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/ENat/Basic.lean | ENat.coe_mul | [] | [
91,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.mul_eq_map₂ | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
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Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mker_prod_map | [
{
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"state_before": "M : Type u_3\nN : Type u_4\nP : Type ?u.142244\ninst✝⁵ : MulOneClass M\ninst✝⁴ : MulOneClass N\ninst✝³ : MulOneClass P\nS : Submonoid M\nA : Type ?u.142265\ninst✝² : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.142289\nmc : MonoidHomClass F M N\nM' ... | [
1227,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.LeftExactFunctor.forget_obj_of | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.176256\nγ : Type ?u.176259\ninst✝ : DecidableEq α\ns t u : Multiset α\na b : α\nx✝ : a ∈ s ∧ a ∈ t\nh₁ : a ∈ s\nh₂ : a ∈ t\n⊢ a ∈ a ::ₘ erase s a ∩ erase t a",
"state_before": "α : Type u_1\nβ : Type ?u.176256\nγ : Type ?u.176259\ninst✝ : DecidableEq α\ns t u : Mu... | [
1794,
71
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1792,
1
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Mathlib/Algebra/Order/WithZero.lean | inv_mul_lt_of_lt_mul₀ | [
{
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"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nh : x < y * z\n⊢ y⁻¹ * x < z",
"tactic": "rw [mul_comm] at *"
},
{
"state_after"... | [
200,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.lipschitz_comp | [
{
"state_after": "case h\nF : Type ?u.376927\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nf✝ g✝ : α →ᵇ β\nx✝ : α\nC✝ : ℝ\nG : β → γ\nC : ℝ≥0\nH : LipschitzWith C G\nf g : α →ᵇ β\nx : α\n⊢ dist (↑f x) (↑g x) ≤ dist f g",
"state_b... | [
430,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Equalizer.Sieve.w | [
{
"state_after": "case w\nC : Type u₁\ninst✝ : Category C\nP : Cᵒᵖ ⥤ Type (max v₁ u₁)\nX : C\nR : Presieve X\nS : Sieve X\n⊢ ∀ (j : Discrete ((Y : C) × (Z : C) × (_ : Z ⟶ Y) × { f' // S.arrows f' })),\n (forkMap P S.arrows ≫ firstMap P S) ≫ limit.π (Discrete.functor fun f => P.obj f.snd.fst.op) j =\n (f... | [
890,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
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Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.nonempty | [] | [
117,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.erase_zero | [
{
"state_after": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\n⊢ Finsupp.erase n 0 = 0",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\n⊢ (erase n 0).toFinsupp = 0.toFinsupp",
"tactic": "simp"
},
{
"state_after": "no goals",
"s... | [
1058,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.exists_finset_coe | [
{
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"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nh : Set.Finite s\n⊢ ∃ s', ↑s' = s",
"tactic": "cases h"
},
{
"state_after": "no goals",
"sta... | [
123,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.isMultiplicative_zeta | [
{
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"state_before": "R : Type ?u.536824\n⊢ ↑ζ 1 = 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "R : Type ?u.536824\n⊢ ∀ {m n : ℕ}, m ≠ 0 → n ≠ 0 → coprime m n → ↑ζ (m * n) = ↑ζ m * ↑ζ n",
"tactic": "simp (config := { contextual := true })"... | [
820,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_finset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1733020\nγ : Type ?u.1733023\nδ : Type ?u.1733026\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSingletonClass α\ns : Finset α\nf : α → ℝ≥0∞\n⊢ (∫⁻ (x : α) in ↑s, f x ∂μ) = ∑ x in s, f x * ↑↑μ {x}",
"tactic": "simp only... | [
1479,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
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Mathlib/Computability/Reduce.lean | OneOneEquiv.congr_right | [] | [
284,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.ext | [] | [
133,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Std/Data/RBMap/Alter.lean | Std.RBNode.modify_eq_alter | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\nf : α → α\nt : RBNode α\n⊢ (match zoom cut t Path.root with\n | (nil, snd) => t\n | (node c a x b, path) => Path.fill path (node c a (f x) b)) =\n match zoom cut t Path.root with\n | (nil, path) =>\n match Option.map f none with\n | none ... | [
380,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
379,
1
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Std/Data/List/Lemmas.lean | List.nil_suffix | [] | [
1574,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1574,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essSup_smul_measure | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝ : CompleteLattice β\nf : α → β\nc : ℝ≥0∞\nhc : c ≠ 0\n⊢ limsup f (Measure.ae (c • μ)) = limsup f (Measure.ae μ)",
"state_before": "α : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nμ ν : MeasureTheory.... | [
219,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Std/Data/List/Lemmas.lean | List.get?_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ get? l 0 = head? l",
"tactic": "cases l <;> rfl"
}
] | [
542,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
542,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.zneg_succ | [
{
"state_after": "case neg\nα : Type ?u.658662\na✝ : PosNum\n⊢ -succ (neg a✝) = pred (-neg a✝)",
"state_before": "α : Type ?u.658662\nn : ZNum\n⊢ -succ n = pred (-n)",
"tactic": "cases n <;> try { rfl }"
},
{
"state_after": "case neg\nα : Type ?u.658662\na✝ : PosNum\n⊢ Num.toZNum (pred' a✝) = pr... | [
1089,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableAt_const | [] | [
1079,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_mono | [] | [
233,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.indicatorConstLp_coeFn_mem | [] | [
741,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_opow_mul_add | [
{
"state_after": "b u v w : Ordinal\nhb : 1 < b\nhv : v ≠ 0\nhvb : v < b\nhw : w < b ^ u\nhne' : b ^ u * v + w ≠ 0\n⊢ log b (b ^ u * v + w) = u",
"state_before": "b u v w : Ordinal\nhb : 1 < b\nhv : v ≠ 0\nhvb : v < b\nhw : w < b ^ u\n⊢ log b (b ^ u * v + w) = u",
"tactic": "have hne' := (opow_mul_add_p... | [
422,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
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Mathlib/Data/Prod/Basic.lean | Prod.swap_leftInverse | [] | [
