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/Data/Sum/Basic.lean | Sum.lex_wf | [] | [
547,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Topology/Separation.lean | eqOn_closure₂' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type u_1\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\ns : Set β\nt : Set γ\nf g : β → γ → α\nh : ∀ (x : β), x ∈ s → ∀ (y : γ), y ∈ t → f x y = g x y\nhf₁ : ∀ (x : β), Conti... | [
1206,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | Subsemigroup.nonUnitalSubsemiringClosure_eq_closure | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring T\nx✝ : R\n⊢ x✝ ∈ nonUnitalSubsemiringClosure M ↔ x✝ ∈ NonUnitalSubsemiring.closure ↑M",
"state_before": "R : Type u... | [
637,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Topology/Constructions.lean | pi_generateFrom_eq_finite | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type ?u.400266\nδ : Type ?u.400269\nε : Type ?u.400272\nζ : Type ?u.400275\nι : Type u_2\nπ✝ : ι → Type ?u.400283\nκ : Type ?u.400286\ninst✝² : TopologicalSpace α\ninst✝¹ : (i : ι) → TopologicalSpace (π✝ i)\nf : α → (i : ι) → π✝ i\nπ : ι → Type u_1\ng : ... | [
1407,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Icc_right | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : Preorder α\na✝ b c a : α\n⊢ (⋃ (b : α), Icc a b) = Ici a",
"tactic": "simp only [← Ici_inter_Iic, ← inter_iUnion, iUnion_Iic, inter_univ]"
}
] | [
78,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Succ.rec_bot | [] | [
1503,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMin.sup | [] | [
451,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
8
] |
Mathlib/Data/List/Permutation.lean | List.permutations_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27175\n⊢ permutations [] = [[]]",
"tactic": "rw [permutations, permutationsAux_nil]"
}
] | [
230,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.add | [] | [
233,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_apply' | [] | [
630,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_pair | [] | [
663,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | strictAnti_vecCons | [] | [
54,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.unitCompPartialBijectiveAux_symm_apply | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝³ : Category C\ninst✝² : Category D\ninst✝¹ : Category E\ni : D ⥤ C\ninst✝ : Reflective i\nA : C\nB : D\nf : i.obj ((leftAdjoint i).obj A) ⟶ i.obj B\n⊢ ↑(unitCompPartialBijectiveAux A B).symm f = (ofRightAdjoint i).uni... | [
123,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.union | [
{
"state_after": "ι : Type ?u.44198\nα : Type u_1\nβ : Type ?u.44204\nr : α → α → Prop\nr' : β → β → Prop\nf✝ : α → β\ns t : Set α\na : α\nhs : PartiallyWellOrderedOn s r\nht : PartiallyWellOrderedOn t r\nf : ℕ → α\nhf : ∀ (n : ℕ), f n ∈ s ∪ t\n⊢ ∃ m n, m < n ∧ r (f m) (f n)",
"state_before": "ι : Type ?u.4... | [
263,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/Circular.lean | not_sbtw_of_btw | [] | [
204,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.ofSets_filter_eq_generate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15898\nγ : Type ?u.15901\nι : Sort ?u.15904\nι' : Sort ?u.15907\nl l' : Filter α\np : ι → Prop\ns✝ : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\ns : Set (Set α)\n⊢ FilterBasis.filter (FilterBasis.ofSets s) = g... | [
338,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.singleton_add | [] | [
628,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.110948\nγ : Type ?u.110951\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b a : α\ns : Finset α\nx : α\n⊢ x ∈ insert a (insert a s) ↔ x ∈ insert a s",
"tactic": "simp only [mem_insert, ←or_assoc, or_self_iff]"
}
] | [
1138,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/RingTheory/ReesAlgebra.lean | mem_reesAlgebra_iff_support | [
{
"state_after": "case h\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nf : R[X]\n⊢ ∀ (a : ℕ), coeff f a ∈ I ^ a ↔ a ∈ support f → coeff f a ∈ I ^ a",
"state_before": "R M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\n... | [
76,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Measurable.aestronglyMeasurable | [] | [
1281,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.sup_N | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Acc.rank_lt_of_rel | [
{
"state_after": "α : Type u\nr : α → α → Prop\na b : α\nhb : Acc r b\nh : r a b\n⊢ succ (rank (_ : Acc r a)) ≤ sup fun b_1 => succ (rank (_ : Acc r ↑b_1))",
"state_before": "α : Type u\nr : α → α → Prop\na b : α\nhb : Acc r b\nh : r a b\n⊢ succ (rank (_ : Acc r a)) ≤ rank hb",
"tactic": "rw [hb.rank_eq... | [
2549,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2545,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | Commute.smul_right | [] | [
437,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.splits_iff | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝⁷ : Field K\ninst✝⁶ : Field L\ninst✝⁵ : Field F\ninst✝⁴ : Algebra K L\ninst✝³ : Algebra F K\ninst✝² : Algebra F L\ninst✝¹ : IsScalarTower F K L\nf : K[X]\ninst✝ : IsSplittingField K L f\nh : Splits (RingHom.id K) f\n⊢ ↑(Multiset.toFinset (Multiset.map (... | [
