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/BigOperators/Multiset/Basic.lean | Multiset.prod_nat_mod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.170595\nα : Type ?u.170598\nβ : Type ?u.170601\nγ : Type ?u.170604\ns : Multiset ℕ\nn : ℕ\n⊢ prod s % n = prod (map (fun x => x % n) s) % n",
"tactic": "induction s using Multiset.induction <;> simp [Nat.mul_mod, *]"
}
] | [
532,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.toPlus_apply | [
{
"state_after": "C : Type u\ninst✝⁵ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝⁴ : Category D\ninst✝³ : ConcreteCategory D\ninst✝² : PreservesLimits (forget D)\ninst✝¹ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\ninst✝ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.inde... | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bmex_le_of_ne | [] | [
2092,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2090,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.memberSubfamily_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜✝ ℬ✝ : Finset (Finset α)\ns : Finset α\na✝ a : α\n𝒜 ℬ : Finset (Finset α)\n⊢ memberSubfamily a (𝒜 ∪ ℬ) = memberSubfamily a 𝒜 ∪ memberSubfamily a ℬ",
"tactic": "simp_rw [memberSubfamily, filter_union, image_union]"
... | [
91,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_diff_of_diff_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.27702\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nf : ℕ → Set α\nA B : Set α\nhA : MeasurableSet A\nhB : MeasurableSet B\nh' : ↑v (B \\ A) = 0\n⊢ ↑v A = ↑v (A \\ B) + ↑v B",
... | [
221,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.assoc_flip | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM : Mon_ C\n⊢ (𝟙 M.X ⊗ M.mul) ≫ M.mul = (α_ M.X M.X M.X).inv ≫ (M.mul ⊗ 𝟙 M.X) ≫ M.mul",
"tactic": "simp"
}
] | [
86,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.diff | [] | [
128,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Std/Data/Int/Lemmas.lean | Int.le.dest | [
{
"state_after": "a b : Int\nh : a ≤ b\nn : Nat\nh₁ : b - a = ↑n\n⊢ b - a + a = b",
"state_before": "a b : Int\nh : a ≤ b\nn : Nat\nh₁ : b - a = ↑n\n⊢ a + ↑n = b",
"tactic": "rw [← h₁, Int.add_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : a ≤ b\nn : Nat\nh₁ : b - a =... | [
567,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
565,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_nnnorm_le_of_unit_nnnorm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.628695\n𝕜₂ : Type ?u.628698\n𝕜₃ : Type ?u.628701\nE : Type u_1\nEₗ : Type ?u.628707\nF : Type u_2\nFₗ : Type ?u.628713\nG : Type ?u.628716\nGₗ : Type ?u.628719\n𝓕 : Type ?u.628722\ninst✝¹⁹ : SeminormedAddCommGroup E\ninst✝¹⁸ : SeminormedAddCommGr... | [
430,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_one | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_equiv_eq_comap_symm | [] | [
943,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Algebra/FreeNonUnitalNonAssocAlgebra.lean | FreeNonUnitalNonAssocAlgebra.of_comp_lift | [] | [
82,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.int_gcd_helper' | [
{
"state_after": "d : ℕ\nx y a b : ℤ\nh₁ : ↑d ∣ x\nh₂ : ↑d ∣ y\nh₃ : x * a + y * b = ↑d\n⊢ Int.gcd x y ∣ d",
"state_before": "d : ℕ\nx y a b : ℤ\nh₁ : ↑d ∣ x\nh₂ : ↑d ∣ y\nh₃ : x * a + y * b = ↑d\n⊢ Int.gcd x y = d",
"tactic": "refine Nat.dvd_antisymm ?_ (Int.coe_nat_dvd.1 (Int.dvd_gcd h₁ h₂))"
},
{... | [
28,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
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Mathlib/GroupTheory/OrderOfElement.lean | finEquivPowers_symm_apply | [
{
"state_after": "no goals",
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756,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_foldr_swap | [] | [
1417,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.equiv'_apply | [] | [
1053,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Iic_pred_of_not_isMin | [] | [
672,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Topology/Order/Basic.lean | le_of_tendsto | [] | [
188,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Order/Monoid/TypeTags.lean | Multiplicative.ofAdd_le | [] | [
150,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsSup_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.85338\nγ : Type ?u.85341\nι : Type ?u.85344\ninst✝ : CompleteLattice α\n⊢ ∀ (b : α), (∀ (x : α), x ≤ b) → b = ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.85338\nγ : Type ?u.85341\nι : Type ?u.85344\ninst✝ : CompleteLattice α\n⊢ ∀ (b : α), b ∈ {a | ∀ᶠ (n : α) in... | [
629,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mul_continuousOn | [
{
"state_after": "ι : Type ?u.6369999\n𝕜 : Type ?u.6370002\nE : Type ?u.6370005\nF : Type ?u.6370008\nA : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedRing A\nf✝ g✝ : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → A\nhf : IntegrableOn f (Ι a b)\nhg : ContinuousOn g [[a, b]]\n⊢ IntegrableOn (f... | [
267,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
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] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_sum_eq_of_disjoint | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nf : S → R[X]\ns : Finset S\nh : Set.Pairwise {i | i ∈ s ∧ f i ≠ 0} (Ne on natDegree ∘ f)\nH : ∃ x, x ∈ s ∧ f x ≠ 0\n⊢ natDegree (Finset.sum s f) = sup s fun i => natDegree (f i)\n\ncase neg\nR : T... | [
253,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_col_zero_eq | [] | [
59,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_subtype_range | [] | [
197,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_def | [] | [
182,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/PathConnected.lean | JoinedIn.ofLine | [] | [
855,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.monomial_mem_lifts | [
{
"state_after": "case intro\nR : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\nn : ℕ\nr : R\nh : ↑f r ∈ Set.range ↑f\n⊢ ↑(monomial n) (↑f r) ∈ lifts f",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\ns : S\nn : ℕ\nh : s ∈ Set.range... | [
127,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.mem_ball_self | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.792081\nR' : Type ?u.792084\n𝕜 : Type u_2\n𝕜₂ : Type ?u.792090\n𝕜₃ : Type ?u.792093\n𝕝 : Type ?u.792096\nE : Type u_1\nE₂ : Type ?u.792102\nE₃ : Type ?u.792105\nF : Type ?u.792108\nG : Type ?u.792111\nι : Type ?u.792114\ninst✝² : SeminormedRing �... | [
