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/Topology/SubsetProperties.lean | isClopen_range_sigmaMk | [] | [
1652,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1650,
1
] |
src/lean/Init/Data/Range.lean | Membership.mem.upper | [
{
"state_after": "i : Nat\nr : Std.Range\nh : r.start ≤ i ∧ i < r.stop\n⊢ i < r.stop",
"state_before": "i : Nat\nr : Std.Range\nh : i ∈ r\n⊢ i < r.stop",
"tactic": "simp [Membership.mem] at h"
},
{
"state_after": "no goals",
"state_before": "i : Nat\nr : Std.Range\nh : r.start ≤ i ∧ i < r.st... | [
81,
12
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
79,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.mul_right' | [
{
"state_after": "m n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ c * a ≡ c * b [ZMOD c * n]",
"state_before": "m n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ a * c ≡ b * c [ZMOD n * c]",
"tactic": "rw [mul_comm a, mul_comm b, mul_comm n]"
},
{
"state_after": "no goals",
"state_before": "m n a b c d : ℤ\nh :... | [
140,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.le_span | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.310827\nR : Type u\ninst✝³ : Ring R\ninst✝² : RankCondition R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nJ : Set M\nv : Basis ι R M\nhJ : span R J = ⊤\nthis... | [
644,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.lt_tsub_iff_right | [] | [
435,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
11
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_def | [] | [
66,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.eq_zero_of_image_eq_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasImage f\nw : image.ι f = 0\n⊢ f = 0",
"tactic": "rw [← image.fac f, w, HasZeroMorphisms.comp_zero]"
}
] | [
151,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSet_iff_measure_inter_eq_mul | [] | [
611,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.coe_support | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ ↑(support p) = {u} + ↑(List.tail (support p))",
"tactic": "cases p <;> rfl"
}
] | [
629,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | exists_eq_pow_of_mul_eq_pow_of_coprime | [
{
"state_after": "M : Type ?u.9200\ninst✝⁵ : CancelMonoidWithZero M\ninst✝⁴ : Finite M\nR : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : IsDomain R\ninst✝¹ : GCDMonoid R\ninst✝ : Unique Rˣ\na b c : R\nn : ℕ\ncp : IsCoprime a b\nh : a * b = c ^ n\n⊢ GCDMonoid.gcd a b ∣ 1",
"state_before": "M : Type ?u.9200\ni... | [
71,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.Pairwise.insert | [] | [
168,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.eqOn_closure_span | [] | [
538,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.induction_on_coprime | [
{
"state_after": "α : Type u_1\nR : Type ?u.1571585\ninst✝⁴ : CancelCommMonoidWithZero R\ninst✝³ : UniqueFactorizationMonoid R\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : UniqueFactorizationMonoid α\nβ : Type ?u.1571612\ninst✝ : CancelCommMonoidWithZero β\nP : α → Prop\na : α\nh0 : P 0\nh1 : ∀ {x : α}, IsUni... | [
1112,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_cons | [] | [
918,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_injective' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.3918\nδ : Type ?u.3921\nf g : α → β\nh : Option.map f = Option.map g\nx : α\n⊢ some (f x) = some (g x)",
"tactic": "simp only [← map_some', h]"
}
] | [
118,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_Ioc_right | [] | [
270,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Basis.coe_toOrthonormalBasis_repr | [] | [
502,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_bihimp_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.82995\nα : Type u_1\nβ : Type ?u.83001\nπ : ι → Type ?u.83006\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ⇔ b ⇔ a = b",
"tactic": "rw [bihimp_comm, bihimp_bihimp_cancel_left]"
}
] | [
653,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basis.lean | Basis.ext_multilinear_fin | [
{
"state_after": "case zero\nR : Type u_1\nι : Type ?u.528\nn : ℕ\nM✝ : Fin n → Type u_2\nM₂ : Type u_3\nM₃ : Type ?u.541\ninst✝⁸ : CommSemiring R\ninst✝⁷ : AddCommMonoid M₂\ninst✝⁶ : AddCommMonoid M₃\ninst✝⁵ : (i : Fin n) → AddCommMonoid (M✝ i)\ninst✝⁴ : (i : Fin n) → Module R (M✝ i)\ninst✝³ : Module R M₂\nins... | [
