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/Set/Intervals/Basic.lean | Set.Ico_subset_Ico_union_Ico | [] | [
1503,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.zpow_aux | [
{
"state_after": "α : Type u\nβ : Type v\np : α → Prop\nf : Perm α\nhf : ∀ (x : α), p x ↔ p (↑f x)\nn : ℕ\n⊢ ∀ (x : α), p x ↔ p (↑(f ^ (n + 1))⁻¹ x)",
"state_before": "α : Type u\nβ : Type v\np : α → Prop\nf : Perm α\nhf : ∀ (x : α), p x ↔ p (↑f x)\nn : ℕ\n⊢ ∀ (x : α), p x ↔ p (↑(f ^ Int.negSucc n) x)",
... | [
417,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
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Mathlib/Algebra/Order/Hom/Basic.lean | le_map_add_map_div' | [
{
"state_after": "no goals",
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"tactic": "simpa only [add_co... | [
259,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_insert_of_lt | [
{
"state_after": "F : Type ?u.90423\nα : Type u_1\nβ : Type ?u.90429\n𝕜 : Type ?u.90432\nE : Type ?u.90435\ninst✝ : OrderedCancelCommMonoid α\ns : Set α\na : α\nhs : ∀ (i : α), i ∈ s → i < a\n⊢ (MulSalemSpencer s ∧\n (∀ ⦃b c : α⦄, b ∈ s → c ∈ s → a * b = c * c → a = b) ∧ ∀ ⦃b c : α⦄, b ∈ s → c ∈ s → b * c... | [
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222,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_iSup_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.59414\nγ : Type ?u.59417\nι : Sort u_2\nκ : ι → Sort ?u.59425\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\nf : ι → UpperSet α\n⊢ (a ∈ ⋂ (i : ι), ↑(f i)) ↔ ∀ (i : ι), a ∈ f i",
"state_before": "α : Type u_1\nβ : Type ?u.59414\nγ : Type ?u.59417\nι ... | [
603,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.inv_iSup | [] | [
210,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/Data/Set/Basic.lean | SetCoe.forall' | [] | [
203,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.irreducible_aux1 | [
{
"state_after": "p q : ℤ[X]\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nu v w : ℤˣ\nhp : p = trinomial k m n ↑u ↑v ↑w\nkey : n - m + k < n\n⊢ ↑C ↑v * (↑C ↑u * X ^ (m + n) + ↑C ↑w * X ^ (n - m + k + n)) =\n { toFinsupp := Finsupp.filter (Set.Ioo (k + n) (n + n)) (p * mirror p).toFinsupp }",
"state_before": "p ... | [
256,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
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Mathlib/LinearAlgebra/FreeModule/PID.lean | Module.free_of_finite_type_torsion_free | [
{
"state_after": "case intro\nι : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsPrincipalIdealRing R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nb : ι → M\ninst✝¹ : _root_.Finite ι\ns : ι → M\nhs : span R (range s) = ⊤\ninst✝ : NoZeroSMulDivisors R M\nval✝ : Finty... | [
410,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.coe_toConvexCone | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Algebra/Divisibility/Basic.lean | MulHom.map_dvd | [] | [
103,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousOn.upperSemicontinuousWithinAt | [] | [
687,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
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Mathlib/Topology/Order/Basic.lean | continuousWithinAt_Ioo_iff_Iio | [
{
"state_after": "no goals",
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... | [
512,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_one_left | [] | [
187,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Set.Subsingleton.differentiableOn | [] | [
1132,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castPred_zero | [] | [
2299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2298,
1
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.eq_mk | [
{
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401,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommProd_add | [
{
"state_after": "case mk\nF : Type ?u.83828\nι : Type ?u.83831\nα : Type u_1\nβ : Type ?u.83837\nγ : Type ?u.83840\nf : α → β → β\nop : α → α → α\ninst✝¹ : Monoid α\ninst✝ : Monoid β\ns t : Multiset α\na✝ : List α\ncomm : Set.Pairwise {x | x ∈ Quot.mk Setoid.r a✝ + t} Commute\n⊢ noncommProd (Quot.mk Setoid.r a... | [
177,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_mul | [] | [
204,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_smul_smul | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ : V\nc : ℝ\nhc : c ≠ 0\nx y : V\nthis : c * c ≠ 0\n⊢ angle (c • x) (c • y) = angle x y",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ : V\nc : ℝ\nhc : c ≠... | [
