file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_def | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_multiset_prod | [] | [
41,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
11
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.restrict_mono | [
{
"state_after": "ι : Type u_1\nI J J₁✝ J₂ : Box ι\nπ π₁✝ π₂✝ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nπ₁ π₂ : Prepartition I\nHle : π₁ ≤ π₂\nJ₁ : WithBot (Box ι)\nhJ₁ : J₁ ∈ Finset.image (fun J' => ↑J ⊓ ↑J') π₁.boxes\nhne : J₁ ≠ ⊥\n⊢ ∃ J', J' ∈ Finset.image (fun J' => ↑J ⊓ ↑J') π... | [
502,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
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Mathlib/LinearAlgebra/Basis.lean | Module.card_fintype | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.640840\nR : Type u_2\nR₂ : Type ?u.640846\nK : Type ?u.640849\nM : Type u_3\nM' : Type ?u.640855\nM'' : Type ?u.640858\nV : Type u\nV' : Type ?u.640863\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCo... | [
907,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | cauchySeq_of_edist_le_geometric_two | [
{
"state_after": "α : Type u_1\nβ : Type ?u.439361\nι : Type ?u.439364\ninst✝ : PseudoEMetricSpace α\nC : ℝ≥0∞\nhC : C ≠ ⊤\nf : ℕ → α\na : α\nha : Tendsto f atTop (𝓝 a)\nhu : ∀ (n : ℕ), edist (f n) (f (n + 1)) ≤ C * 2⁻¹ ^ n\n⊢ CauchySeq f",
"state_before": "α : Type u_1\nβ : Type ?u.439361\nι : Type ?u.439... | [
346,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.coe_id | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.QuotientTorsion.torsion_eq_bot | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nz : M ⧸ torsion R M\nx : M\nx✝ : Quotient.mk'' x ∈ torsion R (M ⧸ torsion R M)\na : { x // x ∈ R⁰ }\nhax : a • x ∈ torsion R M\n⊢ Quotient.mk'' x ∈ ⊥",
"state_before": "R : Type u_2\nM : Type u_1\... | [
739,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_pow_self_of_prime | [] | [
624,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.functorPushforward_comp | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nR : Presieve X\nx : E\n⊢ functorPushforward (F ⋙ G) R = functorPushforward G (functorPushforward F R)",
"state_before": "C : Type u₁\nins... | [
231,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_X_left | [] | [
268,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integral_exp_neg_Ioi | [
{
"state_after": "no goals",
"state_before": "c : ℝ\n⊢ (∫ (x : ℝ) in Ioi c, exp (-x)) = exp (-c)",
"tactic": "simpa only [integral_comp_neg_Ioi] using integral_exp_Iic (-c)"
}
] | [
57,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Logic/Relation.lean | Symmetric.flip_eq | [] | [
85,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/RelIso/Basic.lean | injective_of_increasing | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.15172\nδ : Type ?u.15175\nr✝ : α → α → Prop\ns✝ : β → β → Prop\nt : γ → γ → Prop\nu : δ → δ → Prop\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsTrichotomous α r\ninst✝ : IsIrrefl β s\nf : α → β\nhf : ∀ {x y : α}, r x y → s (f x) (f y)\nx y : α\nhxy : ... | [
178,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_eq_none_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nf : α → β → γ\na : Option α\nb : Option β\nc : Option γ\n⊢ map₂ f a b = none ↔ a = none ∨ b = none",
"tactic": "cases a <;> cases b <;> simp"
}
] | [
86,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | eq_of_dist_eq_zero | [] | [
2847,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2846,
1
] |
Std/Data/Int/DivMod.lean | Int.fmod_def | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ fmod a b = a - b * fdiv a b",
"tactic": "rw [← Int.add_sub_cancel (a.fmod b), fmod_add_fdiv]"
}
] | [
326,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
325,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.parallelFamily_obj_zero | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_eq_zero | [
{
"state_after": "case refine'_3\nd : Nat\nn : Int\nd0 : d ≠ 0\nthis : normalize ?refine'_1 d = normalize ?refine'_2 1 ↔ ?refine'_1 * ↑1 = ?refine'_2 * ↑d\n⊢ normalize n d = 0 ↔ n = 0\n\ncase refine'_1\nd : Nat\nn : Int\nd0 : d ≠ 0\n⊢ Int\n\ncase refine'_2\nd : Nat\nn : Int\nd0 : d ≠ 0\n⊢ Int",
"state_befor... | [
70,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
68,
9
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.SeparatingLeft.toMatrix₂ | [] | [
