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/Finset/Basic.lean | Finset.mem_range_succ_iff | [] | [
3030,
41
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3029,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_le_aleph0 | [] | [
1500,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1499,
1
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Mathlib/Algebra/GeomSum.lean | Commute.mul_geom_sum₂_Ico | [
{
"state_after": "α : Type u\ninst✝ : Ring α\nx y : α\nh : Commute x y\nm n : ℕ\nhmn : m ≤ n\n⊢ (x - y) * (∑ k in range n, x ^ k * y ^ (n - 1 - k) - ∑ k in range m, x ^ k * y ^ (n - 1 - k)) =\n x ^ n - x ^ m * y ^ (n - m)",
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289,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_le_mul_left | [] | [
1029,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_sum | [] | [
1555,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1553,
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Mathlib/Topology/Separation.lean | image_closure_of_isCompact | [] | [
1315,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.injOn_arcsin | [] | [
91,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_neg_orientation | [
{
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254,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Data/Set/Basic.lean | Set.inclusion_right | [
{
"state_after": "case mk\nα : Type u_1\ns t u : Set α\nh : s ⊆ t\nval✝ : α\nproperty✝ : val✝ ∈ t\nm : ↑{ val := val✝, property := property✝ } ∈ s\n⊢ inclusion h { val := ↑{ val := val✝, property := property✝ }, property := m } = { val := val✝, property := property✝ }",
"state_before": "α : Type u_1\ns t u ... | [
2787,
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2785,
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src/lean/Init/Prelude.lean | Nat.le_succ | [] | [
1600,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1599,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_self | [
{
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"state_before": "S : Type ?u.174526\nR : Type u_1\nR₁ : Type ?u.174532\nM : Typ... | [
314,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nat_mul_two_pi_sub_pi | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ cos (↑n * (2 * π) - π) = -1",
"tactic": "simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic"
}
] | [
396,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | interior_convexHull_nonempty_iff_affineSpan_eq_top | [
{
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"state_before": "V : ... | [
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48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.edist_lt_mul_of_lt | [] | [
144,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
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Mathlib/Data/Finset/Basic.lean | Finset.le_iff_subset | [] | [
406,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_dual | [] | [
476,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.coneMorphism_hom | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.to_affineMap_injective | [
{
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62,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
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Mathlib/Order/Filter/Basic.lean | Filter.map_le_iff_le_comap | [] | [
2148,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2147,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_distrib_subset_left | [
{
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456,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ico_eq_Ico | [] | [
1510,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.le_succ_iterate | [
{
"state_after": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : SuccOrder α\na b : α\nk : ℕ\nx : α\n⊢ (id^[k]) x ≤ (succ^[k]) x",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : SuccOrder α\na b : α\nk : ℕ\nx : α\n⊢ x ≤ (succ^[k]) x",
"tactic": "conv_lhs => rw [(by simp only [Function.iterate_i... | [
283,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_apply' | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.someExistsOneDivLT_lt | [] | [
158,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
9
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.toEquiv_mulLeft | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.germ_comp_stalkToFiberRingHom | [] | [
541,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inter_mul_union_subset | [] | [
768,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | differentiableOn_euclidean | [
{
"state_after": "𝕜 : Type u_1\nι : Type u_3\nH : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup H\ninst✝¹ : NormedSpace 𝕜 H\ninst✝ : Fintype ι\nf : H → EuclideanSpace 𝕜 ι\nf' : H →L[𝕜] EuclideanSpace 𝕜 ι\nt : Set H\ny : H\n⊢ (∀ (i : ι), DifferentiableOn 𝕜 (fun x => (↑(EuclideanSpace.equiv ι 𝕜... | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.696\nι : Sort ?u.699\nf f₁ f₂ : Filter α\ng✝ g₁ g₂ g : Set α → Filter β\n⊢ Filter.lift ⊤ g = g univ",
"tactic": "simp [Filter.lift]"
}
] | [
35,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
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Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.multiset_prod_mem | [
{
"state_after": "M✝ : Type ?u.55549\ninst✝² : Monoid M✝\ns✝ : Set M✝\nA : Type ?u.55558\ninst✝¹ : AddMonoid A\nt : Set A\nM : Type u_1\ninst✝ : CommMonoid M\ns : Set M\nhs : IsSubmonoid s\nm : Multiset M\nl : List M\nhl : ∀ (a : M), a ∈ Quotient.mk (List.isSetoid M) l → a ∈ s\n⊢ Multiset.prod (Quotient.mk (Lis... | [
254,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Int.cast_pow | [
{
"state_after": "case zero\nα : Type ?u.285909\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Ring R\nn : ℤ\n⊢ ↑(n ^ Nat.zero) = ↑n ^ Nat.zero\n\ncase succ\nα : Type ?u.285909\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR ... | [
628,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
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Mathlib/Topology/Inseparable.lean | inseparable_def | [] | [
269,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Std/Data/Option/Lemmas.lean | Option.choice_isSome_iff_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nh : Nonempty α\n⊢ isSome (choice α) = true",
"tactic": "simp only [choice, dif_pos h, isSome_some]"
}
] | [
214,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
213,
1
] |
