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/LinearAlgebra/Basis.lean | Basis.coe_sumCoords | [] | [
234,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prod_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\nb : FactorSet α\n⊢ FactorSet.prod (⊤ + b) = FactorSet.prod ⊤ * FactorSet.prod b",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α... | [
1256,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.fin_val | [] | [
1277,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.associated_of_irreducible | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\na b : R\nha✝ : Irreducible a\nha : maximalIdeal R = span {a}\nhb✝ : Irreducible b\nhb : maximalIdeal R = span {b}\n⊢ Associated a b",
"state_before": "R : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R... | [
155,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Algebra/Associated.lean | Associated.of_mul_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.226369\nγ : Type ?u.226372\nδ : Type ?u.226375\ninst✝ : CancelCommMonoidWithZero α\na b c d : α\nh : a * b ~ᵤ c * d\nh₁ : a ~ᵤ c\nha : a ≠ 0\nu : αˣ\nhu : a * b * ↑u = c * d\nv : αˣ\nhv : c * ↑v = a\n⊢ c * ↑v * (b * ↑(u * v)) = ↑v * (a * b * ↑u)",
"state_before": ... | [
662,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.exist_integer_multiples_not_mem | [
{
"state_after": "R : Type ?u.874803\nA : Type u_1\nK : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : IsDedekindDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nJ : Ideal A\nhJ : J ≠ ⊤\nι : Type u_2\ns : Finset ι\nf : ι → K\nj : ι\nhjs : j ∈ s\nhj... | [
822,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
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Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.henstock_le_riemann | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.19641\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I\nl l₁ l₂ : IntegrationParams\n⊢ Henstock ≤ Riemann",
"tactic": "trivial"
}
] | [
278,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.ι_postcompose | [] | [
665,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.tail_think | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ tail (think s) = think (tail s)",
"tactic": "simp [tail]"
}
] | [
714,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_eq_singleton_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Finset α\n⊢ powerset s = {∅} ↔ s = ∅",
"tactic": "rw [← powerset_empty, powerset_inj]"
}
] | [
86,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.nontrivial | [
{
"state_after": "case h\nR✝ : Type ?u.417998\ninst✝¹⁶ : CommRing R✝\nM : Submonoid R✝\nS✝ : Type ?u.418190\ninst✝¹⁵ : CommRing S✝\ninst✝¹⁴ : Algebra R✝ S✝\nP : Type ?u.418427\ninst✝¹³ : CommRing P\nA : Type ?u.418433\ninst✝¹² : CommRing A\ninst✝¹¹ : IsDomain A\nK : Type ?u.418607\nB : Type ?u.418610\ninst✝¹⁰ :... | [
276,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iInter_div_subset | [] | [
786,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Data/Set/Basic.lean | Set.singleton_inter_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ Set.Nonempty ({a} ∩ s) ↔ a ∈ s",
"tactic": "simp only [Set.Nonempty, mem_inter_iff, mem_singleton_iff, exists_eq_left]"
}
] | [
1336,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
1
] |
Std/Data/List/Lemmas.lean | List.tail_eq_tail? | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ tail l = Option.getD (tail? l) []",
"tactic": "simp [tail_eq_tailD]"
}
] | [
452,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
452,
1
] |
Std/Data/AssocList.lean | Std.AssocList.find?_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : BEq α\na : α\nl : AssocList α β\n⊢ find? a l = Option.map (fun x => x.snd) (List.find? (fun x => x.fst == a) (toList l))",
"tactic": "simp [find?_eq_findEntry?]"
