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/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.repr_reindex | [
{
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | multiplicity_eq_multiplicity_span | [
{
"state_after": "case pos\nR : Type u_1\nA : Type ?u.1353425\nK : Type ?u.1353428\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : Field K\ninst✝⁴ : IsDomain A\ninst✝³ : IsDomain R\ninst✝² : IsPrincipalIdealRing R\ninst✝¹ : DecidableRel fun x x_1 => x ∣ x_1\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : ... | [
1453,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1437,
1
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Mathlib/Data/Finset/Card.lean | Finset.exists_subset_or_subset_of_two_mul_lt_card | [
{
"state_after": "α : Type u_1\nβ : Type ?u.45753\ns t : Finset α\nf : α → β\nn✝ : ℕ\ninst✝ : DecidableEq α\nX Y : Finset α\nn : ℕ\nhXY : 2 * n < card (X ∪ Y)\nh₁ : card (X ∩ (Y \\ X)) = 0\n⊢ ∃ C, n < card C ∧ (C ⊆ X ∨ C ⊆ Y)",
"state_before": "α : Type u_1\nβ : Type ?u.45753\ns t : Finset α\nf : α → β\nn✝ ... | [
504,
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496,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_neg | [
{
"state_after": "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⊢ -b - -(toIcoDiv hp (-a) b • p + 1 • p) = p - (b - toIcoDiv hp (-a) b • p)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α... | [
559,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.range_coprod | [
{
"state_after": "no goals",
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444,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Algebra/GroupPower/Order.lean | pow_add_pow_le | [
{
"state_after": "case intro\nβ : Type ?u.204204\nA : Type ?u.204207\nG : Type ?u.204210\nM : Type ?u.204213\nR : Type u_1\ninst✝ : OrderedSemiring R\na x y : R\nm : ℕ\nhx : 0 ≤ x\nhy : 0 ≤ y\nk : ℕ\nhn : Nat.succ k ≠ 0\n⊢ x ^ Nat.succ k + y ^ Nat.succ k ≤ (x + y) ^ Nat.succ k",
"state_before": "β : Type ?u... | [
421,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEmbedding.comap_preimage | [] | [
4221,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4218,
11
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Mathlib/Order/Cover.lean | wcovby_congr_left | [] | [
88,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_geom_sum | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R✝\nm n✝ : ℕ\ninst✝² : CommSemiring R✝\np q : R✝[X]\nx✝ : R✝\ninst✝¹ : CommSemiring S\nf : R✝ →+* S\nR : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\nx : R\n⊢ eval x (∑ i in range n, X ^ i) = ∑ i in range n, x ^... | [
1166,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
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Mathlib/Algebra/Algebra/Prod.lean | AlgHom.coe_prod | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mem_carrier | [] | [
87,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Finset.measurableSet_biInter | [] | [
179,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ c✝ d a b c : α\n⊢ filter (fun x => c ≤ x) (Ico a b) = Ico (max a c) b",
"tactic": "rw [Ico, Ico, ← Finset.filter_val, Finset.Ico_filter_le]"
}
] | [
270,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
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Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : Preadditive C\nn : ℕ\n⊢ πSummand s (IndexSet.id [n].op) ≫ ιSummand s (IndexSet.id [n].op) ≫ HomologicalComplex.Hom.f PInfty n =\n 𝟙 (HomologicalComplex.X K[X] n) ≫ Homologica... | [
149,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Algebra/FreeMonoid/Count.lean | FreeMonoid.count_of | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidableEq α\nx y : α\n⊢ ↑(count x) (of y) = Pi.mulSingle x (↑Multiplicative.ofAdd 1) y",
"tactic": "simp [count, countp_of, Pi.mulSingle_apply, eq_comm, Bool.beq_eq_decide_eq]"
}
] | [
90,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Algebra/Order/Sub/Defs.lean | tsub_tsub_le_tsub_add | [] | [
172,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_comap | [] | [
278,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Order/Filter/Extr.lean | IsMaxOn.inter | [] | [
301,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.coe_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.67774\nR : Type ?u.67777\nR' : Type ?u.67780\nms : Set (OuterMeasure α)\nm : OuterMeasure α\nι : Sort u_1\nf : ι → OuterMeasure α\ns : Set α\n⊢ ↑(⨆ (i : ι), f i) s = iSup (fun i => ↑(f i)) s",