96,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Basic.lean | List.exists_mem_cons_iff | [] | [
307,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.comp_id | [] | [
808,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
9
] |
Mathlib/Algebra/Lie/SkewAdjoint.lean | skewAdjointLieSubalgebraEquiv_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nB : BilinForm R M\nN : Type w\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\ne : N ≃ₗ[R] M\nf : { x // x ∈ skewAdjointLieSubalgebra (comp B ↑e ↑e) }\n⊢ ↑(↑(skewAdjointLieSu... | [
82,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.snorm_one_le_of_le | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.1745269\nF : Type ?u.1745272\n𝕜 : Type ?u.1745275\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup ... | [
1874,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1830,
1
] |
Mathlib/Data/Set/List.lean | Set.range_list_getD | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2053\nl : List α\nd : α\n⊢ (fun o => Option.getD o d) '' range (get? l) = insert d {x | x ∈ l}",
"tactic": "simp only [range_list_get?, image_insert_eq, Option.getD, image_image, image_id']"
}
] | [
62,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/Constructions.lean | CofiniteTopology.isOpen_iff | [] | [
283,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioc_of_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : c < 0\n⊢ (fun x x_1 => x * x_1) c ⁻¹' Ioc a b = Ico (b / c) (a / c)",
"tactic": "simpa only [mul_comm] using preimage_mul_const_Ioc_of_neg a b h"
}
] | [
673,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tendsto_tan_pi_div_two | [
{
"state_after": "case h.e'_3\n\n⊢ tan = fun x => cos⁻¹ x * sin x",
"state_before": "⊢ Tendsto tan (𝓝[Iio (π / 2)] (π / 2)) atTop",
"tactic": "convert tendsto_cos_pi_div_two.inv_tendsto_zero.atTop_mul zero_lt_one tendsto_sin_pi_div_two\n using 1"
},
{
"state_after": "no goals",
"state_befo... | [
1074,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.prod_mono_left | [] | [
799,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Algebra/GradedMonoid.lean | SetLike.pow_mem_graded | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nR : Type u_1\nS : Type u_2\ninst✝³ : SetLike S R\ninst✝² : Monoid R\ninst✝¹ : AddMonoid ι\nA : ι → S\ninst✝ : GradedMonoid A\nn : ℕ\nr : R\ni : ι\nh : r ∈ A i\n⊢ r ^ n ∈ A (n • i)",
"tactic": "match n with\n| 0 =>\n rw [pow_zero, zero_nsmul]\n... | [
566,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : DivisionMonoid G\na b c d : G\nhab : Commute a b\n⊢ (a * b)⁻¹ = a⁻¹ * b⁻¹",
"tactic": "rw [hab.eq, mul_inv_rev]"
}
] | [
322,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.write_self | [
{
"state_after": "case mk\nΓ : Type u_1\ninst✝ : Inhabited Γ\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ write { head := head✝, left := left✝, right := right✝ }.head { head := head✝, left := left✝, right := right✝ } =\n { head := head✝, left := left✝, right := right✝ }",
"state_before": "Γ : Type u_1\ninst... | [
666,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_cons_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nb a : α\n⊢ some (b, s) ∈ destruct (cons b s)",
"tactic": "simp [ret_mem]"
}
] | [
960,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_one_pos | [] | [
1917,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1916,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_zpow | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝⁴ : TopologicalSpace G\ninst✝³ : Group G\ninst✝² : TopologicalGroup G\nS✝ : Subgroup G\ninst✝¹ : Normal S✝\ninst✝ : IsClosed ↑S✝\nS : Subgroup G\nhS : Tendsto (↑(Subgroup.subtype S)) cofinite (cocompact G)\nK L : Set G\nhK : IsCompact K\nhL ... | [
1486,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_of_sigma_eq | [
{
"state_after": "case refl\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i : ι\nxi : β i\n⊢ single i xi = single i xi",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → ... | [
723,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Data/List/Zip.lean | List.revzip_swap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.94286\nγ : Type ?u.94289\nδ : Type ?u.94292\nε : Type ?u.94295\nl : List α\n⊢ map Prod.swap (revzip l) = revzip (reverse l)",
"tactic": "simp [revzip]"
}
] | [
367,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | Monotone.mul | [] | [
294,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12757\ninst✝ : MeasurableSpace α\nj : JordanDecomposition α\nr : ℝ\nhr : 0 ≤ r\n⊢ (r • j).negPart = Real.toNNReal r • j.negPart",
"tactic": "rw [real_smul_def, ← smul_negPart, if_pos hr]"
}
] | [
158,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Group.mulRight_bijective | [] | [
183,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.trans_toRingEquiv_aux | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.tmp_topology_eq | [
{