}
] | [
126,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
125,
9
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.gc_map_comap | [] | [
1389,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | UpperSet.coe_mul | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_inclusion | [] | [
1008,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_sub_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.135550\nα : Type u_1\nβ : Type ?u.135556\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na✝ a : α\nz : ℤ\n⊢ ⌊a - ↑z⌋ = ⌊a + ↑(-z)⌋",
"tactic": "rw [Int.cast_neg, sub_eq_add_neg]"
}
] | [
762,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.eventually_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17529\nγ : Type ?u.17532\nι : Sort u_2\nι' : Sort ?u.17538\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'\nhl : HasBasis l p s\nq : α → Prop\n⊢ (∀ᶠ (x : α) in l, q x) ↔ ∃ i, p i... | [
367,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.degree_prod | [] | [
343,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.nullMeasurableSet_insert | [] | [
358,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Matrix/Basic.lean | AlgEquiv.mapMatrix_refl | [] | [
1632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1631,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.sum_lt' | [
{
"state_after": "case inl\np : ℕ\nhp : Fact (Nat.Prime p)\nα : Type u_1\nF : α → ℚ\nt : ℚ\nht : 0 < t\nhF : ∀ (i : α), i ∈ ∅ → padicNorm p (F i) < t\n⊢ padicNorm p (∑ i in ∅, F i) < t\n\ncase inr\np : ℕ\nhp : Fact (Nat.Prime p)\nα : Type u_1\nF : α → ℚ\nt : ℚ\ns : Finset α\nhF : ∀ (i : α), i ∈ s → padicNorm p ... | [
349,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_mul_left_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.7085574\n𝕜 : Type ?u.7085577\nE : Type u_1\nF : Type ?u.7085583\nA : Type ?u.7085586\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedRing A\nf g : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nc : ℝ\nhc : c ≠ 0\nh : IntervalIntegrable (fun x => f (c * ... | [
312,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_subset_Iic_self | [] | [
539,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inf_eq_inter | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_subset_closedBall | [] | [
527,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Topology/Separation.lean | exists_isOpen_xor'_mem | [] | [
243,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.deriv_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.168645\nr : α → α → Prop\nf : Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nhc' : c ≠ ℵ₀\nhf : ∀ (i : Ordinal), i < ord c → f i < ord c\na : Ordinal\n⊢ lift (#Unit) < c",
"tactic": "simpa using Cardinal.one_lt_aleph0.trans (lt_of_le_of_ne hc... | [
1204,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.not_wSameSide | [] | [
667,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_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 ⟶ Y ⊗ Z\ng : X' ⟶ Z'\n⊢ (𝟙 Y' ⊗ (f ⊗ g) ≫ (α_ Y Z Z').hom) ≫ (α_ Y' Y (Z ⊗ Z')).inv ≫ (ε_ Y Y' ⊗ 𝟙 (Z ⊗ Z')) ≫ (λ_ (Z ⊗ Z')).hom =\n (α_ Y' X X').inv ≫ ((𝟙 Y' ⊗ f) ≫ (α_ Y'... | [
453,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate'_length | [
{
"state_after": "α : Type u\nl : List α\n⊢ drop (length l) l ++ take (length l) l = l",
"state_before": "α : Type u\nl : List α\n⊢ rotate' l (length l) = l",
"tactic": "rw [rotate'_eq_drop_append_take le_rfl]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\n⊢ drop (... | [
89,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_mul_le_right | [
{
"state_after": "l : Type u_2\nm : Type u_3\nn : Type u_4\no : Type ?u.37975\nR : Type u_1\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : CommRing R\ninst✝ : StrongRankCondition R\nA : Matrix l m R\nB : Matrix m n R\n⊢ finrank R { x // x ∈ LinearMap.range (LinearMap.comp (mulVecLin A) (mu... | [
86,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_Ioi_eq_Ici | [
{
"state_after": "case pos\n𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE✝ : Type w\ninst✝³ : NormedAddCommGroup E✝\ninst✝² : NormedSpace 𝕜 E✝\nf✝ f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx✝ : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nE : Typ... | [
557,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Topology/Order.lean | continuous_sup_rng_right | [] | [
