file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/GeomSum.lean | Commute.mul_geom_sum₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Ring α\nx y : α\nh : Commute x y\nn : ℕ\n⊢ (x - y) * ∑ i in range n, x ^ i * y ^ (n - 1 - i) = x ^ n - y ^ n",
"tactic": "rw [← neg_sub (y ^ n), ← h.mul_neg_geom_sum₂, ← neg_mul, neg_sub]"
}
] | [
188,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Topology/Support.lean | HasCompactMulSupport.comp₂_left | [
{
"state_after": "X : Type ?u.16388\nα : Type u_1\nα' : Type ?u.16394\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nM : Type ?u.16406\nE : Type ?u.16409\nR : Type ?u.16412\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace α'\ninst✝² : One β\ninst✝¹ : One γ\ninst✝ : One δ\ng : β → γ\nf : α → β\nf₂ : α → γ\nm ... | [
231,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nf : R →+* S\nn ν : ℕ\n⊢ Polynomial.map f (bernsteinPolynomial R n ν) = bernsteinPolynomial S n ν",
"tactic": "simp [bernsteinPolynomial]"
}
] | [
77,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.equivToUnitHom_symm_coe | [] | [
259,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Compare.lean | LT.lt.cmp_eq_gt | [] | [
274,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomainInv.isDedekindDomain | [] | [
352,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Function.Involutive.toPerm_involutive | [] | [
1717,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1716,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | contDiffWithinAt_ext_coord_change | [] | [
1260,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
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Mathlib/Data/Nat/Order/Lemmas.lean | Nat.le_of_lt_add_of_dvd | [
{
"state_after": "case intro.intro\nm n k a b : ℕ\nh : n * a < n * b + n\n⊢ n * a ≤ n * b",
"state_before": "a b m n k : ℕ\nh : a < b + n\n⊢ n ∣ a → n ∣ b → a ≤ b",
"tactic": "rintro ⟨a, rfl⟩ ⟨b, rfl⟩"
},
{
"state_after": "case intro.intro\nm n k a b : ℕ\nh : n * a < n * (b + 1)\n⊢ n * a ≤ n * b... | [
222,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Data/Holor.lean | Holor.cprankMax_sum | [
{
"state_after": "no goals",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝ : Ring α\nβ : Type u_1\nn : ℕ\ns : Finset β\nf : β → Holor α ds\nthis : DecidableEq β := Classical.decEq β\n⊢ (∀ (x : β), x ∈ ∅ → CPRankMax n (f x)) → CPRankMax (Finset.card ∅ * n) (∑ x in ∅, f x)",
"tactic": "... | [
377,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.const_smul | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.268899\nι : Type ?u.268902\ninst✝⁶ : Countable ι\nm0 : MeasurableSpace α\nμ : Measure α\nf g : α → β\ninst✝⁵ : TopologicalSpace β\n𝕜 : Type u_1\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : AddMonoid β\ninst✝² : Monoid 𝕜\ninst✝¹ : DistribMulAction 𝕜 β\ninst... | [
1101,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
11
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Mathlib/Analysis/Convex/Caratheodory.lean | convexHull_eq_union | [
{
"state_after": "case h₁\n𝕜 : Type u_1\nE : Type u\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\n⊢ ↑(convexHull 𝕜).toOrderHom s ⊆\n ⋃ (t : Finset E) (_ : ↑t ⊆ s) (_ : AffineIndependent 𝕜 Subtype.val), ↑(convexHull 𝕜).toOrderHom ↑t\n\ncase h₂\n𝕜 : Type u_1\nE ... | [
166,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.getLeft_swap | [
{
"state_after": "no goals",
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"tactic": "cases x <;> rfl"
}
] | [
377,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.mem_uIcc_of_ge | [] | [
929,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
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Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.mul_iff | [
{
"state_after": "x y z : ℤ\nh : PythagoreanTriple x y z\nk : ℤ\nhk : k ≠ 0\n⊢ PythagoreanTriple (k * x) (k * y) (k * z) → PythagoreanTriple x y z",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\nk : ℤ\nhk : k ≠ 0\n⊢ PythagoreanTriple (k * x) (k * y) (k * z) ↔ PythagoreanTriple x y z",
"tactic... | [
94,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6628\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ 0 < ncard s ↔ Set.Nonempty s",
"tactic": "rw [pos_iff_ne_zero, Ne.def, ncard_eq_zero hs, nonempty_iff_ne_empty]"
}
] | [
113,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | Subtype.edist_eq | [] | [
412,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup₂_le_iSup | [] | [