62,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_iff_exists_mem_nhds_image_subset_compact | [] | [
84,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.omega_ne_zero | [] | [
194,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/RingTheory/Nilpotent.lean | isNilpotent_neg_iff | [] | [
58,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | ULift.edist_eq | [] | [
438,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Measurable.le | [] | [
571,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.isPrimePow_of_has_chain | [] | [
221,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.adjoinIntegral_eq_one_of_isUnit | [
{
"state_after": "R : Type ?u.114414\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nx : K\nhx : IsIntegral A x\nI : FractionalIdeal A⁰ K := adjoinIntegral A⁰ x hx\nhI : IsUnit I\n⊢ I = 1",
"state... | [
272,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.append_data | [
{
"state_after": "α : Type u_1\narr arr' : Array α\n⊢ (Array.append arr arr').data = arr.data ++ arr'.data",
"state_before": "α : Type u_1\narr arr' : Array α\n⊢ (arr ++ arr').data = arr.data ++ arr'.data",
"tactic": "rw [← append_eq_append]"
},
{
"state_after": "α : Type u_1\narr arr' : Array α... | [
196,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
192,
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] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofRealClm_coe | [] | [
1010,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
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] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.div_eq_iff_eq_of_dvd_dvd | [
{
"state_after": "case mp\na b m n✝ k n x y : ℕ\nhn : n ≠ 0\nhx : x ∣ n\nhy : y ∣ n\n⊢ n / x = n / y → x = y\n\ncase mpr\na b m n✝ k n x y : ℕ\nhn : n ≠ 0\nhx : x ∣ n\nhy : y ∣ n\n⊢ x = y → n / x = n / y",
"state_before": "a b m n✝ k n x y : ℕ\nhn : n ≠ 0\nhx : x ∣ n\nhy : y ∣ n\n⊢ n / x = n / y ↔ x = y",
... | [
80,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.range_sigma_eq_iUnion_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ✝ : Type ?u.148439\nι : Sort ?u.148442\nι' : Sort ?u.148445\nι₂ : Sort ?u.148448\nκ : ι → Sort ?u.148453\nκ₁ : ι → Sort ?u.148458\nκ₂ : ι → Sort ?u.148463\nκ' : ι' → Sort ?u.148468\nγ : α → Type u_1\nf : Sigma γ → β\n⊢ ∀ (x : β), x ∈... | [
1265,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_biUnion_finset | [] | [
192,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_union_le | [] | [
419,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b : α\n⊢ span 1 = ⊤",
"tactic": "rw [← Set.singleton_one, span_singleton_one]"
}
] | [
210,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_to_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\nf : X ⟶ 0\n⊢ f = 0",
"tactic": "ext"
}
] | [
378,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/CategoryTheory/Preadditive/Schur.lean | CategoryTheory.finrank_hom_simple_simple_le_one | [
{
"state_after": "case inl\nC : Type u_3\ninst✝⁸ : Category C\ninst✝⁷ : Preadditive C\n𝕜 : Type u_1\ninst✝⁶ : Field 𝕜\ninst✝⁵ : IsAlgClosed 𝕜\ninst✝⁴ : Linear 𝕜 C\ninst✝³ : HasKernels C\nX Y : C\ninst✝² : FiniteDimensional 𝕜 (X ⟶ X)\ninst✝¹ : Simple X\ninst✝ : Simple Y\nh : Subsingleton (X ⟶ Y)\n⊢ finrank ... | [
183,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Finset/PImage.lean | Finset.pimage_some | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\ninst✝³ : DecidableEq β\nf✝ g : α →. β\ninst✝² : (x : α) → Decidable (f✝ x).Dom\ninst✝¹ : (x : α) → Decidable (g x).Dom\ns✝ t : Finset α\nb : β\ns : Finset α\nf : α → β\ninst✝ : (x : α) → Decidable (Part.some (f x)).Dom\na✝ : β\n⊢ a✝ ∈ pimage (fun x => Part.s... | [
82,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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] |
Mathlib/Deprecated/Ring.lean | RingHom.coe_of | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_mem_diff | [] | [
1807,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1806,
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] |
Mathlib/Topology/DenseEmbedding.lean | denseEmbedding_id | [] | [
302,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_eq | [] | [
386,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/List/Basic.lean | List.map_comp_map | [
{