748,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Std/Logic.lean | Decidable.imp_iff_right_iff | [] | [
613,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
611,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.Dual.transpose_apply | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | DifferentiableOn.div | [] | [
224,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/Bases.lean | Dense.exists_countable_dense_subset | [] | [
509,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ne_top | [] | [
307,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_zpow | [] | [
801,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.const_comp | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.ext_iff | [] | [
295,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.unpaired | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.66894\nσ : Type ?u.66897\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : ℕ → ℕ → α\nh : Primrec (Nat.unpaired f)\n⊢ Primrec₂ f",
"tactic": "simpa using h.comp natPair"
}
] | [
441,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Combinatorics/Derangements/Finite.lean | numDerangements_succ | [
{
"state_after": "case zero\nα : Type ?u.11655\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n⊢ ↑(numDerangements (Nat.zero + 1)) = (↑Nat.zero + 1) * ↑(numDerangements Nat.zero) - (-1) ^ Nat.zero\n\ncase succ\nα : Type ?u.11655\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nhn : ↑(numDerangements (n + 1)) = (↑... | [
96,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.hasBasis_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.60670\ninst✝ : UniformSpace α\nx : α\nt : Set α\n⊢ t ∈ 𝓝 x ↔ ∃ i, (i ∈ 𝓤 α ∧ SymmetricRel i) ∧ ball x i ⊆ t",
"tactic": "simp [UniformSpace.mem_nhds_iff_symm, and_assoc]"
}
] | [
763,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | isUnit_iff_ne_zero | [] | [
257,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.sumCongr_refl_swap | [
{
"state_after": "case H\nα✝ : Sort ?u.121266\ninst✝² : DecidableEq α✝\nα : Type u_1\nβ : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ni j : β\nx : α ⊕ β\n⊢ ↑(sumCongr (Equiv.refl α) (swap i j)) x = ↑(swap (Sum.inr i) (Sum.inr j)) x",
"state_before": "α✝ : Sort ?u.121266\ninst✝² : DecidableEq α✝... | [
1680,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1672,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_top | [] | [
164,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43769\nE : Type ?u.43772\nF : Type ?u.43775\nG : Type ?u.43778\nE' : Type ?u.43781\nF' : Type ?u.43784\nG' : Type ?u.43787\nE'' : Type ?u.43790\nF'' : Type ?u.43793\nG'' : Type ?u.43796\nR : Type ?u.43799\nR' : Type ?u.43802\n𝕜 : Type ... | [
240,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_subset_biInter_left | [] | [
883,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOf.le_max | [] | [
207,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_coe | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left | [] | [
1875,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1875,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.le_one_iff | [] | [
124,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.colLen_transpose | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\nj : ℕ\n⊢ colLen (transpose μ) j = rowLen μ j",
"tactic": "simp [rowLen, colLen]"
}
] | [
370,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Algebra/Order/Hom/Basic.lean | le_map_add_map_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.7573\nF : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.7585\nδ : Type ?u.7588\ninst✝³ : Group α\ninst✝² : AddCommSemigroup β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b : α\n⊢ ↑f a ≤ ↑f b + ↑f (a / b)",
"tactic": "simpa only [... | [
140,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAntiOn.compares | [] | [
832,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
11
] |
Mathlib/Order/RelClasses.lean | comm | [] | [
36,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_div | [] | [
1737,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1735,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.injective_codRestrict | [] | [
652,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_le_map_iff_of_injOn | [] | [