656,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.right_not_mem_Ioo | [] | [
159,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/CategoryTheory/Category/Bipointed.lean | swap_comp_bipointedToPointedSnd | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddMonoidWithOne α\nn : PosNum\n⊢ ↑(succ n) = ↑n + 1",
"tactic": "rw [← add_one, cast_add, cast_one]"
}
] | [
669,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.X_pow_sub_one_eq_prod | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R\nn : ℕ\nhpos : 0 < n\nh : IsPrimitiveRoot ζ n\n⊢ X ^ n - 1 = ∏ ζ in { val := nthRoots n 1, nodup := (_ : Multiset.Nodup (nthRoots n 1)) }, (X - ↑C ζ)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R... | [
145,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_mul_snorm_of_nnnorm | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq✝ : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np q r : ℝ≥0∞\nf : α → E\nhf : AEStronglyMeasurable f μ\ng : α → F\nhg : AE... | [
1441,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1405,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_univ | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set R\na : R\n⊢ torsionBySet R M Set.univ ≤ torsionBySet R M {1}",
"state_before": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : ... | [
313,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_nonempty | [] | [
1152,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Topology/NhdsSet.lean | mem_nhdsSet_iff_forall | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6768\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ s ∈ 𝓝ˢ t ↔ ∀ (x : α), x ∈ t → s ∈ 𝓝 x",
"tactic": "simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]"
}
] | [
51,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.fg_restrictScalars | [
{
"state_after": "case intro\nR✝ : Type ?u.286765\nM✝ : Type ?u.286768\ninst✝¹¹ : Semiring R✝\ninst✝¹⁰ : AddCommMonoid M✝\ninst✝⁹ : Module R✝ M✝\nP : Type ?u.286804\ninst✝⁸ : AddCommMonoid P\ninst✝⁷ : Module R✝ P\nf : M✝ →ₗ[R✝] P\nR : Type u_1\nS : Type u_2\nM : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semir... | [
369,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
src/lean/Init/Control/Lawful.lean | id_map' | [] | [
26,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
25,
9
] |
Mathlib/Data/Finset/Sort.lean | Finset.range_orderEmbOfFin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.39891\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : card s = k\n⊢ Set.range ↑(orderEmbOfFin s h) = ↑s",
"tactic": "simp only [orderEmbOfFin, Set.range_comp ((↑) : _ → α) (s.orderIsoOfFin h),\nRelEmbedding.coe_trans, Set.image_uni... | [
191,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_add_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ (fun x => a + x) ⁻¹' [[b, c]] = [[b - a, c - a]]",
"tactic": "simp only [← Icc_min_max, preimage_const_add_Icc, min_sub_sub_right, max_sub_sub_right]"
}
] | [
430,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | discreteTopology_of_open_singleton_one | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\nh : IsOpen {1}\n⊢ ∀ (a : G), IsOpen {a}",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : Continuo... | [
158,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_inter_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.263829\nγ : Type ?u.263832\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b : α\ns t : Finset α\na : α\n⊢ insert a (s ∩ t) = insert a s ∩ insert a t",
"tactic": "simp_rw [insert_eq, union_distrib_left]"
}
] | [
2270,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2269,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.coe_reAddGroupHom | [] | [
453,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.secondCountable_of_almost_dense_set | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.439085\nι : Type ?u.439088\ninst✝ : PseudoMetricSpace α\nH : ∀ (ε : ℝ), ε > 0 → ∃ s, Set.Countable s ∧ ∀ (x : α), ∃ y, y ∈ s ∧ dist x y ≤ ε\nε : ℝ≥0∞\nε0 : ε > 0\n⊢ ∃ t, Set.Countable t ∧ (⋃ (x : α) (_ : x ∈ t), EMetric.closedBall x ε) = univ",
"state_be... | [
2265,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2258,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.disjoint_map | [
{
"state_after": "no goals",
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"tactic": "simp only [disjoint_iff, ← map_inf hm, map_eq_bot_iff]"
}
] | [
2528,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2526,
1
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Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_Lp_add_le_of_le_one | [
{
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394,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | Homeomorph.toContinuousMap_comp_symm | [
{
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... | [
498,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.equivBool_apply_left | [] | [
97,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_sUnion_of_mem | [] | [
1084,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongr_inv | [] | [
197,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Analysis/VonNeumannAlgebra/Basic.lean | VonNeumannAlgebra.mem_carrier | [] | [
108,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_mono_null_ae | [] | [
582,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_mk | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_sdiff | [] | [
2352,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2351,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_lineMap_left | [] | [
760,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_pos_of_neg | [] | [
148,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.mul_nonneg | [
{
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"tactic": "filter_upwards [hf, hg] with x using _root_.mul_nonneg"
}
] | [
1767,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
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Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.comp_leftAdjointMate | [
{
