninst✝ : NeZero p\n⊢ (∃ k, n = ↑(val z) + ↑p * k) → ↑n = z",
"state_before": "p : ℕ\nn : ℤ\nz : ZMod p\ninst✝ : NeZero p\n⊢ ↑n = z ↔ ∃ k, n = ↑(val z) + ↑p * k",... | [
548,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.symm | [] | [
354,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
8
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.to_real_linear_equiv_apply | [] | [
139,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/Sequences.lean | IsSeqClosed.preimage | [] | [
214,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/Maps.lean | Inducing.nhdsSet_eq_comap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1466\nδ : Type ?u.1469\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : Inducing f\ns : Set α\n⊢ 𝓝ˢ s = comap f (𝓝ˢ (f '' s))",
"tact... | [
101,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.vsub_apply | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_diagonal | [
{
"state_after": "case a.h\nl : Type u_1\nm : Type u_2\nn : Type ?u.116901\no : Type ?u.116904\np : Type ?u.116907\nq : Type ?u.116910\nm' : o → Type ?u.116915\nn' : o → Type ?u.116920\np' : o → Type ?u.116925\nR : Type ?u.116928\nS : Type ?u.116931\nα : Type u_3\nβ : Type ?u.116937\ninst✝² : DecidableEq l\nins... | [
303,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Quot.lean | Quotient.map₂_mk | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | exists_square_le' | [
{
"state_after": "case inl\nα : Type u_1\na b c d : α\ninst✝³ : MulOneClass α\ninst✝² : Zero α\ninst✝¹ : LinearOrder α\ninst✝ : PosMulStrictMono α\na0 : 0 < a\nha : a < 1\n⊢ ∃ b, b * b ≤ a\n\ncase inr\nα : Type u_1\na b c d : α\ninst✝³ : MulOneClass α\ninst✝² : Zero α\ninst✝¹ : LinearOrder α\ninst✝ : PosMulStri... | [
970,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_deriv_comp_smul_deriv' | [
{
"state_after": "ι : Type ?u.1918101\n𝕜 : Type ?u.1918104\nE : Type u_1\nF : Type ?u.1918110\nA : Type ?u.1918113\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝¹ : ℝ → E\ng'✝ g✝ φ : ℝ → ℝ\nf✝ f'✝ : ℝ → E\na b : ℝ\nf f' : ℝ → ℝ\ng g' : ℝ → E\nhf : ContinuousOn f [[a, b]]\... | [
1442,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_sub_eq_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c✝ : α\nn : ℤ\na b c : α\n⊢ toIocMod hp a (b - c) = toIocMod hp (a + c) b - c",
"tactic": "simp_rw [toIocMod, toIocDiv_sub_eq_toIocDiv_add, sub_right_comm]"
}
] | [
537,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.analyticSet_empty | [
{
"state_after": "α : Type u_1\ninst✝ : TopologicalSpace α\nι : Type ?u.465\n⊢ ∅ = ∅ ∨ ∃ f, Continuous f ∧ range f = ∅",
"state_before": "α : Type u_1\ninst✝ : TopologicalSpace α\nι : Type ?u.465\n⊢ AnalyticSet ∅",
"tactic": "rw [AnalyticSet]"
},
{
"state_after": "no goals",
"state_before": ... | [
86,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.eraseNone_union | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.11560\ninst✝¹ : DecidableEq (Option α)\ninst✝ : DecidableEq α\ns t : Finset (Option α)\na✝ : α\n⊢ a✝ ∈ ↑eraseNone (s ∪ t) ↔ a✝ ∈ ↑eraseNone s ∪ ↑eraseNone t",
"state_before": "α : Type u_1\nβ : Type ?u.11560\ninst✝¹ : DecidableEq (Option α)\ninst✝ : Decida... | [
123,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_pow | [] | [
735,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.of_null | [] | [
123,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_get | [] | [
53,
123
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
53,
9
] |
Mathlib/Data/Int/ModEq.lean | Int.add_modEq_left | [
{