"state_after": "case h.a.a\nι : Type ?u.136607\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ng : β → γ\nf : α → β\nl : List α\nn✝ : ℕ\na✝ : γ\n⊢ a✝ ∈ get? ((map g ∘ map f) l) n✝ ↔ a✝ ∈ get? (map (g ∘ f) l) n✝",
"state_before": "ι : Type ?u.136607\nα : Type u\nβ : Type v\nγ : Type w\nδ :... | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
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Std/Data/Option/Lemmas.lean | Option.get_some | [] | [
35,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
35,
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Mathlib/Data/Matrix/Basic.lean | Matrix.scalar_inj | [
{
"state_after": "case mp\nl : Type ?u.458991\nm : Type ?u.458994\nn : Type u_1\no : Type ?u.459000\nm' : o → Type ?u.459005\nn' : o → Type ?u.459010\nR : Type ?u.459013\nS : Type ?u.459016\nα : Type v\nβ : Type w\nγ : Type ?u.459023\ninst✝³ : Semiring α\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : None... | [
1270,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
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] |
Mathlib/Algebra/Order/Monoid/TypeTags.lean | Additive.toMul_le | [] | [
134,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.ι_ne_algebraMap | [
{
"state_after": "R : Type u_1\ninst✝³ : CommSemiring R\nX : Type u_2\nA : Type ?u.733161\ninst✝² : Semiring A\ninst✝¹ : Algebra R A\ninst✝ : Nontrivial R\nx : X\nr : R\nh : ι R x = ↑(algebraMap R (FreeAlgebra R X)) r\nf0 : FreeAlgebra R X →ₐ[R] R := ↑(lift R) 0\n⊢ False",
"state_before": "R : Type u_1\nins... | [
461,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/Topology/Constructions.lean | continuous_quotient_mk' | [] | [
1162,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_sInf_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58938\nγ : Type ?u.58941\nι : Sort ?u.58944\nκ : ι → Sort ?u.58949\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\n⊢ (∃ i j, a ∈ ↑i) ↔ ∃ s, s ∈ S ∧ a ∈ s",
"tactic": "simp only [exists_prop, SetLike.mem_coe]"
}
] | [
597,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_le_one_of_le' | [] | [
859,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_of_neg_of_one_div_le_one_div | [] | [
875,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_const | [] | [
102,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_update | [] | [
832,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.comp_antitone | [] | [
238,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
8
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostMap.bijective_of_invertible | [] | [
338,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x + a) ⁻¹' Ico b c = Ico (b - a) (c - a)",
"tactic": "simp [← Ici_inter_Iio]"
}
] | [
114,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/RingTheory/Nilpotent.lean | Commute.isNilpotent_sub | [
{
"state_after": "R S : Type u\nx y : R\ninst✝ : Ring R\nh_comm✝ : Commute x y\nh_comm : Commute x (-y)\nhx : IsNilpotent x\nhy : IsNilpotent y\n⊢ IsNilpotent (x - y)",
"state_before": "R S : Type u\nx y : R\ninst✝ : Ring R\nh_comm : Commute x y\nhx : IsNilpotent x\nhy : IsNilpotent y\n⊢ IsNilpotent (x - y)... | [
179,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.constantCoeff_zero | [] | [
508,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/Module/Bimodule.lean | Subbimodule.smul_mem' | [
{
"state_after": "R : Type u_4\nA : Type u_2\nB : Type u_1\nM : Type u_3\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Module A M\ninst✝⁵ : Module B M\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : IsScalarTower R A M\ninst✝¹... | [
105,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_mulVec_equiv | [] | [
2509,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2506,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_left_iff | [
{
"state_after": "a b : Cardinal\n⊢ a + b = a ↔ ℵ₀ ≤ a ∧ b ≤ a ∨ b = 0",
"state_before": "a b : Cardinal\n⊢ a + b = a ↔ max ℵ₀ b ≤ a ∨ b = 0",
"tactic": "rw [max_le_iff]"
},
{
"state_after": "case refine'_1\na b : Cardinal\nh : a + b = a\n⊢ ℵ₀ ≤ a ∧ b ≤ a ∨ b = 0\n\ncase refine'_2\na b : Cardina... | [
804,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.arrowCongr_refl | [
{
"state_after": "case H.H\nR : Type u\nA₁ : Type v\nA₂ : Type w\nA₃ : Type u₁\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A₁\ninst✝⁴ : Semiring A₂\ninst✝³ : Semiring A₃\ninst✝² : Algebra R A₁\ninst✝¹ : Algebra R A₂\ninst✝ : Algebra R A₃\ne : A₁ ≃ₐ[R] A₂\nx✝¹ : A₁ →ₐ[R] A₂\nx✝ : A₁\n⊢ ↑(↑(arrowCongr refl refl) ... | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/GroupTheory/Exponent.lean | card_dvd_exponent_pow_rank | [