737,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_sup | [
{
"state_after": "case empty\nF : Type ?u.189518\nα : Type u_3\nβ : Type ?u.189524\nγ : Type ?u.189527\nι : Type u_2\nκ✝ : Type ?u.189533\ninst✝² : DistribLattice α\ninst✝¹ : BoundedOrder α\ninst✝ : DecidableEq ι\nκ : ι → Type u_1\nt : (i : ι) → Finset (κ i)\nf : (i : ι) → κ i → α\n⊢ (inf ∅ fun i => sup (t i) (... | [
601,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_pred_of_ne | [] | [
146,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_isLocallyConstant | [] | [
138,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.kernel.lift.inv | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Mono f\nex : Exact f g\nthis : IsIso (kernel.lift g f (_ : f ≫ g = 0))\n⊢ let_fun this := (_ : IsIso (kernel.lift g f (_ : f ≫ g = 0)));\n CategoryTheory.inv (kernel.lift g f (_ : f ≫ g = 0)) ≫ f = ... | [
206,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_singleton | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9697\nδ : Type ?u.9700\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx : α\ny : β\n⊢ (x, y) ∈ s ×ˢ {b} ↔ (x, y) ∈ (fun a => (a, b)) '' s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9697\nδ : Type ?u.9700\ns s₁ s₂ : Set α\... | [
143,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.mem_cast | [] | [
490,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | cauchySeq_of_le_tendsto_0 | [] | [
1552,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1549,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.linearIsometry_apply_single | [
{
"state_after": "ι : Type u_2\n𝕜 : Type u_4\ninst✝⁴ : IsROrC 𝕜\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G i)\nV : (i : ι) → G i →ₗᵢ[𝕜] E\nhV : ... | [
244,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
11
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.pos_iff_one_le | [
{
"state_after": "no goals",
"state_before": "x : PartENat\n⊢ 0 < ⊤ ↔ 1 ≤ ⊤",
"tactic": "simp only [iff_true_iff, le_top, natCast_lt_top, ← @Nat.cast_zero PartENat]"
},
{
"state_after": "x : PartENat\nn : ℕ\n⊢ 0 < n ↔ 1 ≤ n",
"state_before": "x : PartENat\nn : ℕ\n⊢ 0 < ↑n ↔ 1 ≤ ↑n",
"tac... | [
402,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.30962\nγ : Type ?u.30965\nδ : Type ?u.30968\nδ' : Type ?u.30971\nι✝ : Sort ?u.30974\ns✝ t u : Set α\nι : Sort u_1\nm : ι → MeasurableSpace α\ns : Set α\n⊢ MeasurableSet s ↔ ∀ (i : ι), MeasurableSet s",
"tactic": "rw [iInf, measurabl... | [
493,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.17889\nα : Type u_1\nβ : Type ?u.17895\nπ : ι → Type ?u.17900\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ∆ a = ⊥",
"tactic": "rw [symmDiff, sup_idem, sdiff_self]"
}
] | [
125,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.ext_iff | [] | [
221,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.ofRightExact_obj_fst | [] | [
297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.mul_left' | [
{
"state_after": "case inl\nm n a b c d : ℤ\nh : a ≡ b [ZMOD n]\nhc : c < 0\n⊢ c * a ≡ c * b [ZMOD c * n]\n\ncase inr.inl\nm n a b d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ 0 * a ≡ 0 * b [ZMOD 0 * n]\n\ncase inr.inr\nm n a b c d : ℤ\nh : a ≡ b [ZMOD n]\nhc : 0 < c\n⊢ c * a ≡ c * b [ZMOD c * n]",
"state_before": "m n a b... | [
136,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
11
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.cells_bot | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Logic/Basic.lean | Decidable.not_forall_not | [] | [
693,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
11
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_pos_iff_infinitePos_inv | [
{
"state_after": "no goals",
"state_before": "x : ℝ*\n⊢ Infinitesimal x⁻¹⁻¹ ∧ 0 < x⁻¹⁻¹ ↔ Infinitesimal x ∧ 0 < x",
"tactic": "rw [inv_inv]"
}
] | [
772,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteEdges_le | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.247819\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns : Set (Sym2 V)\n⊢ deleteEdges G' s ≤ G'",
"tactic": "constructor <;> simp (config := { contextual := true }) [subset_rfl]"
}
] | [
1088,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_isLimit | [] | [
849,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_add_constg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\nn : ℤ\nx a k a' : α\nh : a + k = a'\n⊢ termg n x a + k = termg n x a'",