"state_after": "no goals",
"state_before": "m n a b c d : ℤ\n⊢ n ∣ n + a - a",
"tactic": "simp"
}
] | [
263,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_integral | [] | [
489,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/List/Basic.lean | List.foldlM_nil | [] | [
2790,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2789,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_span_le | [
{
"state_after": "case intro.intro.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.566078\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V'\ninst✝² : Module K V'\ninst✝¹ : AddCommGrou... | [
1072,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_trunc | [
{
"state_after": "α : Type ?u.74019\nβ : Type ?u.74022\nM : Type u_1\ninst✝ : CommMonoid M\na b : ℕ\nf : Fin (a + b) → M\nhf : ∀ (j : Fin b), f (↑(natAdd a) j) = 1\n⊢ ∏ i : Fin a, f (↑(castAdd b) i) = ∏ i : Fin a, f (↑(castLE (_ : a ≤ a + b)) i)",
"state_before": "α : Type ?u.74019\nβ : Type ?u.74022\nM : T... | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Algebra/Associated.lean | Associates.one_le | [] | [
909,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists'Aux_eq_array_foldl | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nr₁ r₂ : List (List α)\n⊢ sublists'Aux a r₁ r₂ =\n Array.toList (Array.foldl (fun r l => Array.push r (a :: l)) (toArray r₂) (toArray r₁) 0 (Array.size (toArray r₁)))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\n⊢ ∀ (r₁ r₂ : Lis... | [
61,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.preimage_Ioc | [
{
"state_after": "case h\nF : Type ?u.240835\nα : Type u_1\nβ : Type ?u.240841\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a b : α\nx✝ : ℤ\n⊢ x✝ ∈ Int.cast ⁻¹' Ioc a b ↔ x✝ ∈ Ioc ⌊a⌋ ⌊b⌋",
"state_before": "F : Type ?u.240835\nα : Type u_1\nβ : Type ?u.240841\ninst✝¹ : LinearOrderedRing α\n... | [
1282,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.head_induction_on | [
{
"state_after": "case single\nα : Type u_1\nβ : Type ?u.19922\nγ : Type ?u.19925\nδ : Type ?u.19928\nr : α → α → Prop\na✝¹ b c d a b✝ : α\na✝ : r a b✝\nP : (a : α) → TransGen r a b✝ → Prop\nbase : ∀ {a : α} (h : r a b✝), P a (_ : TransGen r a b✝)\nih : ∀ {a c : α} (h' : r a c) (h : TransGen r c b✝), P c h → P ... | [
399,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_predAbove_succ | [
{
"state_after": "case inl\nn✝ m n : ℕ\na : Fin n\nb : Fin (n + 1)\nh₁ : ↑castSucc a < b\n⊢ predAbove (succ a) (succ b) = succ (predAbove a b)\n\ncase inr\nn✝ m n : ℕ\na : Fin n\nb : Fin (n + 1)\nh₂ : b ≤ ↑castSucc a\n⊢ predAbove (succ a) (succ b) = succ (predAbove a b)",
"state_before": "n✝ m n : ℕ\na : Fi... | [
2448,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2428,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_iff_subset_of_disjoint_closed | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Type ?u.102865\nπ : ι → Type ?u.102870\ninst✝ : TopologicalSpace α\ns t u v : Set α\nh : IsPreconnected s\n⊢ ∀ (u v : Set α), IsClosed u → IsClosed v → s ⊆ u ∪ v → s ∩ (u ∩ v) = ∅ → s ⊆ u ∨ s ⊆ v\n\ncase mpr\nα : Type u\nβ : Type v\nι : Type ?u.102865\nπ : ... | [
969,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.isLUB_of_tendsto | [] | [
2083,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2080,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_eq | [] | [
1446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.represents_iff | [] | [
102,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.nonempty_boxes | [] | [