{
"state_after": "case intro.intro\nG : Type u\ninst✝¹ : CommGroup G\ninst✝ : Group.FG G\nS : Finset G\nhS1 : Finset.card S = Group.rank G\nhS2 : closure ↑S = ⊤\n⊢ Nat.card G ∣ Monoid.exponent G ^ Group.rank G",
"state_before": "G : Type u\ninst✝¹ : CommGroup G\ninst✝ : Group.FG G\n⊢ Nat.card G ∣ Monoid.exp... | [
379,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Coplanar.finiteDimensional_vectorSpan | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.339734\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\nh : Coplanar k s\n⊢ 2 < Cardinal.aleph0",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.339734\n... | [
614,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.sub_snd | [] | [
285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.cases_on | [] | [
185,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
11
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_natDegree_lt | [] | [
194,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Std/Logic.lean | iff_iff_eq | [] | [
51,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
51,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.continuous_inv' | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝ : Group α\ng : GroupTopology α\nthis : TopologicalSpace α := g.toTopologicalSpace\n⊢ Continuous Inv.inv",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝ : Group α\ng : GroupTopology α\n⊢ Continuous Inv.inv",
... | [
1868,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1863,
1
] |
Mathlib/Algebra/AlgebraicCard.lean | Algebraic.infinite_of_charZero | [] | [
35,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_of_mul_dvd_mul_left | [
{
"state_after": "k m n : Nat\nkpos : 0 < k\nH✝ : k * m ∣ k * n\nl : Nat\nH : k * n = k * m * l\n⊢ m ∣ n",
"state_before": "k m n : Nat\nkpos : 0 < k\nH : k * m ∣ k * n\n⊢ m ∣ n",
"tactic": "let ⟨l, H⟩ := H"
},
{
"state_after": "k m n : Nat\nkpos : 0 < k\nH✝ : k * m ∣ k * n\nl : Nat\nH : k * n =... | [
750,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
746,
11
] |
Mathlib/Data/Sum/Interval.lean | Sum.Icc_inl_inl | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/Convex/Topology.lean | isClosed_stdSimplex | [] | [
68,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_indicator_subset | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.58761\ns₂✝ : Finset ι₂\nw : ι → k\np : ι → P\nb : P\ns₁ s₂ : Finset ι\nh : s₁ ⊆ s₂\n⊢ ∑ i in s₁, w i • (p i -ᵥ b) = ∑ i in s₂, S... | [
174,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.one_lt_coe | [] | [
521,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | Disjoint.edgeSet | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.125448\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nH₁ H₂ : Subgraph G\nh : Disjoint H₁ H₂\n⊢ SimpleGraph.Subgraph.edgeSet H₁ ⊓ SimpleGraph.Subgraph.edgeSet H₂ ≤ ⊥",
"tactic": "simpa using edgeSet_mono h.le_bot"
}
] | [
639,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Order/Max.lean | isTop_ofDual_iff | [] | [
258,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasStrictFDerivAt.comp_hasStrictDerivAt | [] | [
265,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.map_id | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.39044\nδ : Type ?u.39047\nl : Filter α\nf✝ g h : α → β\nx✝ : Germ l β\nf : α → β\n⊢ map id (Quot.mk Setoid.r f) = id (Quot.mk Setoid.r f)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.39044\nδ : Type ?u.39047\nl : Filter α\nf ... | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.sub_conj | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (z - ↑(starRingEnd ℂ) z).re = (↑(2 * z.im) * I).re ∧ (z - ↑(starRingEnd ℂ) z).im = (↑(2 * z.im) * I).im",
"tactic": "simp [two_mul, sub_eq_add_neg, ofReal']"
}
] | [
719,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Std/Data/List/Lemmas.lean | List.mem_diff_of_mem | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ : List α\nb : α\nl₂ : List α\nh₁ : a ∈ l₁\nh₂ : ¬a ∈ b :: l₂\n⊢ a ∈ List.diff (List.erase l₁ b) l₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ : List α\nb : α\nl₂ : List α\nh₁ : a ∈ l₁\nh₂ : ¬a ∈ b :: l₂\n⊢ a ∈ List.diff ... | [
1539,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1535,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_finset_sup | [