57,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.comp_inf'_eq_inf'_comp | [] | [
961,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_mem_factors | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\nx : α\nhx : x ≠ 0\nh : ¬IsUnit x\np' : α\nhp' : Irreducible p'\nhp'x : p' ∣ x\n⊢ ∃ p, p ∈ factors x",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWi... | [
506,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.im_eq_complex_im | [] | [
434,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.of_P | [
{
"state_after": "case h\nC : Type u_1\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\nj : Fin (n + 1)\nhj₁ : n + 1 ≤ ↑j + 0\n⊢ False",
"state_before": "C : Type u_1\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\nj : Fin (n + 1)\nhj₁ : n + 1 ≤ ↑j + 0\... | [
118,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_of_shell | [] | [
233,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.coe_toGL | [] | [
178,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean | PrimeSpectrum.iInf_localization_eq_bot | [
{
"state_after": "case h\nR : Type u\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\nK : Type v\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nx : K\n⊢ (x ∈\n ⨅ (v : PrimeSpectrum R),\n Localization.subalgebra.ofField K (Ideal.primeCompl v.asIdeal)\n (_ : Ideal.primeCompl v... | [
143,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_comap | [] | [
580,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_const_mul_pow_nhds_iff' | [
{
"state_after": "case inl\n𝕜 : Type u_1\nα : Type ?u.36297\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nc d : 𝕜\n⊢ Tendsto (fun x => c * x ^ 0) atTop (𝓝 d) ↔ (c = 0 ∨ 0 = 0) ∧ c = d\n\ncase inr\n𝕜 : Type u_1\nα : Type ?u.36297\ninst✝² ... | [
185,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.pow_subset_pow | [] | [
692,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.denseInducing | [] | [
118,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumProdDistrib_apply_right | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_nil | [] | [
756,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_mul_zero | [
{
"state_after": "a : Ordinal\n⊢ ∀ (n : ℕ), ((fun x => a * x)^[n]) 0 ≤ 0",
"state_before": "a : Ordinal\n⊢ nfp (fun x => a * x) 0 = 0",
"tactic": "rw [← Ordinal.le_zero, nfp_le_iff]"
},
{
"state_after": "a : Ordinal\nn : ℕ\n⊢ ((fun x => a * x)^[n]) 0 ≤ 0",
"state_before": "a : Ordinal\n⊢ ∀ (... | [
633,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.mk_toList | [] | [
86,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Tactic/IrreducibleDef.lean | Lean.Elab.Command.$n_def | [] | [
110,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
39
] |
Mathlib/RingTheory/Int/Basic.lean | Int.Prime.dvd_mul | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\np : ℕ\nhp : Nat.Prime p\nh : ↑p ∣ m * n\n⊢ p ∣ natAbs m ∨ p ∣ natAbs n",
"tactic": "rwa [← hp.dvd_mul, ← Int.natAbs_mul, ←Int.coe_nat_dvd_left]"
}
] | [
272,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.lift_of_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\nX : Type v\ninst✝² : CommRing R\nL : Type w\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nf : X → L\nx : X\n⊢ ↑(↑(lift R) f) (of R x) = f x",
"tactic": "rw [← @Function.comp_apply _ _ _ (lift R f) (of R) x, of_comp_lift]"
}
] | [
261,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasurableEquiv.memℒp_map_measure_iff | [] | [
948,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_comp_le_left | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1108176\ninst✝⁸ : Ring K\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module K V\ninst✝⁵ : AddCommGroup V₁\ninst✝⁴ : Module K V₁\ninst✝³ : AddCommGroup V'\ninst✝² : Module K V'\nins... | [
1336,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_eq_blsub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.349286\nβ : Type ?u.349289\nγ : Type ?u.349292\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nr r' : ι → ι → Prop\ninst✝¹ : IsWellOrder ι r\ninst✝ : IsWellOrder ι r'\nf : ι → Ordinal\n⊢ blsub (type r) (bfamilyOfFamily' r f) = bls... | [
1788,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_ofFunction | [
{
"state_after": "α : Type u_2\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\nβ : Type u_1\nf : α → β\nhf : Injective f\ns : Set β\n⊢ ↑(OuterMeasure.ofFunction (fun s => m (f ⁻¹' s)) m_empty) s ≤ ↑(↑(map f) (OuterMeasure.ofFunction m m_empty)) s",
