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/Algebra/FilterBasis.lean | GroupFilterBasis.nhds_one_hasBasis | [
{
"state_after": "G : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\n⊢ HasBasis (FilterBasis.filter toFilterBasis) (fun V => V ∈ B) id",
"state_before": "G : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\n⊢ HasBasis (𝓝 1) (fun V => V ∈ B) id",
"tactic": "rw [B.nhds_one_eq]"
},
{
"stat... | [
228,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_le_Iio | [] | [
183,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/Algebra/GroupPower/Order.lean | lt_max_of_sq_lt_mul | [
{
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311,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_inv | [
{
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"state_before": "α : Type u_2\nβ : T... | [
247,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_sub | [
{
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20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | AffineIsometry.coe_toAffineIsometryEquiv | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_toContinuousLinearMap | [] | [
358,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.max_eq_max | [] | [
170,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
170,
11
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Mathlib/Order/Heyting/Basic.lean | compl_anti | [] | [
903,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_eq_mul | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.vecAlt0_vecAppend | [
{
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"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.38823\nn' : Type ?u.38826\no' : Typ... | [
335,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Data/Real/Irrational.lean | irrational_neg_iff | [] | [
593,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.copy_eq | [] | [
162,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_union_Ioo' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.164237\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\nh₂ : a < d\nx : α\n⊢ x ∈ Ioo a b ∪ Ioo c d ↔ x ∈ Ioo (min a c) (max b d)",
"state_before": "α : Type u_1\nβ : Type ?u.164237\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\nh₂... | [
1701,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1692,
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_domDomCongr | [] | [
798,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_succ | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ X.map (SimplexCategory.σ i).op ≫ X.map (SimplexCategory.δ (Fin.succ i)).op = 𝟙 (X.obj [n].op)",
"state_before": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ σ X i ≫ δ X ... | [
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86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Multiset.Nat.mem_antidiagonalTuple | [] | [
203,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/Algebra/Associated.lean | associated_unit_mul_left | [
{
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"state_before": "α : Type ?u.161759\nβ✝ : Type ?u.161762\nγ : Type ?u.161765\nδ : Type ?u.161768\nβ : Type u_1\ninst✝ : CommMonoid β\n... | [
461,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.not_modEq_iff_toIcoMod_eq_toIocMod | [] | [
660,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_ball | [] | [
1524,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
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src/lean/Init/SimpLemmas.lean | let_body_congr | [] | [
53,
28
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
51,
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] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_of_infinite_dimensional | [] | [
200,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Order/Synonym.lean | toLex_ofLex | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.total_dualBasis | [
{
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435,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_of_dvd | [
{
"state_after": "α : Type ?u.252332\nβ : Type ?u.252335\nγ : Type ?u.252338\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nb0 : a * b ≠ 0\n⊢ a ≤ a * b",
"state_before": "α : Type ?u.252332\nβ : Type ?u.252335\nγ : Type ?u.252338\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\n... | [
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87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
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Mathlib/Data/Real/EReal.lean | EReal.eq_bot_iff_forall_lt | [
{
"state_after": "case mp\nx : EReal\n⊢ x = ⊥ → ∀ (y : ℝ), x < ↑y\n\ncase mpr\nx : EReal\n⊢ (∀ (y : ℝ), x < ↑y) → x = ⊥",
"state_before": "x : EReal\n⊢ x = ⊥ ↔ ∀ (y : ℝ), x < ↑y",
"tactic": "constructor"
},
{
"state_after": "case mp\n\n⊢ ∀ (y : ℝ), ⊥ < ↑y",
"state_before": "case mp\nx : ERea... | [