2316,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2310,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp | [] | [
190,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Balanced.alter | [
{
"state_after": "α : Type u_1\nc : RBColor\nn : Nat\ncut : α → Ordering\nf : Option α → Option α\nt : RBNode α\nh : Balanced t c n\n⊢ ∃ c n,\n Balanced\n (match zoom cut t Path.root with\n | (nil, path) =>\n match f none with\n | none => t\n | some y => Path.insertNew path y\n... | [
377,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
361,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.isSubgraph_eq_le | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.smul_measure | [] | [
155,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.subtype_mono | [] | [
675,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.mul_one | [
{
"state_after": "case zero\nm : ℕ\ninst✝ : NeZero zero\nk : Fin zero\n⊢ k * 1 = k\n\ncase succ\nm n : ℕ\ninst✝ : NeZero (Nat.succ n)\nk : Fin (Nat.succ n)\n⊢ k * 1 = k",
"state_before": "n m : ℕ\ninst✝ : NeZero n\nk : Fin n\n⊢ k * 1 = k",
"tactic": "cases' n with n"
},
{
"state_after": "case su... | [
2524,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2519,
11
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_neg' | [
{
"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\n⊢ toIcoMod hp (-a) b = p - toIocMod hp a (-b)",
"tactic": "simpa only [neg_neg] using toIcoMod_neg hp (-a) (-b)"
}
] | [
554,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BoundedLatticeHom.asBoolRing_id | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.exp_log | [
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : x ≠ 0\n⊢ exp (log x) = x",
"tactic": "rw [log, exp_add_mul_I, ← ofReal_sin, sin_arg, ← ofReal_cos, cos_arg hx, ← ofReal_exp,\n Real.exp_log (abs.pos hx), mul_add, ofReal_div, ofReal_div,\n mul_div_cancel' _ (ofReal_ne_zero.2 <| abs.ne_zero hx),... | [
52,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.hasSum_iff_tendsto_nat | [
{
"state_after": "α : Type u_1\nβ : Type ?u.238111\nγ : Type ?u.238114\nδ : Type ?u.238117\ninst✝² : AddCommMonoid α\ninst✝¹ : TopologicalSpace α\nf✝ g : β → α\na✝ b : α\ns : Finset β\ninst✝ : T2Space α\nf : ℕ → α\na : α\nhf : Summable f\nh : Tendsto (fun n => ∑ i in range n, f i) atTop (𝓝 a)\n⊢ HasSum f a",
... | [
300,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.isOpen_singleton_iff | [
{
"state_after": "case refine'_1\ns : Set Ordinal\na : Ordinal\nh : IsOpen {a}\nx✝ : IsLimit a\nh₀ : a ≠ 0\nhsucc : ∀ (a_1 : Ordinal), a_1 < a → succ a_1 < a\n⊢ False\n\ncase refine'_2\ns : Set Ordinal\na : Ordinal\nha : ¬IsLimit a\n⊢ IsOpen {a}",
"state_before": "s : Set Ordinal\na : Ordinal\n⊢ IsOpen {a} ... | [
56,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.top_ne_nat | [] | [
388,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝⁵ : MetricSpace α\nβ : Type u\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : MeasureTheory.Measure α\ninst✝ : IsFiniteMeasure μ\nf : α → Set ℝ\ns : Set α\nhf : ∀... | [
822,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.Measure.completion_apply | [] | [
512,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_union_of_subset | [] | [
1933,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1932,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_subset_mul_right | [] | [
430,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Finset.sum_powerset_neg_one_pow_card_of_nonempty | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.210079\nα : Type u_1\nx : Finset α\nh0 : Finset.Nonempty x\n⊢ ∑ m in powerset x, (-1) ^ card m = 0",
"tactic": "classical\n rw [sum_powerset_neg_one_pow_card, if_neg]\n rw [← Ne.def, ← nonempty_iff_ne_empty]\n apply h0"
},
{
"state_aft... | [
180,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_iSup_left | [
{
"state_after": "ι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\ns : ι → Submodule R M\nt : Submodule ... | [
157,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.coe_le_coe | [
{
"state_after": "no goals",
"state_before": "x y : ℕ\n⊢ ↑x ≤ ↑y ↔ x ≤ y",
"tactic": "exact ⟨fun ⟨_, h⟩ => h trivial, fun h => ⟨fun _ => trivial, fun _ => h⟩⟩"
}
] | [
276,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.bit0 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.7666\ninst✝¹ : AddMonoid R\ninst✝ : StarAddMonoid R\nx : R\nhx : IsSelfAdjoint x\n⊢ IsSelfAdjoint (_root_.bit0 x)",