"state_before": "α : Type u_2\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\nβ... | [
809,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_comap | [] | [
2054,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2054,
9
] |
Mathlib/Data/Nat/Size.lean | Nat.size_eq_zero | [
{
"state_after": "n : ℕ\nthis : 0 < size n ↔ 0 < n\n⊢ size n = 0 ↔ n = 0",
"state_before": "n : ℕ\n⊢ size n = 0 ↔ n = 0",
"tactic": "have := @size_pos n"
},
{
"state_after": "n : ℕ\nthis : ¬size n = 0 ↔ ¬n = 0\n⊢ size n = 0 ↔ n = 0",
"state_before": "n : ℕ\nthis : 0 < size n ↔ 0 < n\n⊢ size ... | [
166,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_coe_def | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np : K[X]\nq : { x // x ∈ K[X]⁰ }\n⊢ RatFunc.mk p ↑q = { toFractionRing := IsLocalization.mk' (FractionRing K[X]) p q }",
"tactic": "simp only [mk_eq_div', ← Localization.mk_eq_mk', FractionRing.mk_eq_div]"... | [
210,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node4L_lemma₃ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.284064\ninst✝ : Preorder α\nb c d : ℕ\nmr₁ : 2 * d ≤ b + c + 1\nmm₁ : b ≤ 3 * c\n⊢ d ≤ 3 * c",
"tactic": "linarith"
}
] | [
1150,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.mem_factors'_of_dvd | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na p : α\nha0 : a ≠ 0\nhp : Irreducible p\nhd : p ∣ a\nq : α\nhq : q ∈ Uniq... | [
1609,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | zpow_bit1₀ | [
{
"state_after": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nn : ℤ\n⊢ a ≠ 0 ∨ bit0 n + 1 ≠ 0 ∨ bit0 n = 0 ∧ 1 = 0",
"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nn : ℤ\n⊢ a ^ bit1 n = a ^ n * a ^ n * a",
"tactic": "rw [← zpow_bit0, bit1, zpow_add', zpow_one]"
},
{
"stat... | [
151,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/LiminfLimsup.lean | GaloisConnection.l_limsup_le | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Type ?u.205644\ninst✝¹ : ConditionallyCompleteLattice β\ninst✝ : ConditionallyCompleteLattice γ\nf : Filter α\nv : α → β\nl : β → γ\nu : γ → β\ngc : GaloisConnection l u\nhlv : autoParam (IsBoundedUnder (fun x x_1 => x ≤ x_1) f fun x => l (v x)) _a... | [
1214,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.Prepartition.forall_biUnionTagged | [
{
"state_after": "ι : Type u_1\nI J : Box ι\np : (ι → ℝ) → Box ι → Prop\nπ : Prepartition I\nπi : (J : Box ι) → TaggedPrepartition J\n⊢ (∀ (J : Box ι), (∃ J', J' ∈ π ∧ J ∈ πi J') → p (TaggedPrepartition.tag (biUnionTagged π πi) J) J) ↔\n ∀ (J : Box ι), J ∈ π → ∀ (J' : Box ι), J' ∈ πi J → p (TaggedPrepartitio... | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.comp_apply | [] | [
653,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.one_neBot | [] | [
110,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_le_of_trailingDegree_le | [
{
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"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nhp : p ≠ 0\nH : ↑n ≤ trailingDeg... | [
189,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_nNReal | [] | [
274,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | Submodule.le_orthogonalBilin_orthogonalBilin | [] | [
349,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.has_smallest_coproducts_of_hasCoproducts | [] | [
304,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_Lp | [] | [
363,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasCoequalizer_of_hasCokernel | [] | [
424,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.equicontinuousAt_of_continuity_modulus | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nι✝ : Type ?u.3074\ninst✝¹ : PseudoMetricSpace α\nι : Type u_1\ninst✝ : TopologicalSpace β\nx₀ : β\nb : β → ℝ\nb_lim : Tendsto b (𝓝 x₀) (𝓝 0)\nF : ι → β → α\nH : ∀ᶠ (x : β) in 𝓝 x₀, ∀ (i : ι), dist (F i x₀) (F i x) ≤ b x\n⊢ ∀ (ε : ℝ), ε > 0 → ∀ᶠ (x : β) in 𝓝 x₀, ... | [
100,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.coe_indicatorConst | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.congr' | [] | [
889,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_nonempty_iff | [] | [
321,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.comp | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