753,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Algebra/Group/Units.lean | inv_eq_one_divp | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b c : α\nu : αˣ\n⊢ ↑u⁻¹ = 1 /ₚ u",
"tactic": "rw [one_divp]"
}
] | [
509,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.eventually_mul_div_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.617198\nE : Type ?u.617201\nF : Type ?u.617204\nG : Type ?u.617207\nE' : Type ?u.617210\nF' : Type ?u.617213\nG' : Type ?u.617216\nE'' : Type ?u.617219\nF'' : Type ?u.617222\nG'' : Type ?u.617225\nR : Type ?u.617228\nR' : Type ?u.617231... | [
1905,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1904,
1
] |
Mathlib/Algebra/Jordan/Basic.lean | aux2 | [
{
"state_after": "A : Type u_1\ninst✝¹ : NonUnitalNonAssocRing A\ninst✝ : IsCommJordan A\na b c : A\n⊢ ⁅↑L a, ↑L (b * b)⁆ + ⁅↑L a, ↑L (c * c)⁆ + ⁅↑L a, 2 • ↑L (a * b)⁆ + ⁅↑L a, 2 • ↑L (c * a)⁆ + ⁅↑L a, 2 • ↑L (b * c)⁆ +\n (⁅↑L b, ↑L (a * a)⁆ + ⁅↑L b, ↑L (c * c)⁆ + ⁅↑L b, 2 • ↑L (a * b)⁆ + ⁅↑L b, 2 • ↑L (... | [
230,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
9
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝² : MeasurableSpace Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → ProbabilityMeasure Ω\nμ : ProbabilityMeasure Ω\n⊢ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 (toFiniteMeasure μ)) ↔\n ∀ (f : Ω →ᵇ ℝ≥0), Tendsto (fun i => ∫⁻ ... | [
282,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Std/Data/List/Lemmas.lean | List.isPrefix.isInfix | [] | [
1568,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1568,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.closedEmbedding | [] | [
298,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
11
] |
Mathlib/Data/List/Duplicate.lean | List.duplicate_iff_two_le_count | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nx : α\ninst✝ : DecidableEq α\n⊢ x ∈+ l ↔ 2 ≤ count x l",
"tactic": "simp [duplicate_iff_sublist, le_count_iff_replicate_sublist]"
}
] | [
146,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Units.coe_mapEquiv | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.op_act_op_eq | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one | [
{
"state_after": "k : Type u_1\nV : Type u_4\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.38533\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\nh : ∑ i in s, w i = 1\nb₁ b₂ : P\n⊢ b₁ -ᵥ b₂ + ∑ x in s, (w x • (p x -ᵥ b₁) - w x •... | [
144,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Logic/Embedding/Set.lean | subtypeOrEquiv_symm_inl | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.IsEquivalence.exact_iff | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\ninst✝³ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nD : Type u₁\ninst✝² : Category D\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : IsEquivalence F\n⊢ F.map f ≫ F.map g = 0 ∧ kernel.ι (F.map g) ≫ cokernel.π (F.map f) = 0 ↔\n F.map f ≫ F.map g = 0 ∧\n kernelC... | [
114,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
8
] |
Mathlib/RingTheory/IntegralClosure.lean | map_isIntegral | [
{
"state_after": "case intro\nR : Type u_4\nA : Type u_5\nB✝ : Type ?u.113227\nS : Type ?u.113230\ninst✝¹⁴ : CommRing R\ninst✝¹³ : CommRing A\ninst✝¹² : CommRing B✝\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Algebra R A\ninst✝⁹ : Algebra R B✝\nf✝ : R →+* S\nB : Type u_1\nC : Type u_2\nF : Type u_3\ninst✝⁸ : Ring B\ninst✝... | [
133,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.pair_injective | [
{