"tactic": "simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]"
}
] | [
122,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_ndunion | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : DecidableEq α\ns₁ s₂ : Multiset α\n⊢ ∀ (a : α), a ∈ ndunion s₁ s₂ ↔ a ∈ s₁ + s₂",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : Decidable... | [
109,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Deprecated/Group.lean | IsMulHom.to_isMonoidHom | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : MulOneClass α\ninst✝ : Group β\nf : α → β\nhf : IsMulHom f\n⊢ ?m.14380 hf * f 1 = ?m.14380 hf",
"tactic": "rw [← hf.map_mul, one_mul]"
}
] | [
197,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.id_apply | [] | [
677,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le | [] | [
772,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_int_mul_cast_int_mul | [] | [
1165,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_eq_pi_single | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.78390\nm : Type ?u.78393\nn : Type u_1\no : Type ?u.78399\nm' : o → Type ?u.78404\nn' : o → Type ?u.78409\nR : Type ?u.78412\nS : Type ?u.78415\nα : Type v\nβ : Type w\nγ : Type ?u.78422\ninst✝² : DecidableEq n\ninst✝¹ : Zero α\ninst✝ : One α\ni j : ... | [
563,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_eq_re_inner | [] | [
2218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2216,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.apply_symm_apply | [] | [
283,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
9
] |
Mathlib/Topology/Maps.lean | Inducing.isClosed_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.5624\nδ : Type ?u.5627\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⊢ IsClosed s ↔ ∃ t, IsClosed t ∧ f ⁻¹' t = s... | [
162,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.zero_powerlt | [
{
"state_after": "α β : Type u\na : Cardinal\nh : a ≠ 0\n⊢ 1 ≤ 0 ^< a",
"state_before": "α β : Type u\na : Cardinal\nh : a ≠ 0\n⊢ 0 ^< a = 1",
"tactic": "apply (powerlt_le.2 fun c _ => zero_power_le _).antisymm"
},
{
"state_after": "α β : Type u\na : Cardinal\nh : a ≠ 0\n⊢ ?m.690119 ^ 0 ≤ 0 ^< a... | [
2317,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2314,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBounded.mono | [] | [
99,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_add_cond_compl_eq | [
{
"state_after": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\ninst✝ : IsFiniteMeasure μ\nhms : MeasurableSet s\nhcs : ↑↑μ s ≠ 0\nhcs' : ↑↑μ (sᶜ) ≠ 0\n⊢ ↑↑μ (t ∩ s) + ↑↑μ (t ∩ sᶜ) = ↑↑μ t",
"state_before": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns... | [
159,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformContinuous₂.tendstoUniformly | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : UniformSpace β\nF : ι → α → β\nf✝ : α → β\ns s' : Set α\nx✝ : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace γ\nf : α → β → γ\nh : UniformContinuous₂ f\nx : α\n⊢ U... | [
395,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | factorization_pow | [
{
"state_after": "case h\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : UniqueFactorizationMonoid α\ninst✝¹ : NormalizationMonoid α\ninst✝ : DecidableEq α\nx : α\nn : ℕ\na✝ : α\n⊢ ↑(factorization (x ^ n)) a✝ = ↑(n • factorization x) a✝",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoid... | [
2040,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2038,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.filter_apply_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.163622\nγ : Type ?u.163625\np : Pmf α\ns : Set α\nh : ∃ a, a ∈ s ∧ a ∈ support p\na : α\n⊢ ↑(filter p s h) a = 0 ↔ ¬a ∈ s ∨ ¬a ∈ support p",
"tactic": "erw [apply_eq_zero_iff, support_filter, Set.mem_inter_iff, not_and_or]"
}
] | [
293,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_toAffineIsometry | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.dist_comm | [
{
"state_after": "no goals",
"state_before": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nx y : X ⊕ Y\n⊢ Sum.dist x y = Sum.dist y x",
"tactic": "cases x <;> cases y <;> simp [Sum.dist, _root_.dist_comm, add_comm, add_left_comm, add_assoc]"
}
] | [
219,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
9
] |
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