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Mathlib/RingTheory/Subring/Basic.lean | Subring.toSubmonoid_mono | [] | [
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.frequently_iff_eventually | [] | [
131,
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130,
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_symm_of_eq_add | [
{
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203,
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.subtype_mk | [
{
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227,
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Mathlib/Data/Matrix/Block.lean | Matrix.toBlock_diagonal_self | [
{
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289,
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Std/Data/List/Init/Lemmas.lean | List.map_nil | [] | [
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51
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Colorable.chromaticNumber_mono_of_embedding | [] | [
340,
71
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.triangle_assoc_comp_right | [
{
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coeFn_smul | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_subset_ball' | [] | [
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614,
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Mathlib/Control/Basic.lean | joinM_pure | [] | [
176,
29
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsRegular.ord_pos | [
{
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{
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968,
14
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPullback.iso_hom_fst | [
{
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123,
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Mathlib/Data/Real/CauSeq.lean | CauSeq.bounded | [
{
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195,
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182,
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_eq_zero_iff | [
{
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133,
55
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131,
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Mathlib/RingTheory/Algebraic.lean | inv_eq_of_root_of_coeff_zero_ne_zero | [
{
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351,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | SemilinearIsometryClass.ediam_image | [] | [
111,
53
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109,
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Mathlib/Topology/LocalExtr.lean | IsMaxOn.localize | [] | [
137,
33
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136,
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Mathlib/Order/SymmDiff.lean | le_bihimp_iff | [
{
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}
] | [
275,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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Mathlib/Algebra/Order/Floor.lean | Nat.preimage_Ioo | [
{
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384,
31
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Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.polar_def | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.top_ne_ofReal | [] | [
298,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
9
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Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.comp_id | [] | [
280,
19
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Std/Data/Int/DivMod.lean | Int.div_add_mod | [] | [
314,
43
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313,
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Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.comp_PInfty_eq_zero_iff | [
{
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127,
72
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104,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_one_of_forall_eq_one | [
{
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544,
74
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543,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_le_nnreal_smul_snorm'_of_ae_le_mul | [
{
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1265,
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1255,
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Mathlib/Computability/Halting.lean | ComputablePred.rice | [
{
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214,
18
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Mathlib/Topology/Algebra/Order/Compact.lean | isCompact_uIcc | [] | [
127,
16
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125,
1
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Mathlib/Order/Closure.lean | ClosureOperator.closure_sup_closure | [
{
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267,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.mono_comp | [
{
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318,
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313,