"state_after": "x x' y y' : ZFSet\nH : pair x y = pair x' y'\nae : ∀ (z : ZFSet), z ∈ pair x y ↔ z ∈ pair x' y'\n⊢ x = x' ∧ y = y'",
"state_before": "x x' y y' : ZFSet\nH : pair x y = pair x' y'\n⊢ x = x' ∧ y = y'",
"tactic": "have ae := ext_iff.1 H"
},
{
"state_after": "x x' y y' : ZFSet\nH :... | [
1330,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1311,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieAlgebra.nilpotent_of_nilpotent_quotient | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI : LieIdeal R L\nh₁ : I ≤ center R L\nh₂ : IsNilpotent R (L ⧸ I)\n⊢ LieModule.IsNilpotent R L (L ⧸ I)",
"state_before": "R : Type u\nL : Typ... | [
595,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | MonotoneOn.quasilinearOn | [] | [
193,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean | AlgebraicTopology.DoldKan.MorphComponents.id_φ | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX X' : SimplicialObject C\nn : ℕ\nZ Z' : C\nf : MorphComponents X n Z\ng : X' ⟶ X\nh : Z ⟶ Z'\n⊢ HomologicalComplex.Hom.f PInfty (n + 1) ≫ (id X n).a +\n ∑ x : Fin (n + 1),\n HomologicalComplex.Hom.f (P ↑x) (n + 1) ≫\n ... | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_product_right' | [] | [
691,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.trace_kroneckerTMul | [] | [
530,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_zsmul_add' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIocMod hp (m • p + a) b = m • p + toIocMod hp a b",
"tactic": "rw [add_comm, toIocMod_add_zsmul', add_comm]"
}
] | [
447,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.ofList_subset | [
{
"state_after": "case nil\nα : Type u_1\nl₁ l₂ : List (Lists α)\nh✝ : l₁ ⊆ l₂\nh : [] ⊆ l₂\n⊢ ofList [] ⊆ ofList l₂\n\ncase cons\nα : Type u_1\nl₁ l₂ : List (Lists α)\nh✝ : l₁ ⊆ l₂\nhead✝ : Lists α\ntail✝ : List (Lists α)\nl₁_ih : tail✝ ⊆ l₂ → ofList tail✝ ⊆ ofList l₂\nh : head✝ :: tail✝ ⊆ l₂\n⊢ ofList (head✝ ... | [
181,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.148388\ninst✝⁹ : CommRing R\nM : Submonoid R\nS : Type ?u.148594\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nP : Type ?u.148848\ninst✝⁶ : CommRing P\nA : Type u_1\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : UniqueFactorizationMonoid A\nK : Ty... | [
95,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.extract | [
{
"state_after": "case refl\nl m r : List Char\nit₂ : Iterator\nh₂ : ValidFor (List.reverse m ++ l) r it₂\nh₁ : ValidFor l (m ++ r) { s := { data := List.reverseAux l (m ++ r) }, i := { byteIdx := utf8Len l } }\n⊢ Iterator.extract { s := { data := List.reverseAux l (m ++ r) }, i := { byteIdx := utf8Len l } } it... | [
599,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
595,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.compactOpen_eq_sInf_induced | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.19379\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\n⊢ compactOpen ≤ ⨅ (s : Set α) (_ : IsCompact s), TopologicalSpace.induced (restrict s) compactOpen\n\ncase refine'_2\nα : Type u_1\nβ : Type u_2\... | [
246,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_tensor | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX X' Y Y' Z Z' : C\ninst✝ : ExactPairing Y Y'\nf : X ⟶ Z ⊗ Y'\ng : X' ⟶ Z'\n⊢ ((g ⊗ f) ≫ (α_ Z' Z Y').inv ⊗ 𝟙 Y) ≫ (α_ (Z' ⊗ Z) Y' Y).hom ≫ (𝟙 (Z' ⊗ Z) ⊗ ε_ Y Y') ≫ (ρ_ (Z' ⊗ Z)).hom =\n (α_ X' X Y).hom ≫ (g ⊗ (f ⊗ 𝟙 Y) ≫ (α_... | [
467,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Std/Classes/BEq.lean | beq_eq_false_iff_ne | [
{