697,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.measurable | [] | [
1188,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
11
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.map_smul_univ | [] | [
472,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.radical_minimalPrimes | [
{
"state_after": "R : Type u_1\nS : Type ?u.3948\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI J : Ideal R\n⊢ minimals (fun x x_1 => x ≤ x_1) {p | IsPrime p ∧ radical I ≤ p} =\n minimals (fun x x_1 => x ≤ x_1) {p | IsPrime p ∧ I ≤ p}",
"state_before": "R : Type u_1\nS : Type ?u.3948\ninst✝¹ : CommRing R\ni... | [
85,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Std/Data/String/Lemmas.lean | String.extract_cons_addChar | [
{
"state_after": "c : Char\ncs : List Char\nb e : Pos\n⊢ (if e.byteIdx ≤ b.byteIdx then \"\" else { data := extract.go₁ (c :: cs) 0 (b + c) (e + c) }) =\n if b.byteIdx ≥ e.byteIdx then \"\" else { data := extract.go₁ cs 0 b e }",
"state_before": "c : Char\ncs : List Char\nb e : Pos\n⊢ extract { data := c... | [
436,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
433,
1
] |
Std/Data/List/Lemmas.lean | List.filterMap_append | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\nl' : List α\nf : α → Option β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : filterMap f (tail✝ ++ l') = filterMap f tail✝ ++ filterMap f l'\n⊢ (match f head✝ with\n | none => filterMap f (tail✝ ++ l')\n | some b => b :: filterMap f (tail✝ ++ l')) =\n (m... | [
1164,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1162,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.factorial_mul_factorial_dvd_factorial | [
{
"state_after": "n k : ℕ\nhk : k ≤ n\n⊢ k ! * (n - k)! ∣ choose n k * (k ! * (n - k)!)",
"state_before": "n k : ℕ\nhk : k ≤ n\n⊢ k ! * (n - k)! ∣ n !",
"tactic": "rw [← choose_mul_factorial_mul_factorial hk, mul_assoc]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\nhk : k ≤ n\n⊢... | [
185,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Iic | [] | [
139,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/Constructions.lean | IsClosed.closedEmbedding_subtype_val | [] | [
1038,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
8
] |
Mathlib/RingTheory/Localization/AtPrime.lean | Localization.localRingHom_comp | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.339407\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS✝ : Type ?u.339596\ninst✝³ : CommSemiring S✝\ninst✝² : Algebra R S✝\nP : Type ?u.339776\ninst✝¹ : CommSemiring P\nI : Ideal R\nhI : Ideal.IsPrime I\nS : Type ?u.339916\ninst✝ : CommSemiring S\nJ : Id... | [
266,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_ennreal | [] | [
48,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_injective | [] | [
240,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.leftInvOn_of_rightInvOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.62981\nι : Sort ?u.62984\nπ : α → Type ?u.62989\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nhf : SurjOn f s t\nhf' : RightInvOn f f' s\ny : β\nhy : y ∈ t\nx : α\nhx : x ... | [
1161,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1158,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_ne_zero_of_pos_of_ne_one | [] | [
240,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pf_add_overlap | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ b₁ a₂ b₂ : R\n⊢ a₁ + a₂ + (b₁ + b₂) = a₁ + b₁ + (a₂ + b₂)",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ b₁ c₁ a₂ b₂ c₂ ... | [
315,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Topology/Basic.lean | mapClusterPt_iff | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nι : Type u_1\nx : α\nF : Filter ι\nu : ι → α\n⊢ (∀ {p : α → Prop}, (∀ᶠ (x : α) in 𝓝 x, p x) → ∃ᶠ (a : ι) in F, p (u a)) ↔\n ∀ (s : Set α), s ∈ 𝓝 x → ∃ᶠ (a : ι) in F, u a ∈ s",
... | [
1153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Std/Logic.lean | forall_and | [] | [
424,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
423,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod | [
{
"state_after": "case nil\nn : Type u_1\np : Type u_2\nR : Type u₂\n𝕜 : Type ?u.68668\ninst✝⁵ : Field 𝕜\ninst✝⁴ : DecidableEq n\ninst✝³ : DecidableEq p\ninst✝² : CommRing R\ni j : n\ninst✝¹ : Fintype n\ninst✝ : Fintype p\nM✝ : Matrix n n R\nN✝ : Matrix p p R\nM : Matrix n n R\nN : Matrix p p R\n⊢ fromBlocks ... | [