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Mathlib/Data/Set/NAry.lean | Set.mem_image2_of_mem | [] | [
48,
22
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47,
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Mathlib/RingTheory/IntegrallyClosed.lean | IsIntegrallyClosed.isIntegral_iff | [] | [
93,
35
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92,
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Mathlib/Computability/TuringMachine.lean | Turing.BlankRel.equivalence | [] | [
169,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/Topology/MetricSpace/Basic.lean | Real.dist_le_of_mem_Icc | [
{
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"tactic": "simpa only [Real.dist_eq, abs_of_nonpos (sub_nonpos.2 <| hx.1.trans hx.2), n... | [
1382,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1379,
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Mathlib/Data/Finset/Basic.lean | Finset.union_eq_union_iff_right | [] | [
1498,
23
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1497,
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Mathlib/Order/Bounded.lean | Set.unbounded_le_Ioi | [] | [
283,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vadd_mem_iff_mem_direction | [
{
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281,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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Mathlib/Order/Concept.lean | Concept.inf_fst | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Mathlib/Data/List/Sigma.lean | List.mem_keys_kerase_of_ne | [
{
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455,
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449,
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Std/Data/Int/Lemmas.lean | Int.ne_of_lt | [
{
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{
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629,
35
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628,
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Mathlib/Algebra/CharP/Two.lean | orderOf_neg_one | [
{
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143,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Topology/Category/Compactum.lean | Compactum.continuous_of_hom | [
{
"state_after": "X Y : Compactum\nf : X ⟶ Y\n⊢ ∀ (x : X.A) (g : Ultrafilter X.A), ↑g ≤ 𝓝 x → Tendsto f.f (↑g) (𝓝 (Monad.Algebra.Hom.f f x))",
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"tactic": "rw [continuous_iff_ultrafilter]"
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{
"state_after": "X Y : Compactum\nf : X... | [
394,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.symm_ne | [] | [
771,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Data/Int/Parity.lean | Int.emod_two_ne_zero | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ ¬n % 2 = 0 ↔ n % 2 = 1",
"tactic": "cases' emod_two_eq_zero_or_one n with h h <;> simp [h]"
}
] | [
37,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Topology/PathConnected.lean | Path.truncate_continuous_family | [] | [
674,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisors_prime_pow | [
{
"state_after": "case a\nn p : ℕ\npp : Prime p\nk a : ℕ\n⊢ a ∈ divisors (p ^ k) ↔ a ∈ map { toFun := Nat.pow p, inj' := (_ : Function.Injective fun n => p ^ n) } (range (k + 1))",
"state_before": "n p : ℕ\npp : Prime p\nk : ℕ\n⊢ divisors (p ^ k) = map { toFun := Nat.pow p, inj' := (_ : Function.Injective f... | [
337,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nX✝ Y✝ X Y : C\nh : IsTerminal Y\nc : BinaryFan X Y\n⊢ Nonempty (IsLimit c) → IsIso (fst c)\n\ncase mpr\nC : Type u\ninst✝ : Category C\nX✝ Y✝ X Y : C\nh : IsTerminal Y\nc : BinaryFan X Y\n⊢ IsIso (fst c) → Nonempty (IsLimit c)",
"state_before": "C :... | [
425,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_of_bijOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type ?u.356139\nG : Type ?u.356142\nM : Type u_3\nN : Type ?u.356148\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf✝ g✝ : α → M\na b : α\ns✝ t✝ s : Set α\nt : Set β\nf : α → M\ng : β → M\ne : α → β\nhe₀ : BijOn e s t\nhe₁ : ∀ (x : α), x ∈ s → f x = g (e x)\n⊢ (... | [
970,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_C | [
{
"state_after": "case h.e'_3.h₁.a\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ n = 0 ↔ 0 = n",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff (↑C a) n = if n = 0 then a else 0",
"tactic": "convert coeff_monomial (a := a) (m := n) (n := 0) usin... | [
722,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.edist_eq | [] | [
190,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
11
] |
Mathlib/Data/Set/Finite.lean | Set.finite_pure | [] | [
842,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_image | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.82936\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : Isometry Φ\n⊢ hausdorffDist (Φ '' s) (Φ '' t) = hausdorffDist s t",
"tactic": "simp [hausdorffDist, hausdorffEdist_im... | [
835,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
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