"tactic": "simp"
}
] | [
424,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Order/Basic.lean | LE.le.lt_iff_ne | [] | [
260,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Logic/Equiv/Fintype.lean | Equiv.Perm.viaFintypeEmbedding_sign | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : Fintype α\ninst✝² : DecidableEq β\ne : Perm α\nf : α ↪ β\ninst✝¹ : DecidableEq α\ninst✝ : Fintype β\n⊢ ↑sign (viaFintypeEmbedding e f) = ↑sign e",
"tactic": "simp [Equiv.Perm.viaFintypeEmbedding]"
}
] | [
95,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.dual_comp | [] | [
733,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right | [] | [
860,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
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Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_of_is_kernel | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nh : IsLimit (KernelFork.ofι f w)\n⊢ kernel.ι g ≫ cokernel.π f = 0",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nh :... | [
239,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Biprod.ofComponents_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nX₁ X₂ Y₁ Y₂ : C\nf₁₁ : X₁ ⟶ Y₁\nf₁₂ : X₁ ⟶ Y₂\nf₂₁ : X₂ ⟶ Y₁\nf₂₂ : X₂ ⟶ Y₂\nf : X₁ ⊞ X₂ ⟶ Y₁ ⊞ Y₂\n⊢ ofComponents (biprod.inl ≫ f ≫ biprod.fst) (biprod.inl ≫ f ≫ biprod.snd)... | [
711,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.mul_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h σ τ : Perm α\nhστ : Disjoint σ τ\n⊢ σ * τ = 1 ↔ σ = 1 ∧ τ = 1",
"tactic": "simp_rw [ext_iff, one_apply, hστ.mul_apply_eq_iff, forall_and]"
}
] | [
188,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.continuousOn | [] | [
872,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
11
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.valuation_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ (if h : const (padicNorm p) 1 ≈ 0 then (fun hf => 0) h\n else (fun hf => padicValRat p (↑(const (padicNorm p) 1) (PadicSeq.stationaryPoint hf))) h) =\n 0",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ valuation 1 = 0",
"tactic": "change dit... | [
1049,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Topology/Separation.lean | insert_mem_nhdsWithin_of_subset_insert | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\nx : α\ns t : Set α\nhu : t ⊆ insert x s\n⊢ insert x s ∈ 𝓝[t] x\n\ncase inr\nα : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\nx y : α\ns t : Set α\nhu : t ⊆ insert y s\nh : x ≠ y\n⊢ insert ... | [
663,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.VectorsProdEqOne.rotate_zero | [] | [
443,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_arrow' | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝ : HasKernel f\n⊢ (kernelSubobjectIso f).inv ≫ arrow (kernelSubobject f) = kernel.ι f",
"tactic": "simp [kernelSubobjectIso]"
}
] | [
109,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Data/Set/Image.lean | Subtype.image_preimage_coe | [] | [
1432,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.trans | [
{
"state_after": "case H\nε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // ¬p a }\nx : ε\n⊢ ↑((subtypeCongr ep en).trans (subtypeCongr ep' en')) x = ↑(subtypeCongr (ep.trans ep') (en.trans en')) x",
"state_before": "ε : Type u_1\np : ε → Prop\ninst✝ : Dec... | [
610,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.isBigO_id | [] | [
191,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.BlankExtends.above_of_le | [
{
"state_after": "case intro.intro\nΓ : Type u_1\ninst✝ : Inhabited Γ\nl₁ l₂ : List Γ\ni j : ℕ\ne : l₁ ++ List.replicate i default = l₂ ++ List.replicate j default\nh : List.length l₁ ≤ List.length l₂\n⊢ BlankExtends l₁ l₂",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nl l₁ l₂ : List Γ\n⊢ BlankExtend... | [
115,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Order/Bounds/Basic.lean | bddAbove_iff_exists_ge | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\na b : α\ninst✝ : SemilatticeSup γ\ns : Set γ\nx₀ : γ\n⊢ Monotone fun x => ∀ (y : γ), y ∈ s → y ≤ x",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\... | [
486,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Topology/Basic.lean | tendsto_atBot_of_eventually_const | [] | [
1047,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.map_le_iff_le_comap | [] | [