"tactic": "simp [h.symm, termg, add_assoc]"
}
] | [
140,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_strictMono | [] | [
220,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.leadingCoeff_of_b_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.555902\nF : Type ?u.555905\nK : Type ?u.555908\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b ≠ 0\n⊢ leadingCoeff (toPoly P) = P.b",
"tactic": "rw [of_a_eq_zero ha, leadingCoeff_quadratic hb]"
... | [
214,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.sup_iterate_eq_nfp | [
{
"state_after": "case refine'_1\nf✝ f : Ordinal → Ordinal\na : Ordinal\n⊢ (sup fun n => (f^[n]) a) ≤ nfp f a\n\ncase refine'_2\nf✝ f : Ordinal → Ordinal\na : Ordinal\nl : List Unit\n⊢ List.foldr (fun x => f) a l ≤ sup fun n => (f^[n]) a",
"state_before": "f✝ f : Ordinal → Ordinal\n⊢ (fun a => sup fun n => ... | [
435,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.sum_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.62145\ninst✝ : AddCommMonoid α\nn : ℕ\nx : α\n⊢ ∑ _i : Fin n, x = n • x",
"tactic": "simp"
}
] | [
171,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.smul | [] | [
620,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Iic_eq_cons_Iio | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.119351\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrderBot α\nb : α\n⊢ Iic b = cons b (Iio b) (_ : ¬b ∈ Iio b)",
"tactic": "classical rw [cons_eq_insert, Iio_insert]"
},
{
"state_after": "no goals",
"state_before": "... | [
732,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_le_iff_le_coe | [] | [
387,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_dvd | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd m n ∣ m ∧ gcd m n ∣ n",
"tactic": "induction m, n using gcd.induction with\n| H0 n => rw [gcd_zero_left]; exact ⟨Nat.dvd_zero n, Nat.dvd_refl n⟩\n| H1 m n _ IH => rw [← gcd_rec] at IH; exact ⟨IH.2, (dvd_mod_iff IH.2).1 IH.1⟩"
},
{
"s... | [
39,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
36,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_apply | [] | [
1765,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.principal_top | [] | [
334,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Std/Data/Nat/Gcd.lean | Nat.lcm_dvd | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\nH1 : m ∣ k\nH2 : n ∣ k\n⊢ lcm m n ∣ k",
"tactic": "match eq_zero_or_pos k with\n| .inl h => rw [h]; exact Nat.dvd_zero _\n| .inr kpos =>\n apply Nat.dvd_of_mul_dvd_mul_left (gcd_pos_of_pos_left n (pos_of_dvd_of_pos H1 kpos))\n rw [gcd_mul_lcm,... | [
212,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
206,
1
] |
Mathlib/Order/Hom/Basic.lean | WithBot.toDualTopEquiv_coe | [] | [
1248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_image2_eq_csSup_csSup | [] | [
1431,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1428,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.lt_succ_iff_ne_top | [] | [
533,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomainInv.dimensionLEOne | [
{
"state_after": "R : Type ?u.136881\nA : Type u_1\nK : Type ?u.136887\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nh : IsDedekindDomainInv A\nP : Ideal A\nP_ne : P ≠ ⊥\nhP : Ideal.IsPrime P\n⊢ Ideal.IsMaximal P",
"state_... | [
346,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.IsSymmetric.toSelfAdjoint_apply | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_quotient_mk | [] | [
969,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.odd_add | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ Odd (m + n) ↔ (Odd m ↔ Even n)",
"tactic": "rw [odd_iff_not_even, even_add, not_iff, odd_iff_not_even]"
}
] | [
187,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
17
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.sigma_add | [
{
"state_after": "α : Type u_2\nβ : Type ?u.71688\nγ : Type ?u.71691\nδ : Type ?u.71694\nσ : α → Type u_1\na✝ : α\ns✝ : Multiset α\nt✝ : (a : α) → Multiset (σ a)\na : α\ns : Multiset α\nIH : ∀ (t u : (a : α) → Multiset (σ a)), (Multiset.sigma s fun a => t a + u a) = Multiset.sigma s t + Multiset.sigma s u\nt u ... | [
347,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.colon_mono | [] | [
375,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.Meq.equiv_apply | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.len_lt_of_mono | [