445,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.266278\nγ : Type ?u.266281\np : α → Prop\ninst✝¹ : DecidablePred p\nq : α → Prop\ninst✝ : DecidablePred q\ns : Multiset α\nl : List α\n⊢ filter p (filter q (Quot.mk Setoid.r l)) = filter (fun a => p a ∧ q a) (Quot.mk Setoid.r l)",
"... | [
2076,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.sup | [] | [
1912,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1909,
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] |
Std/Data/List/Lemmas.lean | List.range'_eq_nil | [
{
"state_after": "no goals",
"state_before": "s n step : Nat\n⊢ range' s n step = [] ↔ n = 0",
"tactic": "rw [← length_eq_zero, length_range']"
}
] | [
1814,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1813,
9
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Mathlib/Data/Multiset/Basic.lean | Multiset.inter_zero | [] | [
1754,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1753,
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] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_id_tensor | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\ninst✝² : MonoidalCategory C\nX Y : C\ninst✝¹ : HasLeftDual X\ninst✝ : HasLeftDual Y\nf : X ⟶ Y\n⊢ (η_ (ᘁX) X ≫ (𝟙 ᘁX ⊗ f) ⊗ 𝟙 ᘁY) ≫ (α_ (ᘁX) Y ᘁY).hom ≫ (𝟙 ᘁX ⊗ ε_ (ᘁY) Y) ≫ (ρ_ ᘁX).hom =\n (λ_ ᘁY).hom ≫\n (λ_ ᘁY).inv ≫ (η_ (ᘁX) X ⊗ 𝟙 ᘁY) ≫ ((𝟙 ᘁX... | [
494,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph0_le_beth | [] | [
473,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Order/Bounds/OrderIso.lean | OrderIso.isGLB_image | [] | [
47,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.dual_comp | [] | [
1534,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.mem_coe_basicOpen | [] | [
399,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_neg | [] | [
387,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
11
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderCobaseChange.op | [] | [
278,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.specializes_coe | [] | [
402,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Submonoid.coe_topologicalClosure | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.147412\nα : Type ?u.147415\nX : Type ?u.147418\nM : Type u_1\nN : Type ?u.147424\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\ns : Submonoid M\n⊢ ↑(topologicalClosure s) = _root_.closure ↑s",
... | [
441,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
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] |
Mathlib/FieldTheory/IsAlgClosed/Classification.lean | IsAlgClosed.cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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] |
Mathlib/Data/Polynomial/PartialFractions.lean | div_eq_quo_add_rem_div_add_rem_div | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.card_eq_card_quotient_mul_card | [
{
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"state_before": "R : Ty... | [
306,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
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Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.counit_X | [] | [
107,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.subtype_comp_codRestrict | [] | [
819,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.nsmul_eq_mul | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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] |
Mathlib/Topology/Constructions.lean | embedding_graph | [] | [
842,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
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] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Icc_eq_Iic | [] | [
1457,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
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Mathlib/Data/Finset/Image.lean | Finset.image_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.89300\ninst✝ : DecidableEq β\nf✝ g : α → β\ns : Finset α\nt : Finset β\na✝ : α\nb c : β\nf : α → β\na : α\nx : β\n⊢ x ∈ image f {a} ↔ x ∈ {f a}",
"tactic": "simpa only [mem_image, exists_prop, mem_singleton, exists_eq_... | [
500,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
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Mathlib/Order/RelIso/Basic.lean | RelHomClass.isAsymm | [] | [
87,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.le_sup_of_le_left | [] | [
1787,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
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Mathlib/Analysis/Normed/Group/Quotient.lean | QuotientAddGroup.norm_lt_iff | [
{
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"state_before": "M : Type u_1\nN : Type ?u.194075\ninst✝¹ : SeminormedAddC... | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/Normed/Order/UpperLower.lean | IsLowerSet.cthickening' | [
{