833,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.injective | [] | [
278,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | exists_reduced_fraction' | [
{
"state_after": "case intro.mk\nR : Type u_2\ninst✝⁶ : CommRing R\nx : R\nB : Type u_1\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : IsLocalization.Away x B\ninst✝² : IsDomain R\ninst✝¹ : NormalizationMonoid R\ninst✝ : UniqueFactorizationMonoid R\nb : B\nhb : b ≠ 0\nhx : Irreducible x\na₀ : R\ny : { x_1... | [
334,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nsmul_lt_aleph0_iff | [
{
"state_after": "no goals",
"state_before": "case zero\nα β : Type u\na : Cardinal\n⊢ Nat.zero • a < ℵ₀ ↔ Nat.zero = 0 ∨ a < ℵ₀",
"tactic": "simpa using nat_lt_aleph0 0"
},
{
"state_after": "case succ\nα β : Type u\na : Cardinal\nn : ℕ\n⊢ Nat.succ n • a < ℵ₀ ↔ a < ℵ₀",
"state_before": "case... | [
1546,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
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Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.iInf_N | [] | [
182,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_map | [] | [
267,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.finrank_eq_four | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.259837\nT : Type ?u.259840\nR : Type u_1\ninst✝¹ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\ninst✝ : StrongRankCondition R\n⊢ FiniteDimensional.finrank R ℍ[R,c₁,c₂] = 4",
"tactic": "rw [FiniteDimensional.finrank, rank_eq_four, Cardinal.t... | [
575,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_ne_zero | [] | [
93,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinite_neg | [] | [
604,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Order/Iterate.lean | Function.Commute.iterate_pos_lt_of_map_lt' | [] | [
189,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Topology/Constructions.lean | nhds_subtype | [] | [
229,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.map_coeff | [] | [
294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_subtype | [
{
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"state_before": "ι : Type ?... | [
927,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousOn.lean | continuousOn_iff_isClosed | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.315580\nδ : Type ?u.315583\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nthis : ∀ (t : Set β), IsClosed (restrict s f ⁻¹' t) ↔ ∃ u, IsClosed u ∧ f ⁻¹' t ∩ s = u ∩... | [
651,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
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Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.tail_map | [
{
"state_after": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nl : ListBlank Γ\n⊢ tail (map f (cons (head l) (tail l))) = map f (tail l)",
"state_before": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nl : ListB... | [
408,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.mul_toMatrix' | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.834155\nM✝ : Type ?u.834158\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M✝\ninst✝¹⁶ : Module R M✝\nR₁ : Type ?u.834194\nM₁ : Type ?u.834197\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type ?u.834809\n... | [
265,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
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] |
Mathlib/Topology/UniformSpace/Cauchy.lean | cauchySeq_const | [] | [
194,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
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] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_le | [] | [
534,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
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Mathlib/Data/Set/Basic.lean | Set.inter_nonempty | [] | [
520,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
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Mathlib/Order/UpperLower/Basic.lean | lowerClosure_prod | [
{
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"state_before": "α : Type u_1\nβ : T... | [
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1756,
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Mathlib/MeasureTheory/Measure/Sub.lean | MeasureTheory.Measure.sub_eq_zero_of_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nh : μ ≤ ν\n⊢ μ ≤ 0 + ν",
"tactic": "rwa [zero_add]"
}
] | [
50,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.coe_toModule_eq_coe_toAddMonoid | [] | [