532,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.zipWith_apply | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.is_lub_mem | [] | [
1733,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
1
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Std/Classes/Order.lean | Std.OrientedCmp.cmp_refl | [] | [
41,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
37,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_ofEquiv | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_left_iff | [] | [
150,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.mem_factors_iff_dvd | [
{
"state_after": "case mp\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\n⊢ Associates.mk p ∈ factors (Associates.m... | [
1633,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_eq_span_vsub_set_right_ne | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.271589\ns : Set P\np : P\nhp : p ∈ s\n⊢ Submodule.span k (insert (p -ᵥ p) ((fun x => x -ᵥ p) '' (s \\ {p}))) =\n Submodule.span k ((fun x => x -ᵥ p) ... | [
1069,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.eq_of_perm_factors | [
{
"state_after": "no goals",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\nh : factors a ~ factors b\n⊢ a = b",
"tactic": "simpa [prod_factors ha, prod_factors hb] using List.Perm.prod_eq h"
}
] | [
138,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_nonneg_of_forall_set_integral_nonneg | [
{
"state_after": "case intro.intro\nα : Type u_1\nE : Type ?u.77645\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf : α → ℝ\nhf : Integrable f\nhf_zero : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → 0 ≤ ∫ (x : α... | [
294,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym_filterNe_mem | [] | [
237,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.symm_trans | [] | [
1098,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_nonempty | [] | [
375,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_mul_X_pow | [
{
"state_after": "case h₀\nR : Type u_1\ninst✝ : Semiring R\np : PowerSeries R\nn d : ℕ\n⊢ ∀ (b : ℕ × ℕ), b ∈ Finset.Nat.antidiagonal (d + n) → b ≠ (d, n) → ↑(coeff R b.fst) p * ↑(coeff R b.snd) (X ^ n) = 0\n\ncase h₁\nR : Type u_1\ninst✝ : Semiring R\np : PowerSeries R\nn d : ℕ\n⊢ ¬(d, n) ∈ Finset.Nat.antidiag... | [
1595,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/Data/Ordmap/Ordnode.lean | Ordnode.size_nil | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/CategoryTheory/Preadditive/Generator.lean | CategoryTheory.Preadditive.isSeparator_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nG : C\nhG : IsSeparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : G ⟶ X), h ≫ f = 0\n⊢ ∀ (h : G ⟶ X), h ≫ f = h ≫ 0",
"tactic": "simpa only [Limits.comp_zero] using hf"
},
{
"state_after": "no goals",
... | [
47,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.comap_lt_comap_of_integral_mem_sdiff | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝² : CommRing R\nS : Type u_2\ninst✝¹ : CommRing S\nf : R →+* S\nI J : Ideal S\ninst✝ : Algebra R S\nhI : IsPrime I\nhIJ : I ≤ J\nx : S\nmem : x ∈ ↑J \\ ↑I\np : R[X]\np_monic : Monic p\nhpx : eval₂ (algebraMap R S) x p = 0\n⊢ comap (algebraMap R S) I < comap... | [
250,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_smul | [] | [
1058,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.mod_pow_succ | [
{
"state_after": "case pos\nb w m : ℕ\nb_h : b = 0\n⊢ m % b ^ succ w = b * (m / b % b ^ w) + m % b\n\ncase neg\nb w m : ℕ\nb_h : ¬b = 0\n⊢ m % b ^ succ w = b * (m / b % b ^ w) + m % b",
"state_before": "b w m : ℕ\n⊢ m % b ^ succ w = b * (m / b % b ^ w) + m % b",
"tactic": "by_cases b_h : b = 0"
},
{... | [
194,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.injective_module_of_injective_object | [
{
"state_after": "R : Type u\ninst✝³ : Ring R\nQ : TypeMax\ninst✝² : AddCommGroup Q\ninst✝¹ : Module R Q\ninst✝ : CategoryTheory.Injective (ModuleCat.mk Q)\nX Y : TypeMax\nins1 : AddCommGroup X\nins2 : AddCommGroup Y\nins3 : Module R X\nins4 : Module R Y\nf : X →ₗ[R] Y\nhf : Function.Injective ↑f\ng : X →ₗ[R] Q... | [
82,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Real.deriv_exp | [] | [
204,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.Connected.dist_triangle | [
{
"state_after": "case intro\nV : Type u_1\nG : SimpleGraph V\nhconn : Connected G\nu v w : V\np : Walk G u v\nhp : Walk.length p = dist G u v\n⊢ dist G u w ≤ dist G u v + dist G v w",