283,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback_symmetry_hom_of_epi_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶ Y\ninst✝ : Epi f\n⊢ (pushoutSymmetry f f).hom = 𝟙 (pushout f f)",
"tactic": "ext <;> simp [inl_eq_inr_of_epi_eq]"
}
] | [
1972,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1971,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_C | [] | [
114,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.move_right_mk' | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nL R : ListBlank Γ\n⊢ move Dir.right (mk' L R) = mk' (ListBlank.cons (ListBlank.head R) L) (ListBlank.tail R)",
"tactic": "simp only [Tape.move, Tape.mk', ListBlank.head_cons, eq_self_iff_true, ListBlank.cons_head_tail,\n a... | [
594,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_add_adjacent_intervals | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.15374404\n𝕜 : Type ?u.15374407\nE : Type u_1\nF : Type ?u.15374413\nA : Type ?u.15374416\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nhab : IntervalIntegrab... | [
905,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Init/Function.lean | Function.LeftInverse.injective | [] | [
99,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_mul | [
{
"state_after": "case h.e'_4\nF : Type u\nK : Type v\nL : Type w\ninst✝² : CommRing K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nf g : K[X]\nhf : Splits i f\nhg : Splits i g\nh : ¬map i (f * g) = 0\np : L[X]\nhp : Irreducible p\nhpf : p ∣ map i (f * g)\n⊢ map i f * map i g = map i (f * g)",
"state_be... | [
121,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.antitone | [] | [
182,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.out_injective | [] | [
264,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.analyticAt | [] | [
424,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_eq_iff_sq_eq | [] | [
64,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.coe_ofIsClosedGraph | [
{
"state_after": "case h\n𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\ng : E →ₗ[𝕜] F\nhg : Is... | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Logic/Relation.lean | Equivalence.comap | [] | [
117,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_subset_div_left | [] | [
644,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolRing_inj | [] | [
424,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_eq_toIocMod | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\nh : toIocMod hp a b = toIocMod hp a c\n⊢ c - b = (toIocDiv hp a c - toIocDiv hp a b) • p\n\ncase refine'_2\nα : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archim... | [
583,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.sMod_lt | [
{
"state_after": "p : ℕ\nw : 0 < p\ni : ℕ\n⊢ sMod p i % (2 ^ p - 1) < 2 ^ p - 1",
"state_before": "p : ℕ\nw : 0 < p\ni : ℕ\n⊢ sMod p i < 2 ^ p - 1",
"tactic": "rw [← sMod_mod]"
},
{
"state_after": "p : ℕ\nw : 0 < p\ni : ℕ\n⊢ abs (2 ^ p - 1) = 2 ^ p - 1",
"state_before": "p : ℕ\nw : 0 < p\ni ... | [
120,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_subtype | [] | [
1202,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/Data/Real/Sign.lean | Real.inv_sign | [
{
"state_after": "case inl\nr : ℝ\nhn : sign r = -1\n⊢ (sign r)⁻¹ = sign r\n\ncase inr.inl\nr : ℝ\nhz : sign r = 0\n⊢ (sign r)⁻¹ = sign r\n\ncase inr.inr\nr : ℝ\nhp : sign r = 1\n⊢ (sign r)⁻¹ = sign r",
"state_before": "r : ℝ\n⊢ (sign r)⁻¹ = sign r",
"tactic": "obtain hn | hz | hp := sign_apply_eq r"
... | [
115,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.ext | [] | [
181,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/Basic.lean | isClosed_iff_clusterPt | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ closure s ⊆ s ↔ ∀ (a : α), ClusterPt a (𝓟 s) → a ∈ s",
"tactic": "simp only [subset_def, mem_closure_iff_clusterPt]"
}
] | [
1368,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mk_d_2_0 | [
{
"state_after": "ι : Type ?u.184152\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nX₀ X₁ X₂ : V\nd₀ : X₁ ⟶ X₀\nd₁ : X₂ ⟶ X₁\ns : d₁ ≫ d₀ = 0\nsucc :\n (t : (X₀ : V) ×' (X₁ : V) ×' (X₂ : V) ×' (d₀ : X₁ ⟶ X₀) ×' (d₁ : X₂ ⟶ X₁) ×' d₁ ≫ d₀ = 0) →\n (X₃ : V) ×' (d₂ : X₃ ⟶ t.snd.snd.fst) ×' d₂ ≫ t... | [
744,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
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