114,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.isSubterminal_of_isIso_diag | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nA : C\ninst✝¹ : HasBinaryProduct A A\ninst✝ : IsIso (diag A)\nZ : C\nf g : Z ⟶ A\nthis : prod.fst = prod.snd\n⊢ f = g",
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112,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.ae_lt_top | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.1736279\nγ : Type ?u.1736282\nδ : Type ... | [
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39
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1495,
1
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Mathlib/Data/Nat/Prime.lean | Nat.exists_infinite_primes | [] | [
484,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nf₁ f₂ g₁ g₂ : R\nU : Opens ↑(PrimeSpectrum.Top R)\nhu₁ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₁ ∈ Ideal.primeCompl x.asIdeal\nhu₂ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₂ ∈ Ideal.primeCompl x.asIdeal\nx : { x // x ∈ U.op.u... | [
382,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/RingTheory/PrincipalIdealDomain.lean | PrincipalIdealRing.factors_spec | [
{
"state_after": "R : Type u\nM : Type v\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : IsPrincipalIdealRing R\na : R\nh : a ≠ 0\n⊢ (∀ (b : R),\n (b ∈\n if h : a = 0 then ∅\n else choose (_ : ∃ f, (∀ (b : R), b ∈ f → Irreducible b) ∧ Associated (Multiset.prod f) a)) →\n Irreduc... | [
286,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.get_push_eq | [
{
"state_after": "α : Type u_1\na : Array α\nx : α\n⊢ List.get (a.data ++ [x])\n { val := size a, isLt := (_ : (fun xs i => i < size xs) { data := a.data ++ [x] } (size a)) } =\n x",
"state_before": "α : Type u_1\na : Array α\nx : α\n⊢ (push a x)[size a] = x",
"tactic": "simp only [push, getElem... | [
133,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
131,
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Mathlib/Data/Matrix/Basic.lean | Matrix.neg_of | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.eq_top_iff_forall_le | [] | [
394,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.34299\na : α\ns✝ t : Multiset α\nf✝ g✝ : α → Multiset β\ns : Multiset α\nf : α → Multiset β\ng : β → Multiset γ\n⊢ bind (bind 0 f) g = bind 0 fun a => bind (f a) g",
"tactic": "simp"
},
{
"state_a... | [
174,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.forall_coe_one_iff_one | [] | [
641,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableAt_add_const_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.207343\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
216,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_bot | [] | [
357,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.mul_smul' | [
{
"state_after": "case h\nR : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf g : ArithmeticFunction R\nh : ArithmeticFunction M\nn : ℕ\n⊢ ↑((f * g) • h) n = ↑(f • g • h) n",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid... | [
334,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/Algebra/GradedMonoid.lean | List.dProd_cons | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_one | [] | [
72,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_ofBounded_iff | [
{
"state_after": "no goals",
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256,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.irreducible_iff_natDegree | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\nhp : Monic p\nhp1 : p = 1\n⊢ Irreducible p ↔ p ≠ 1 ∧ ∀ (f g : R[X]), Monic f → Monic g → f * g = p → natDegree f = 0 ∨ natDegree g = 0\n\ncase neg\nR : Type u\nS : Type ... | [
296,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | LinearMap.subtype_compMultilinearMap_codRestrict | [] | [
803,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.revOrderIso_symm_apply | [] | [
516,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_of_differentiable_iteratedFDeriv | [] | [
1666,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1663,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | isOpen_setOf_linearIndependent | [] | [
262,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_preserving_piEquivPiSubtypeProd | [] | [
753,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_countp | [] | [
2199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2198,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_left_right₀ | [
{