"state_before": "V : Type u_1\nG : SimpleGraph V\nhconn : Connected G\nu v w : V\n⊢ dist G u w ≤ dist G u v + dist G v w",
... | [
113,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
11
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | IsUnit.det_zpow | [
{
"state_after": "case ofNat\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nh : IsUnit (det A)\nn : ℕ\n⊢ IsUnit (det (A ^ ofNat n))\n\ncase negSucc\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nh : I... | [
126,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/List/Perm.lean | List.bind_append_perm | [
{
"state_after": "case cons\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\nf g : α → List β\na : α\nl : List α\nIH : List.bind l f ++ List.bind l g ~ List.bind l fun x => f x ++ g x\n⊢ f a ++ (List.bind l f ++ (g a ++ List.bind l g)) ~ f a ++ (g a ++ List.bind l fun x => f x ++ g x)",
"state_before": "α : Type ... | [
1098,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Std/Data/Int/Lemmas.lean | Int.self_le_toNat | [
{
"state_after": "a : Int\n⊢ a ≤ max a 0",
"state_before": "a : Int\n⊢ a ≤ ↑(toNat a)",
"tactic": "rw [toNat_eq_max]"
},
{
"state_after": "no goals",
"state_before": "a : Int\n⊢ a ≤ max a 0",
"tactic": "apply Int.le_max_left"
}
] | [
1378,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1378,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.algebraMap_eq | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_comp_topHom | [] | [
665,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | Ideal.closure_ne_top | [
{
"state_after": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nI : Ideal R\nhI : I ≠ ⊤\nh : closure ↑I ⊆ nonunits R\n⊢ Ideal.closure I ≠ ⊤",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nI : Ideal R\nhI : I ≠ ⊤\n⊢ Ideal.closure I ≠ ⊤",
"tactic": "have h ... | [
260,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_erase | [] | [
1004,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.generateFrom_anti | [] | [
215,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_iff_count | [
{
"state_after": "α : Type u_1\nβ : Type ?u.411904\nγ : Type ?u.411907\ninst✝ : DecidableEq α\ns t : Multiset α\nal : ∀ (a : α), count a s ≤ count a t\n⊢ s ≤ s ∪ t",
"state_before": "α : Type u_1\nβ : Type ?u.411904\nγ : Type ?u.411907\ninst✝ : DecidableEq α\ns t : Multiset α\nal : ∀ (a : α), count a s ≤ co... | [
2522,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2520,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioi_of_Ioi | [] | [
184,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_target_mem_nhdsWithin' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.197578\nM' : Type ?u.197581\nH' : Type ?u.197584\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : Topologi... | [
1109,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : CommSemiring R\nl : Type ?u.2673265\nm : Type ?u.2673268\nn : Type u_3\ninst✝⁸ : Fintype n\ninst✝⁷ : Fintype m\ninst✝⁶ : DecidableEq n\nM₁ : Type u_2\nM₂ : Type ?u.2673292\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Mod... | [
805,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/List/Sublists.lean | List.range_bind_sublistsLen_perm | [
{
"state_after": "case nil\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\n⊢ (List.bind (range (length [] + 1)) fun n => sublistsLen n []) ~ sublists' []\n\ncase cons\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nh : α\ntl : List α\nl_ih : (List.bind (range (length tl + 1)) fun n => sublistsLen n tl) ... | [
475,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.appendFun_comp_splitFun | [] | [
257,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.symm_trans_self | [] | [
647,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.nonneg_add | [
{
"state_after": "a✝ b✝ c a b : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nd₁0 : 0 < ↑d₁\n⊢ Rat.Nonneg (n₁ /. ↑d₁) → Rat.Nonneg (n₂ /. ↑d₂) → Rat.Nonneg (n₁ /. ↑d₁ + n₂ /. ↑d₂)",
"state_before": "a✝ b✝ c a b : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\n⊢ Rat.Nonneg (n₁ /.... | [
64,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_coe_angle | [
{
"state_after": "case inl\nx : ℂ\nhx : x ≠ 0\nhi : x.im < 0\n⊢ ↑(arg (-x)) = ↑(arg x) + ↑π\n\ncase inr.inl\nx : ℂ\nhx : x ≠ 0\nhi : x.im = 0\n⊢ ↑(arg (-x)) = ↑(arg x) + ↑π\n\ncase inr.inr\nx : ℂ\nhx : x ≠ 0\nhi : 0 < x.im\n⊢ ↑(arg (-x)) = ↑(arg x) + ↑π",