"state_after": "α : Type u_1\nι : Type ?u.1902\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsLowerSet s\nε : ℝ\n⊢ IsLowerSet (⋂ (ε_1 : ℝ) (_ : max 0 ε < ε_1), thickening ε_1 s)",
"state_before": "α : Type u_1\nι : Type ?u.1902\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsLowerSet s\nε : ℝ\n⊢ IsLowe... | [
64,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.cons | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nf : Vector ℕ n → ℕ\ng : Vector ℕ n → Vector ℕ m\nhf : Partrec' ↑f\nhg : Vec g\ni : Fin (succ m)\n⊢ Partrec' fun v => ↑(some (Vector.get ((fun v => f v ::ᵥ g v) v) 0))",
"tactic": "simpa using hf"
},
{
"state_after": "no goals",
"state_be... | [
355,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
11
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | eq_one_or_one_lt | [] | [
252,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | AlgEquiv.coe_restrictScalars' | [] | [
230,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.mker_norm_eq_unitary | [] | [
1089,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_nonneg | [] | [
371,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
369,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Set.Subsingleton.convex | [] | [
171,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_div_distrib | [] | [
1813,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1812,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.isPath_cons | [
{
"state_after": "F : PFunctor\nX : Type ?u.20790\nf✝ : X → Obj F X\nxs : Path F\na a' : F.A\nf : B F a → M F\ni : B F a'\nx : M F\nh : M.mk { fst := a, snd := f } = x\n⊢ IsPath ({ fst := a', snd := i } :: xs) x → a = a'",
"state_before": "F : PFunctor\nX : Type ?u.20790\nf✝ : X → Obj F X\nxs : Path F\na a'... | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_zero_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.581097\nα : Type u_1\nβ : Type ?u.581103\nγ : Type ?u.581106\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : MulZeroClass α\ns✝ t s : Finset α\n⊢ s * 0 ⊆ 0",
"tactic": "simp [subset_iff, mem_mul]"
}
] | [
1091,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.continuous_set_coe | [] | [
144,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Std/Data/List/Init/Lemmas.lean | List.drop_length | [] | [
147,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
147,
9
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_C | [
{
"state_after": "case hn\nσ : Type u_1\nτ : Type ?u.129675\nR : Type u_2\nS : Type ?u.129681\ninst✝ : CommSemiring R\nr : R\n⊢ ∑ i in 0.support, ↑0 i = 0",
"state_before": "σ : Type u_1\nτ : Type ?u.129675\nR : Type u_2\nS : Type ?u.129681\ninst✝ : CommSemiring R\nr : R\n⊢ IsHomogeneous (↑C r) 0",
"tac... | [
140,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_lt_iff_lt_coe | [
{
"state_after": "no goals",
"state_before": "p✝ q : ℚ\np : ℚ≥0\nhq : 0 ≤ q\n⊢ toNNRat q < p ↔ q < ↑p",
"tactic": "rw [← coe_lt_coe, Rat.coe_toNNRat q hq]"
}
] | [
400,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_div_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LE α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na✝ b✝ c d a b : α\n⊢ a ≤ a / b ↔ b ≤ 1",
"tactic": "simp only [... | [
372,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.IsFraction.eq_mk' | [
{
"state_after": "case intro.intro\nR : Type u\ninst✝ : CommRing R\nU : Opens ↑(PrimeSpectrum.Top R)\nf : (x : { x // x ∈ U }) → Localizations R ↑x\nr s : R\nh :\n ∀ (x : { x // x ∈ U }),\n ¬s ∈ (↑x).asIdeal ∧ f x * ↑(algebraMap R (Localizations R ↑x)) s = ↑(algebraMap R (Localizations R ↑x)) r\n⊢ ∃ r s,\n ... | [
121,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_inf | [] | [
503,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.retraction_ι_eq_id_sub | [] | [
285,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/Atoms.lean | GaloisInsertion.isCoatom_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : PartialOrder α\ninst✝³ : PartialOrder β\ninst✝² : OrderTop α\ninst✝¹ : IsCoatomic α\ninst✝ : OrderTop β\nl : α → β\nu : β → α\ngi : GaloisInsertion l u\nh_coatom : ∀ (a : α), IsCoatom a → u (l a) = a\nb : β\nhb : IsCoatom b\n⊢ IsCoatom (u b)",
"state_be... | [
760,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.Prod.mk_left | [] | [
412,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | IsUnit.ring_inverse | [] | [
160,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.finsetIntegerMultiple_image | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nP : Type ?u.47772\ninst✝² : CommRing P\ninst✝¹ : IsLocalization M S\ninst✝ : DecidableEq R\ns : Finset S\n⊢ ↑(algebraMap R S) '' ↑(Finset.image (fun t => integerMultiple M s id t) (Fins... | [
165,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.leftUnitor_naturality | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g : a ⟶ b\nη : f ⟶ g\n⊢ 𝟙 a ◁ η ≫ (λ_ g).hom = (λ_ f).hom ≫ η",