"state_after": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\n⊢ (a == b) = false ↔ ¬(a == b) = true",
"state_before": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\n⊢ (a == b) = false ↔ a ≠ b",
"tactic": "rw [ne_eq, ← beq_iff_eq a b]"
},
{
"state_after": "no goals",... | [
23,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
9
] |
Mathlib/GroupTheory/GroupAction/Sigma.lean | Sigma.FaithfulSMul' | [] | [
71,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Data/Complex/Cardinality.lean | not_countable_complex | [
{
"state_after": "⊢ ℵ₀ < 𝔠",
"state_before": "⊢ ¬Set.Countable Set.univ",
"tactic": "rw [← le_aleph0_iff_set_countable, not_le, mk_univ_complex]"
},
{
"state_after": "no goals",
"state_before": "⊢ ℵ₀ < 𝔠",
"tactic": "apply cantor"
}
] | [
40,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/List/Count.lean | List.filter_beq | [] | [
297,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_iff | [] | [
316,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | hasDerivAt_zpow | [] | [
69,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.card_powerset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Multiset α\n⊢ ∀ (a : List α), ↑card (powerset (Quotient.mk (isSetoid α) a)) = 2 ^ ↑card (Quotient.mk (isSetoid α) a)",
"tactic": "simp"
}
] | [
124,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tmul_ite | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝¹⁷ : CommSemiring R\nR' : Type ?u.449877\ninst✝¹⁶ : Monoid R'\nR'' : Type ?u.449883\ninst✝¹⁵ : Semiring R''\nM : Type u_1\nN : Type u_2\nP✝ : Type ?u.449895\nQ : Type ?u.449898\nS : Type ?u.449901\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : AddCommM... | [
382,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Std/Data/Int/DivMod.lean | Int.sub_ediv_of_dvd_sub | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nhcab : c ∣ a - b\n⊢ (a - b) / c = a / c - b / c",
"tactic": "rw [← Int.add_sub_cancel ((a-b) / c), ← Int.add_ediv_of_dvd_left hcab, Int.sub_add_cancel]"
}
] | [
812,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
810,
1
] |
Mathlib/Algebra/CharP/Basic.lean | Ring.two_ne_zero | [
{
"state_after": "R✝ : Type ?u.950230\nR : Type u_1\ninst✝¹ : NonAssocSemiring R\ninst✝ : Nontrivial R\nhR : ringChar R ≠ 2\n⊢ ¬(ringChar R = 1 ∨ ringChar R = 2)",
"state_before": "R✝ : Type ?u.950230\nR : Type u_1\ninst✝¹ : NonAssocSemiring R\ninst✝ : Nontrivial R\nhR : ringChar R ≠ 2\n⊢ 2 ≠ 0",
"tacti... | [
622,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
11
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.monic_geom_sum_X | [
{
"state_after": "R : Type u\nS : Type ?u.60633\ninst✝ : Semiring R\nn : ℕ\nhn : n ≠ 0\n✝ : Nontrivial R\n⊢ Monic (∑ i in range n, X ^ i)",
"state_before": "R : Type u\nS : Type ?u.60633\ninst✝ : Semiring R\nn : ℕ\nhn : n ≠ 0\n⊢ Monic (∑ i in range n, X ^ i)",
"tactic": "nontriviality R"
},
{
"s... | [
255,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.numerator_isUnit | [] | [
376,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_iUnion_nat | [
{
"state_after": "α : Type u\nm : OuterMeasure α\ns✝ s₁ s₂ : Set α\ns : ℕ → Set α\nh : ∀ (i : ℕ), IsCaratheodory m (s i)\nhd : Pairwise (Disjoint on s)\n⊢ ∀ (t : Set α), ↑m (t ∩ ⋃ (i : ℕ), s i) + ↑m (t \\ ⋃ (i : ℕ), s i) ≤ ↑m t",
"state_before": "α : Type u\nm : OuterMeasure α\ns✝ s₁ s₂ : Set α\ns : ℕ → Set... | [
1020,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.map_le_gfp | [] | [
132,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
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