"state_after": "case mk\nΓ : Type u_1\ninst✝ : Inhabited Γ\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ mk' { head := head✝, left := left✝, right := right✝ }.left\n (right₀ { head := head✝, left := left✝, right := right✝ }) =\n { head := head✝, left := left✝, right := right✝ }",
"state_before": "Γ : ... | [
576,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_monomial | [] | [
367,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.Equivalent.trans | [] | [
642,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.natAbs_mod_two | [
{
"state_after": "case ofNat\na✝ : ℕ\n⊢ ↑(Int.natAbs (Int.ofNat a✝)) = ↑(Int.ofNat a✝)\n\ncase negSucc\na✝ : ℕ\n⊢ ↑(Int.natAbs (Int.negSucc a✝)) = ↑(Int.negSucc a✝)",
"state_before": "a : ℤ\n⊢ ↑(Int.natAbs a) = ↑a",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_before": "case of... | [
835,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_length_sub_one | [
{
"state_after": "ι : Type ?u.89110\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nh : length [] - 1 < length []\n⊢ False",
"state_before": "ι : Type ?u.89110\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nh : length l - 1 < length l\n⊢ l ≠ []",
"tactic": "rintro rf... | [
1363,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
] |
Mathlib/Algebra/Module/GradedModule.lean | DirectSum.Gmodule.of_smul_of | [] | [
109,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain'_apply | [] | [
1366,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.eq_of_direction_eq_of_nonempty_of_le | [] | [
661,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.count_dedup | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3980\ninst✝ : DecidableEq α\nm : Multiset α\na : α\nx✝ : List α\n⊢ List.count a (List.dedup x✝) = if a ∈ x✝ then 1 else 0",
"state_before": "α : Type u_1\nβ : Type ?u.3980\ninst✝ : DecidableEq α\nm : Multiset α\na : α\nx✝ : List α\n⊢ count a (dedup (Quot.mk Setoid... | [
93,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.subtype_image | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.60270\nγ : Type ?u.60273\nδ : Type ?u.60276\nδ' : Type ?u.60279\nι : Sort uι\ns✝ t u✝ : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\ns : Set α\nhs : MeasurableSet s\nu : Set α\nhu : MeasurableSet u\n⊢ MeasurableSet (Subtype.val '' (Subtype.v... | [
558,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | derivWithin_sinh | [] | [
901,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.append_inj_left | [] | [
505,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Computability/Ackermann.lean | ack_one | [
{
"state_after": "case zero\n\n⊢ ack 1 zero = zero + 2\n\ncase succ\nn : ℕ\nIH : ack 1 n = n + 2\n⊢ ack 1 (succ n) = succ n + 2",
"state_before": "n : ℕ\n⊢ ack 1 n = n + 2",
"tactic": "induction' n with n IH"
},
{
"state_after": "no goals",
"state_before": "case zero\n\n⊢ ack 1 zero = zero +... | [
87,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/Cover.lean | Covby.unique_right | [] | [
451,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_eq_zero_iff | [
{
"state_after": "α : Type u_1\ninst✝³ : LinearOrderedField α\nβ : Type u_2\ninst✝² : Ring β\nabv : β → α\ninst✝¹ : IsAbsoluteValue abv\ninst✝ : IsComplete β abv\nf : CauSeq β abv\nh : lim f = 0\nhf : f ≈ const abv (lim f)\n⊢ LimZero f",
"state_before": "α : Type u_1\ninst✝³ : LinearOrderedField α\nβ : Type... | [
408,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.isUnit_iff_bijective | [
{
"state_after": "no goals",
"state_before": "f✝ g f : CircleDeg1Lift\nh : Bijective ↑f\nx y : ℝ\nhxy : x ≤ y\n⊢ ↑f (↑(Equiv.ofBijective (↑f) h).symm x) ≤ ↑f (↑(Equiv.ofBijective (↑f) h).symm y)",
"tactic": "simp only [Equiv.ofBijective_apply_symm_apply f h, hxy]"
},
{
"state_after": "no goals",... | [
262,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/Category/ModuleCat/Biproducts.lean | ModuleCat.binaryProductLimitCone_cone_π_app_left | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_at_apply | [
{
"state_after": "R : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r✝ : R[X]\nx : R\nS : Type u_1\ninst✝ : Semiring S\nf : R →+* S\nr : R\n⊢ ∑ n in support p, ↑f (coeff p n) * ↑f r ^ n = ∑ x in support p, ↑f (coeff p x * r ^ x)",
"state_before": "R : Type u\nS✝ : T... | [
335,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/LinearAlgebra/Pi.lean | Submodule.biInf_comap_proj | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝² : Semiring R\nφ : ι → Type u_1\ninst✝¹ : (i : ι) → AddCommMonoid (φ i)\ninst✝ : (i : ι) → Module R (φ i)\nI : Set ι\np q : (i : ι) → Sub... | [