"state_before": "x : ℂ\nhx : x ≠ 0\n⊢ ↑(arg (-x)) = ... | [
427,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/List/Zip.lean | List.revzip_map_snd | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.93614\nγ : Type ?u.93617\nδ : Type ?u.93620\nε : Type ?u.93623\nl : List α\n⊢ map Prod.snd (revzip l) = reverse l",
"tactic": "rw [← unzip_right, unzip_revzip]"
}
] | [
359,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.lof_apply | [] | [
220,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.subset_dedup | [] | [
65,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Iic | [] | [
141,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.range_logb | [] | [
124,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.id_c | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Logic/IsEmpty.lean | IsEmpty.exists_iff | [] | [
125,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.sum_single | [] | [
1204,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_subset_left | [] | [
459,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.disjoint | [] | [
340,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | Finsupp.toFreeAbelianGroup_toFinsupp | [
{
"state_after": "no goals",
"state_before": "X✝ : Type ?u.72357\nX : Type u_1\nx : FreeAbelianGroup X\n⊢ ↑toFreeAbelianGroup (↑toFinsupp x) = x",
"tactic": "rw [← AddMonoidHom.comp_apply, Finsupp.toFreeAbelianGroup_comp_toFinsupp, AddMonoidHom.id_apply]"
}
] | [
81,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Std/Data/String/Lemmas.lean | String.validFor_mkIterator | [] | [
527,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
527,
1
] |
Mathlib/Data/Set/Equitable.lean | Set.equitableOn_iff_exists_image_subset_icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4654\ns : Set α\nf : α → ℕ\n⊢ EquitableOn s f ↔ ∃ b, f '' s ⊆ Icc b (b + 1)",
"tactic": "simpa only [image_subset_iff] using equitableOn_iff_exists_le_le_add_one"
}
] | [
62,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.atEnd | [
{
"state_after": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ utf8Len l ≥ utf8Len l + utf8Len r ↔ r = []",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ Iterator.atEnd it = true ↔ r = []",
"tactic": "simp [Iterator.atEnd, h.pos, h.toString]"
},
{
"state_after... | [
567,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
564,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.star_dotProduct | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.213834\nm : Type u_1\nn : Type ?u.213840\no : Type ?u.213843\nm' : o → Type ?u.213848\nn' : o → Type ?u.213853\nR : Type ?u.213856\nS : Type ?u.213859\nα : Type v\nβ : Type w\nγ : Type ?u.213866\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : NonUn... | [
902,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.mem_inv_pointwise_smul_iff | [] | [
117,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.image_ι_comp_eq_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\ninst✝² : HasZeroMorphisms C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝¹ : HasImage f\ninst✝ : Epi (factorThruImage f)\nh : f ≫ g = 0\n⊢ factorThruImage f ≫ image.ι f ≫ g = 0",
"tactic": "simp [h... | [
571,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Nat.Prime.sum_four_squares | [
{
"state_after": "p : ℕ\nhp : Prime p\nthis : Fact (Prime p)\n⊢ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = p",
"state_before": "p : ℕ\nhp : Prime p\n⊢ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = p",
"tactic": "have := Fact.mk hp"
},
{
"state_after": "p : ℕ\nhp : Prime p\nthis : Fact (Prime p)\nna... | [
226,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
11
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_sup_distrib_left | [] | [
548,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.smul_span | [] | [
246,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_neg | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.905489\n𝕜 : Type ?u.905492\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
880,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_nat_mul | [] | [
378,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | TensorProduct.LieModule.map_tmul | [] | [
161,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
8
] |
Mathlib/FieldTheory/Normal.lean | normal_iff | [] | [
62,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
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