{
"state_after": "case inl\nΔ' Δ : SimplexCategory\ni : Δ' ⟶ Δ\nhi : Mono i\nhi' : Δ ≠ Δ'\nh : len Δ' < len Δ\n⊢ len Δ' < len Δ\n\ncase inr\nΔ' Δ : SimplexCategory\ni : Δ' ⟶ Δ\nhi : Mono i\nhi' : Δ ≠ Δ'\nh : len Δ' = len Δ\n⊢ len Δ' < len Δ",
"state_before": "Δ' Δ : SimplexCategory\ni : Δ' ⟶ Δ\nhi : Mono i\... | [
763,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_mod_mod | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\n⊢ (m + n % k) % k = (m + n) % k",
"tactic": "rw [Nat.add_comm, mod_add_mod, Nat.add_comm]"
}
] | [
789,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
788,
9
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.bit_false | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.atEnd | [
{
"state_after": "no goals",
"state_before": "p : Nat\nx✝ : Substring\nh✝ : Valid x✝\nw✝² w✝¹ w✝ : List Char\nh : ValidFor w✝² w✝¹ w✝ x✝\n⊢ Substring.atEnd x✝ { byteIdx := p } = true ↔ p = utf8ByteSize (toString x✝)",
"tactic": "simp [h.atEnd, h.toString]"
}
] | [
1034,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1033,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotToQuotSupₐ | [] | [
708,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_strictMono_of_injective | [] | [
602,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.sub_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonUnitalNonAssocRing R\na b x y x' y' : R\nha : SemiconjBy a x y\nhb : SemiconjBy b x y\n⊢ SemiconjBy (a - b) x y",
"tactic": "simpa only [sub_eq_add_neg] using ha.add_left hb.neg_left"
}
] | [
100,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/RingTheory/ClassGroup.lean | card_classGroup_eq_one | [
{
"state_after": "R : Type u_1\nK : Type ?u.1948840\nL : Type ?u.1948843\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : DecidableEq L\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : Algebra K L\ninst✝⁴ : FiniteDimensional K L\ninst✝³ : Algebra R L\ninst✝² : IsScalarTower R K L... | [
406,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_int | [] | [
1887,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1886,
1
] |
Std/Data/List/Lemmas.lean | List.take_prefix | [] | [
1716,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1715,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_neg | [
{
"state_after": "case a.h\nl : Type ?u.380296\nm : Type u_1\nn : Type u_2\no : Type u_3\nm' : o → Type ?u.380310\nn' : o → Type ?u.380315\nR : Type ?u.380318\nS : Type ?u.380321\nα : Type v\nβ : Type w\nγ : Type ?u.380328\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype n\nM : Matrix m n α\nN : Matrix n o α\... | [
1189,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
11
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsInt.of_raw | [] | [
86,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Icc_self | [] | [
246,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_smul_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.304510\nβ : Type ?u.304513\na✝ b✝ c d : ℝ≥0∞\nr✝ p q : ℝ≥0\na b : ℝ≥0∞\nr : ℝ≥0\nhr₀ : r ≠ 0\n⊢ r⁻¹ • a ≤ b ↔ a ≤ r • b",
"tactic": "simpa only [inv_inv] using (ENNReal.le_inv_smul_iff (inv_ne_zero hr₀)).symm"
}
] | [
1668,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1667,
11
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_eq_one_iff | [] | [
569,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.mul_card_image_le_card_of_maps_to | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.99968\nα : Type u_1\nβ : Type u_2\nM : Type ?u.99977\nN : Type ?u.99980\nG : Type ?u.99983\nk : Type ?u.99986\nR : Type ?u.99989\ninst✝ : DecidableEq β\nf : α → β\ns : Finset α\nt : Finset β\nHf : ∀ (a : α), a ∈ s → f a ∈ t\nn : ℕ\nhn : ∀ (a : β), a ... | [
305,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns✝ : Finset ι\nι₂ : Type ?u.373025\ns₂ : Finset ι₂\nv : V\nx : k\ns : Set ι\np : ι → P\nb : P\n⊢ (∃ fs h w h, v = ∑ i in fs, w i • (p i -ᵥ b)) ↔ ∃ fs w h, ... | [
597,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMin.max | [] | [
526,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
8
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.tendsto_rightLim | [] | [
180,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_fixed_iff | [] | [
821,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sum_lt_top | [] | [