Mathlib/Order/Filter/CountableInter.lean | Filter.mem_ofCountableInter | [] | [
154,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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] |
Mathlib/Algebra/Order/UpperLower.lean | mul_lowerClosure | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\n⊢ (⋃ (a : α) (_ : a ∈ s), a • ↑(lowerClosure t)) = ⋃ (i : α) (_ : i ∈ s), ↑(i • lowerClosure t)",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\n⊢ s * ↑(lowerClosure t) = ↑(lowerClosure (s * t))",... | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.equiv_mk | [
{
"state_after": "R : Type u_2\nK : Type u_3\nL : Type ?u.741973\ninst✝¹³ : CommRing R\ninst✝¹² : Field K\ninst✝¹¹ : Field L\ninst✝¹⁰ : DecidableEq L\ninst✝⁹ : Algebra R K\ninst✝⁸ : IsFractionRing R K\ninst✝⁷ : Algebra K L\ninst✝⁶ : FiniteDimensional K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : IsScalarTower R K L\ninst... | [
219,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Filter.TendstoNhdsWithinIio.mul_const | [] | [
196,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_min | [
{
"state_after": "G : Type u\ninst✝ : Monoid G\nm : ℕ\nhpos : 0 < m\nhm : m < exponent G\nh : ∀ (g : G), g ^ m = 1\n⊢ False",
"state_before": "G : Type u\ninst✝ : Monoid G\nm : ℕ\nhpos : 0 < m\nhm : m < exponent G\n⊢ ∃ g, g ^ m ≠ 1",
"tactic": "by_contra' h"
},
{
"state_after": "G : Type u\ninst... | [
142,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.trans | [] | [
358,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
8
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.alternatingProd_cons | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.167752\nα : Type u_1\nM : Type ?u.167758\nN : Type ?u.167761\nP : Type ?u.167764\nM₀ : Type ?u.167767\nG : Type ?u.167770\nR : Type ?u.167773\ninst✝ : CommGroup α\na : α\nl : List α\n⊢ alternatingProd (a :: l) = a / alternatingProd l",
"tactic": ... | [
664,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.app_eq_coe | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_d_ne_zero' | [] | [
365,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_forall_le | [] | [
251,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.nonempty_of_mem_countableBasis | [] | [
656,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.aeval_gen_minpoly | [
{
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"state_before": "F : Type u_2\ninst✝⁴ : Field F\nE : Type u_1\ni... | [
811,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Order/Bounds/Basic.lean | mem_lowerBounds_image2_of_mem_lowerBounds_of_mem_upperBounds | [] | [
1412,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
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] |
Mathlib/Order/Bounds/Basic.lean | BddAbove.insert | [] | [
931,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
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] |
Mathlib/Algebra/MonoidAlgebra/NoZeroDivisors.lean | AddMonoidAlgebra.NoZeroDivisors.of_left_ordered | [
{
"state_after": "R : Type u_1\nA : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : NoZeroDivisors R\ninst✝² : AddRightCancelSemigroup A\ninst✝¹ : LinearOrder A\ninst✝ : CovariantClass A A (fun x x_1 => x + x_1) fun x x_1 => x < x_1\nf g : AddMonoidAlgebra R A\nfg : f ≠ 0 ∧ g ≠ 0\n⊢ f * g ≠ 0",
"state_before": "R :... | [
122,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.inv | [] | [
1526,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1524,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.multiset_prod_mem | [] | [
63,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Trident.app_zero | [
{
"state_after": "no goals",
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"tactic": "rw [← s.w (line j), parallelFamily_map_left]"
}
] | [
223,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Rel.lean | Rel.image_subset | [] | [
139,
17
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138,
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Mathlib/Order/Filter/Basic.lean | Filter.iSup_principal | [
{
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977,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.le_add_left | [
{
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] | [
973,
69
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv'_id | [] | [
495,
25
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493,
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Mathlib/Data/Num/Lemmas.lean | PosNum.cast_to_znum | [] | [
1185,
74
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1182,
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_iInf | [
{
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3007,
49
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3005,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_c_eq_zero' | [] | [
161,
27
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160,
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Mathlib/LinearAlgebra/Dimension.lean | LinearMap.le_rank_iff_exists_linearIndependent | [
{
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.congr_fun | [] | [
111,
24
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110,
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Mathlib/Order/BooleanAlgebra.lean | sdiff_sdiff_eq_sdiff_sup | [
{
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] | [
376,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_const_mul | [] | [
275,
36
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273,
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Mathlib/AlgebraicTopology/DoldKan/Normalized.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap | [
{
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49,
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Mathlib/Order/Atoms.lean | IsCoatom.lt_iff | [] | [
159,
16
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158,
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.coeff_divMonomial | [] | [
56,
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Mathlib/Algebra/Order/Floor.lean | Int.ceil_lt_add_one | [
{
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1176,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
1
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_to_continuousMap | [] | [
113,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.le_comap_map | [] | [
234,
38
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233,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Iio_subset | [] | [