{
"state_after": "α : Type u_2\nβ : Type ?u.34252\nγ : Type ?u.34255\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nι : Type u_1\ns✝ : Finset ι\nf : ι → Compacts α\na : ι\ns : Finset ι\nx✝ : ¬a ∈ s\nh : ↑(Finset.sup s f) = Finset.sup s fun i => ↑(f i)\n⊢ ↑(Finset.sup (Fin... | [
131,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.inv_limsup | [] | [
525,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.finrank_range_dualMap_eq_finrank_range | [
{
"state_after": "K : Type u\ninst✝⁵ : Field K\nV₁ : Type v'\nV₂ : Type v''\ninst✝⁴ : AddCommGroup V₁\ninst✝³ : Module K V₁\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V₂\nf : V₁ →ₗ[K] V₂\nthat : finrank K (V₂ ⧸ range f) + finrank K { x // x ∈ range f } = finrank K V₂\n⊢ finrank... | [
1494,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1481,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Function.Injective.summable_iff | [] | [
140,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Group/WithOne/Basic.lean | WithOne.lift_unique | [] | [
90,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Topology/Order.lean | induced_compose | [] | [
474,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.matrix_vecEmpty_coeff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR✝ : Type ?u.636245\nS : Type ?u.636248\nT : Type ?u.636251\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R✝\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.636266\nβ : Type ?u.636269\nx y : 𝕎 R✝\nR : Type u_1\ni : Fin 0\nj : ℕ\n⊢ coeff ![] j = ![]",... | [
186,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Symmetric.pairwise_on | [] | [
55,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_fintypeIci | [
{
"state_after": "case b\nn : ℕ\na b : Fin n\n⊢ Fin n",
"state_before": "n : ℕ\na b : Fin n\n⊢ Fintype.card ↑(Set.Ici a) = n - ↑a",
"tactic": "rw [Fintype.card_ofFinset, card_Ici]"
},
{
"state_after": "no goals",
"state_before": "case b\nn : ℕ\na b : Fin n\n⊢ Fin n",
"tactic": "assumptio... | [
203,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.lmul'_apply_tmul | [] | [
943,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_zero_scanl | [] | [
2631,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2630,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp a (b - p) = toIcoDiv hp a b - 1",
"tactic": "simpa only [one_zsmul] using toIcoDiv_sub_zsmul hp a b 1"
}
] | [
340,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/Complex/Liouville.lean | Differentiable.exists_const_forall_eq_of_bounded | [] | [
129,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | fn_min_mul_fn_max | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : CommSemigroup β\nf : α → β\nn m : α\n⊢ f (min n m) * f (max n m) = f n * f m",
"tactic": "cases' le_total n m with h h <;> simp [h, mul_comm]"
}
] | [
29,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Order/SymmDiff.lean | compl_bihimp | [] | [
743,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/LinearAlgebra/Ray.lean | exists_nonneg_left_iff_sameRay | [
{
"state_after": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhx : x ≠ 0\nh : ∃ r, 0 ≤ r ∧ r • x = y\n⊢ SameRay R x y",
"state_before": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M... | [
731,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.exists_pos | [] | [
204,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_zero | [
{
"state_after": "case a.h\nl : Type ?u.47813\nm : Type ?u.47816\nn : Type u_1\no : Type ?u.47822\nm' : o → Type ?u.47827\nn' : o → Type ?u.47832\nR : Type ?u.47835\nS : Type ?u.47838\nα : Type v\nβ : Type w\nγ : Type ?u.47845\ninst✝¹ : DecidableEq n\ninst✝ : Zero α\ni✝ x✝ : n\n⊢ diagonal (fun x => 0) i✝ x✝ = O... | [
461,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Algebra/Order/Chebyshev.lean | Monovary.sum_smul_sum_le_card_smul_sum | [] | [
85,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.toFinsupp_comp_toFreeAbelianGroup | [
{
"state_after": "case H.h1.h\nX : Type u_1\nx y : X\n⊢ ↑(↑(AddMonoidHom.comp (AddMonoidHom.comp toFinsupp toFreeAbelianGroup) (singleAddHom x)) 1) y =\n ↑(↑(AddMonoidHom.comp (AddMonoidHom.id (X →₀ ℤ)) (singleAddHom x)) 1) y",
"state_before": "X : Type u_1\n⊢ AddMonoidHom.comp toFinsupp toFreeAbelianGro... | [
66,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
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