303,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_mul | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Order/BoundedOrder.lean | min_top_right | [] | [
851,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.oreDiv_mul_char | [] | [
264,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.memℓp_of_tendsto | [
{
"state_after": "case intro.intro\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_3\nl : Filter ι\ninst✝ : NeBot l\n_i : Fact (1 ≤ p)\nF : ι → { x // x ∈ lp E p }\nhF : Metric.Bounded (Set.range F)\nf : (a : α) → E a\nhf : Tendsto (id fun i => ↑(F i)) l (𝓝 ... | [
1185,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/Init/Algebra/Order.lean | compare_eq_iff_eq | [
{
"state_after": "α : Type u\ninst✝ : LinearOrder α\na b : α\n⊢ (if a < b then Ordering.lt else if a = b then Ordering.eq else Ordering.gt) = Ordering.eq ↔ a = b",
"state_before": "α : Type u\ninst✝ : LinearOrder α\na b : α\n⊢ compare a b = Ordering.eq ↔ a = b",
"tactic": "rw [LinearOrder.compare_eq_com... | [
440,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_subset_Ioi | [] | [
602,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/LinearAlgebra/Ray.lean | eq_zero_of_sameRay_self_neg | [
{
"state_after": "R : Type u_1\ninst✝⁵ : StrictOrderedCommRing R\nM : Type u_2\nN : Type ?u.156166\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nx y : M\ninst✝ : NoZeroSMulDivisors R M\nh : SameRay R x (-x)\n✝ : Nontrivial M\n⊢ x = 0",
"state_before": "R : Type... | [
423,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_eq_left_of_subset_of_measure_add_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.136128\nγ : Type ?u.136131\nδ : Type ?u.136134\nι : Type ?u.136137\nR : Type ?u.136140\nR' : Type ?u.136143\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t : Set α\nh : ↑↑(μ + ν) t ≠ ⊤\nh'... | [
925,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_iUnion | [] | [
1193,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
1
] |
Mathlib/Order/WellFounded.lean | WellFounded.not_lt_min | [] | [
74,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | image_smul_set | [] | [
388,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_comp | [
{
"state_after": "ι : Type ?u.722181\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq γ\nf : γ → β\ng : α → γ\n⊢ ∀ (a : α), a ∈ s → (∃ a_1, a_1 ∈ s ∧ g a_1 = g a) ∧ a ∈ s",
"state_before": "ι : Type ?u.722181\nβ : Type u\nα : Type v\nγ... | [
1532,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1518,
1
] |
Std/Data/List/Lemmas.lean | List.mem_bind_of_mem | [] | [
200,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
199,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_finsupp_sum | [] | [
277,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
11
] |
Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.pd_inv | [
{
"state_after": "n : Type ?u.121810\np : Type ?u.121813\nq : Type ?u.121816\nl : Type u_1\nR : Type u₂\ninst✝⁸ : DecidableEq n\ninst✝⁷ : DecidableEq p\ninst✝⁶ : DecidableEq q\ninst✝⁵ : DecidableEq l\ninst✝⁴ : CommRing R\ninst✝³ : Fintype p\ninst✝² : Fintype q\ninst✝¹ : Fintype l\ninst✝ : Invertible 2\n⊢ fromBl... | [
285,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/ODE/Gronwall.lean | dist_le_of_trajectories_ODE_of_mem_set | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.46221\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nv : ℝ → E → E\ns : ℝ → Set E\nK : ℝ\nhv : ∀ (t : ℝ) (x : E), x ∈ s t → ∀ (y : E), y ∈ s t → dist (v t x) (v t y) ≤ K * dist x y\nf g : ℝ → E\na b δ ... | [
214,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.card_support_eq_one' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.135476\nγ : Type ?u.135479\nι : Type ?u.135482\nM : Type u_2\nM' : Type ?u.135488\nN : Type ?u.135491\nP : Type ?u.135494\nG : Type ?u.135497\nH : Type ?u.135500\nR : Type ?u.135503\nS : Type ?u.135506\ninst✝ : Zero M\na a' : α\nb : M\n... | [
490,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_map | [
{
"state_after": "ι : Type ?u.273965\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\ne : α ↪ γ\nf : γ → β\n⊢ Multiset.prod (Multiset.map ((fun x => f x) ∘ ↑e) s.val) = ∏ x in s, f (↑e x)",
"state_before": "ι : Type ?u.273965\nβ : Type u\nα :... | [
374,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mk'_X_1 | [] | [
1043,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
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