1222,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | generatePiSystem_eq | [] | [
247,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_eq_zero | [] | [
175,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.prod | [] | [
330,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.setPreimage_id | [] | [
934,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/Data/Finset/Image.lean | Multiset.toFinset_map | [] | [
770,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.antilipschitzWith_equiv_aux | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.57170\n𝕜' : Type ?u.57173\nι : Type u_1\nα : ι → Type ?u.57181\nβ : ι → Type u_2\ninst✝³ : Fact (1 ≤ p)\ninst✝² : (i : ι) → PseudoMetricSpace (α i)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nx y : PiLp p β\n⊢ edist x y ≤ ↑(↑(Fintype.card ι) ^ ENNRe... | [
422,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Associates.exists_mem_multiset_le_of_prime | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.49199\nγ : Type ?u.49202\nδ : Type ?u.49205\ninst✝ : CancelCommMonoidWithZero α\ns✝ : Multiset (Associates α)\np : Associates α\nhp : Prime p\na : Associates α\ns : Multiset (Associates α)\nih : p ≤ Multiset.prod s → ∃ a, a ∈ s ∧ p ≤ a\... | [
159,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Bounds.lean | mul_ciSup | [] | [
171,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.coe_inj | [
{
"state_after": "case mk\nF : Type u → Type v\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\nG : Type u → Type w\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nη' : ApplicativeTransformation F G\napp✝ : (α : Type u) → F α → G α\npreserves_pure'✝ : ∀ {α : Type u} (x : α), app✝ α (pure x) = pure x... | [
122,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.preimage_metric_ball | [
{
"state_after": "case h\nR : Type ?u.1006960\nR' : Type ?u.1006963\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1006969\n𝕜₃ : Type ?u.1006972\n𝕝 : Type ?u.1006975\nE : Type u_1\nE₂ : Type ?u.1006981\nE₃ : Type ?u.1006984\nF : Type ?u.1006987\nG : Type ?u.1006990\nι : Type ?u.1006993\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : Ad... | [
809,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | IsCompact.mul | [
{
"state_after": "ι : Type ?u.168240\nα : Type ?u.168243\nX : Type ?u.168246\nM : Type u_1\nN : Type ?u.168252\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\ns t : Set M\nhs : IsCompact s\nht : IsCompact t\n⊢ IsCompact ((fun x => x.fst * x.snd) '' s ×ˢ t)"... | [
520,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.abs_sin_le_one | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sin x * sin x ≤ 1",
"tactic": "simp only [← sq, sin_sq_le_one]"
}
] | [
1259,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.prod_eq_biUnion_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.257901\nι : Sort ?u.257904\nι' : Sort ?u.257907\nι₂ : Sort ?u.257910\nκ : ι → Sort ?u.257915\nκ₁ : ι → Sort ?u.257920\nκ₂ : ι → Sort ?u.257925\nκ' : ι' → Sort ?u.257930\nf : α → β → γ\ns : Set α\nt : Set β\n⊢ s ×ˢ t = ⋃ (b... | [
1937,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1936,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_tail | [] | [
1829,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.vecEmpty_apply | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | ContinuedFraction.convergents_eq_convergents' | [
{
"state_after": "case a\nK : Type u_1\nn✝ : ℕ\ninst✝ : LinearOrderedField K\nc : ContinuedFraction K\nn : ℕ\n⊢ Stream'.nth (convergents ↑↑c) n = Stream'.nth (convergents' ↑↑c) n",
"state_before": "K : Type u_1\nn : ℕ\ninst✝ : LinearOrderedField K\nc : ContinuedFraction K\n⊢ convergents ↑↑c = convergents' ↑... | [
413,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
8
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_bit0_succ | [] | [
195,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | inv_smul_eq_iff₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : GroupWithZero α\ninst✝ : MulAction α β\na✝ a : α\nha : a ≠ 0\nx y : β\nh : a⁻¹ • x = y\n⊢ x = a • y",
"tactic": "rw [← h, smul_inv_smul₀ ha]"
},
{
"state_after": "no goals",
"state_before": "α : Type u... | [
205,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | derivWithin_div | [] | [
236,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
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