"tactic": "simp"
}
] | [
391,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_mul_right | [] | [
611,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
611,
11
] |
Mathlib/Algebra/Group/OrderSynonym.lean | pow_toDual | [] | [
156,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/List/Range.lean | List.nodup_iota | [] | [
122,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Ring R\np : R[X]\n⊢ natTrailingDegree (-p) = natTrailingDegree p",
"tactic": "simp [natTrailingDegree]"
}
] | [
468,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_comap | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G' →* G\n⊢ comap f H = comap (MonoidHom.rangeRestrict f) (subgroupOf H (MonoidHom.range f))",
"tactic": "rfl"
}
] | [
86,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left | [] | [
1635,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1634,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.SimpleFunc.stronglyMeasurable | [] | [
152,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/PFun.lean | PFun.coe_id | [] | [
569,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofDual_inv | [] | [
129,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.Iso.op_unop | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX✝ Y✝ X Y : C\nf : X ≅ Y\n⊢ unop (Iso.op f) = f",
"tactic": "(ext; rfl)"
},
{
"state_after": "case w\nC : Type u₁\ninst✝ : Category C\nX✝ Y✝ X Y : C\nf : X ≅ Y\n⊢ (unop (Iso.op f)).hom = f.hom",
"state_before": "C... | [
494,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesMonomorphisms.iso_iff | [] | [
134,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.gcd_fib_add_self | [
{
"state_after": "case inl\nm n : ℕ\nh : n = 0\n⊢ gcd (fib m) (fib (n + m)) = gcd (fib m) (fib n)\n\ncase inr\nm n : ℕ\nh : n > 0\n⊢ gcd (fib m) (fib (n + m)) = gcd (fib m) (fib n)",
"state_before": "m n : ℕ\n⊢ gcd (fib m) (fib (n + m)) = gcd (fib m) (fib n)",
"tactic": "cases' Nat.eq_zero_or_pos n with... | [
264,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Nat.measurable_ceil | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11637\nR : Type u_1\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : LinearOrderedSemiring R\ninst✝⁴ : FloorSemiring R\ninst✝³ : TopologicalSpace R\ninst✝² : OrderTopology R\ninst✝¹ : MeasurableSpace R\ninst✝ : OpensMeasurableSpace R\nf : α → R\nn : R\n⊢ Measur... | [
87,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.interUnionPullbackConeLift_left | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : TopCat\nF : Sheaf C X\nU V : Opens ↑X\ns : PullbackCone (F.val.map (homOfLE (_ : U ⊓ V ≤ U)).op) (F.val.map (homOfLE (_ : U ⊓ V ≤ V)).op)\n⊢ IsLimit.lift\n (Nonempty.some\n (_ :\n Nonempty\n (IsLimit ((presheaf F).mapC... | [
393,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | MonoidHom.pi_ext | [
{
"state_after": "case intro\nF : Type ?u.241399\nι : Type u_1\nα : Type ?u.241405\nβ : Type ?u.241408\nγ : Type u_3\nf✝ : α → β → β\nop : α → α → α\ninst✝⁴ : Monoid β\ninst✝³ : Monoid γ\nM : ι → Type u_2\ninst✝² : (i : ι) → Monoid (M i)\ninst✝¹ : Finite ι\ninst✝ : DecidableEq ι\nf g : ((i : ι) → M i) →* γ\nh :... | [
447,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_nsmul | [] | [
107,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_le_bsup_succ | [] | [
1831,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1829,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.epi_of_isColimit_cofork | [] | [
1027,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | lt_mem_sets_of_limsSup_lt | [] | [
140,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Std/Data/List/Init/Lemmas.lean | List.nil_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → List β\n⊢ List.bind [] f = []",
"tactic": "simp [join, List.bind]"
}
] | [
100,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
9
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.ofFinsupp_algebraMap | [] | [
71,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Logic/Equiv/List.lean | Denumerable.list_ofNat_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.38944\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\n⊢ ofNat (List α) 0 = []",
"tactic": "rw [← @encode_list_nil α, ofNat_encode]"
}
] | [
272,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.lcoeff_apply | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Deprecated/Ring.lean | IsRingHom.to_isAddGroupHom | [] | [
140,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.neg | [] | [
387,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.398294\nδ : Type ?u.398297\nι : Type ?u.398300\nR : Type ?u.398303\nR' : Type ?u.398306\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\nh ... | [
2397,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2396,
11
] |
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