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292,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_neighborSet | [] | [
954,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.coe_lcs_range_toEndomorphism_eq | [
{
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338,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.span_smul | [] | [
250,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
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Mathlib/Algebra/GradedMonoid.lean | List.dProd_nil | [] | [
395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
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] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodal_eq_mul_nodal_erase | [
{
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"tactic": "simp_rw [nodal, mul_prod_erase _ _ hi, Finset.mul_prod_e... | [
520,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_inv | [] | [
1332,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Data/Set/Function.lean | Set.injOn_insert | [
{
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647,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
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Mathlib/Data/Polynomial/Div.lean | Polynomial.dvd_iff_isRoot | [
{
"state_after": "no goals",
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"tactic": "rwa [← dvd_iff_modByMonic_eq_zero (monic_X_sub_C _), modByMonic_X_sub_C_eq_C_eval, ← C_0,\n C_inj] at h"
},
{
... | [
454,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.invOfUnit_eq | [] | [
972,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.type_prod_lex | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter_idem | [] | [
170,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.restrict_measure_eq | [] | [
282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback.diagonal_snd | [] | [
55,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_union | [
{
"state_after": "no goals",
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"tactic": "simp_rw [cthickening, infEdist_union, inf_eq_min, min_le_if... | [
1186,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_le_cons | [] | [
576,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.unop_zero | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.haveLebesgueDecomposition_add | [] | [
111,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.1210777\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : Normed... | [
1122,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
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Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_dist | [] | [
45,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
11
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_insert_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.48423\ninst✝ : PartialOrder α\na b c : α\nh : a < b\n⊢ insert a (Ioo a b) = Ico a b",
"tactic": "rw [insert_eq, union_comm, Ioo_union_left h]"
}
] | [
887,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eq_of_localEquiv_eq | [] | [
233,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/List/Sigma.lean | List.Perm.kerase | [
{
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"state_before": "α : Type u\nβ : α → Type v\nl l₁✝ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl₁ l₂... | [
482,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_add_self | [] | [
137,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | homTensorHomEquiv_apply | [
{
"state_after": "no goals",
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330,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.prod_mem | [] | [
171,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.nodup_toCycle | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : Perm α\nhf : IsCycle f\nx : α\nhx : ↑f x ≠ x\n⊢ Cycle.Nodup (toCycle f hf)",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nf : Perm α\nhf : IsCy... | [
420,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | closure_smul | [] | [
274,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_neg | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ EReal.abs (-↑x) = EReal.abs ↑x",
"tactic": "rw [abs_def, ← coe_neg, abs_def, abs_neg]"
}
] | [
1090,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_pair | [
{
"state_after": "no goals",
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948,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_ofBoolAlg | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.sigmaCurry_apply | [] | [
328,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_iff_factorization_le_one | [] | [
65,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.order_dvd_exponent | [] | [
159,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : Ring R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nU U₁ U₂ : Submodule R M\nx x₁ x₂ y y₁ y₂ z z₁ z₂ : M\nN : Type ?u.67581\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nV V₁ V₂ : Submodule R N\n⊢ x ≡ 0 [SMOD U] ↔ x ∈ U",
... | [
98,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_subset_ball | [] | [
576,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_zero | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.le_topologicalClosure | [] | [
164,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | Submodule.finrank_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nN : Type w\ninst✝⁶ : Ring R\ninst✝⁵ : StrongRankCondition R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : Module.Finite R M\ns : Submodule R M\n⊢ finrank R { x // x ∈ s } ≤ finrank R ... | [
206,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Order/WithBot.lean | WithTop.toDual_le_iff | [] | [
798,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_iff_le_iff | [] | [
321,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_map | [] | [
1340,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1338,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | AddSubmonoid.closure_singleton_zero | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.251546\nA : Type u_1\nB : Type ?u.251552\ninst✝ : AddMonoid A\n⊢ closure {0} = ⊥",
"tactic": "simp [eq_bot_iff_forall, mem_closure_singleton, nsmul_zero]"
}
] | [
604,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
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