72,
48
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71,
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Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean | CategoryTheory.IsKernelPair.cancel_right | [
{
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127,
76
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114,
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_right_of_neg | [] | [
1137,
37
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1136,
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Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_sorted | [
{
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177,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Logic/Equiv/List.lean | Denumerable.raise'_sorted | [] | [
383,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.eq_zero_of_norm_pow_within | [
{
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2046,
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.map_tail | [
{
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712,
55
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711,
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Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.det_one_smulRight | [
{
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1233,
94
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1225,
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Mathlib/Data/Multiset/Fold.lean | Multiset.fold_hom | [
{
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109,
86
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106,
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Mathlib/Algebra/Lie/Solvable.lean | Function.Injective.lieAlgebra_isSolvable | [
{
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232,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two | [
{
"state_after": "θ : Angle\n⊢ 0 ≤ cos ↑(toReal θ) ↔ abs (toReal θ) ≤ π / 2",
"state_before": "θ : Angle\n⊢ 0 ≤ cos θ ↔ abs (toReal θ) ≤ π / 2",
"tactic": "nth_rw 1 [← coe_toReal θ]"
},
{
"state_after": "θ : Angle\n⊢ 0 ≤ Real.cos (toReal θ) ↔ -(π / 2) ≤ toReal θ ∧ toReal θ ≤ π / 2",
"state_b... | [
748,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.prod_left_snd | [] | [
1036,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
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Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.nsmul_add | [] | [
148,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
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Mathlib/Data/Rat/Lemmas.lean | Rat.den_div_eq_of_coprime | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nhb0 : 0 < b\nh : Nat.coprime (Int.natAbs a) (Int.natAbs b)\n⊢ ↑(↑a / ↑b).den = b",
"tactic": "rw [←Int.natAbs_of_nonneg hb0.le, ← Rat.divInt_eq_div,\n ←mk_eq_divInt _ _ (Int.natAbs_ne_zero.mpr hb0.ne') h]"
}
] | [
222,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE' | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.112015\nm :... | [
518,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.measurableSet_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.796326\nδ : Type ?u.796329\nδ' : Type ?u.796332\nι : Sort uι\ns✝ t u : Set α\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\ne : α ≃ᵐ β\ns : Set α\n⊢ Measurab... | [
1312,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1311,
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] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.one_bind | [] | [
1065,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_pi | [] | [
458,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | map_rootsOfUnity | [
{
"state_after": "case intro.intro\nM : Type u_1\nN : Type u_2\nG : Type ?u.365670\nR : Type ?u.365673\nS : Type ?u.365676\nF : Type ?u.365679\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk✝ l : ℕ+\nf : Mˣ →* Nˣ\nk : ℕ+\nζ : Mˣ\nh : ζ ∈ ↑(rootsOfUnity k M)\n⊢ ↑f ζ ∈ rootsOfUnity ... | [
130,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_neg | [
{
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1303,
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1301,
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Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.isPreconnected_of_isPreconnected_op | [] | [
244,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.id_comp | [] | [
484,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_symm_mk | [] | [
551,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/FieldTheory/Subfield.lean | Subfield.gc_map_comap | [] | [
536,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
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] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_iSup | [
{
"state_after": "α β : Type u\nι : Type v\nf : ι → Cardinal\nhf : BddAbove (range f)\n⊢ sSup (range (lift ∘ f)) = sSup (range fun i => lift (f i))",
"state_before": "α β : Type u\nι : Type v\nf : ι → Cardinal\nhf : BddAbove (range f)\n⊢ lift (iSup f) = ⨆ (i : ι), lift (f i)",
"tactic": "rw [iSup, iSup,... | [
1189,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_iff_tendsto | [] | [
1839,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_nonneg_of_pos | [] | [
233,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.range_toContinuousLinearMap | [] | [
330,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.iInf_span_singleton | [
{
"state_after": "case hI\nR : Type u\nι✝ : Type ?u.255689\ninst✝¹ : CommSemiring R\nI✝ J K L : Ideal R\nι : Type u_1\ninst✝ : Fintype ι\nI : ι → R\nhI : ∀ (i j : ι), i ≠ j → IsCoprime (I i) (I j)\n⊢ Set.Pairwise (↑Finset.univ) (IsCoprime on fun i => I i)",
"state_before": "R : Type u\nι✝ : Type ?u.255689\n... | [
639,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.induction_on | [
{
"state_after": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.167807\ninst✝ : Monoid N\nC : FreeProduct M → Prop\nm : FreeProduct M\nh_one : C 1\nh_of : ∀ (i : ι) (m : M i), C (↑of m)\nh_mul : ∀ (x y : FreeProduct M), C x → C y → C (x * y)\nS : Submonoid (FreeProduct M) :=\n { ... | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/MetricSpace/Algebra.lean | lipschitzWith_lipschitz_const_mul_edist | [] | [
71,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | map_mul_left_nhds | [] | [
821,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
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