188,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.limitRecOn_limit | [
{
"state_after": "α : Type ?u.97233\nβ : Type ?u.97236\nγ : Type ?u.97239\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nC : Ordinal → Sort u_2\no : Ordinal\nH₁ : C 0\nH₂ : (o : Ordinal) → C o → C (succ o)\nH₃ : (o : Ordinal) → IsLimit o → ((o' : Ordinal) → o' < o → C o') → C o\nh : IsLimit o\n⊢ (H₃ o (... | [
341,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_map | [
{
"state_after": "G : Type u_1\nG' : Type ?u.242723\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.242732\ninst✝² : AddGroup A\nH K✝ : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.242759\ninst✝ : Group P\nf : G →* N\nK : Subgroup G\ny : N\n⊢ (∃ x x_1, ↑f x = y) ↔ ∃ x, x ∈ K ∧ ↑f x = y",... | [
1414,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1413,
1
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_unique | [] | [
186,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_eq_coe | [] | [
131,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | deriv_arctan | [] | [
157,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.div | [] | [
353,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_injective | [] | [
159,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/EisensteinCriterion.lean | Polynomial.EisensteinCriterionAux.isUnit_of_natDegree_eq_zero_of_isPrimitive | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\np q : R[X]\nhu : IsPrimitive (p * q)\nhpm : natDegree p = 0\n⊢ IsUnit (coeff p 0)",
"state_before": "R : Type u_1\ninst✝ : CommRing R\np q : R[X]\nhu : IsPrimitive (p * q)\nhpm : natDegree p = 0\n⊢ IsUnit p",
"tactic": "rw [eq_C_of_degree_le_zero (natD... | [
83,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_mul_left_ball | [] | [
305,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_boole | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.22144\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✝² : Monoid M\ninst✝¹ : AddMonoid A\nP : Prop\ninst✝ : Decidable P\na : M\n⊢ (a ^ if P then 1 else 0) = if P then a else 1",
"tactic": "s... | [
155,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.apply | [] | [
61,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Order/Basic.lean | countable_setOf_covby_right | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n✝ : Nontrivial α\n⊢ Set.Countable {x | ∃ y, x ⋖ y}",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝... | [
1411,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.lipschitz_infNndist_pt | [] | [
669,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.map_id | [] | [
146,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_iSup | [] | [
1477,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_le_of_ae_lt | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.100460\nγ :... | [
438,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Algebra/AddTorsor.lean | vadd_vsub_assoc | [
{
"state_after": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\ng : G\np1 p2 : P\n⊢ g +ᵥ p1 -ᵥ p2 +ᵥ p2 = g + (p1 -ᵥ p2) +ᵥ p2",
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"tactic": "apply ... | [
122,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Limits.lean | CategoryTheory.lift_comp_preservesLimitsIso_hom | [
{
"state_after": "case w\nC : Type u₁\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nG : C ⥤ D\nJ : Type w\ninst✝³ : Category J\nF : J ⥤ C\ninst✝² : PreservesLimit F G\ninst✝¹ : HasLimit F\ninst✝ : HasLimit (F ⋙ G)\nt : Cone F\nj✝ : J\n⊢ (G.map (limit.lift F t) ≫ (preservesLimitIso G F).hom) ≫ limit.π ... | [
80,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Trident.IsLimit.homIso_natural | [] | [
402,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.LiftRel.swap | [
{
"state_after": "case inl\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type u_2\nr r₁ r₂ : α → γ → Prop\ns s₁ s₂ : β → δ → Prop\na : α\nb : β\nc : γ\nd : δ\na✝¹ : α\nc✝ : γ\na✝ : r a✝¹ c✝\n⊢ LiftRel s r (swap (inl a✝¹)) (swap (inl c✝))\n\ncase inr\nα : Type u\nα' : Type w\nβ : Type v\nβ... | [
447,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
11
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_top | [] | [
901,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
11
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.coe_top | [] | [
345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Data/List/Basic.lean | List.drop_sizeOf_le | [
{
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2197,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2192,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_Ioc | [] | [
2550,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2549,
1
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Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement_top_singleton | [] | [
115,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_eq' | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.420411\nγ : Type ?u.420414\ninst✝ : DecidableEq α\ns ... | [
2574,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2571,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_upper_bounds_eq_csSup | [] | [
595,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_algebraMap | [
{
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111,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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src/lean/Init/SimpLemmas.lean | Eq.mpr_prop | [] | [
62,
72
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
62,
1
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Mathlib/Computability/Partrec.lean | Partrec.map_encode_iff | [] | [
491,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_le_set_union | [] | [
466,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Matrix.toEuclideanLin_eq_toLin | [] | [
1002,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.eq | [] | [
86,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
11
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.compContinuous_apply | [] | [
384,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.cliqueFree_of_chromaticNumber_lt | [] | [
459,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.orderIsoIicCoe_symm_apply_coe | [] | [
1804,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cmp_to_nat | [
{
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"state_before": "α : Type ?u.145219\na b : PosNum\n⊢ Ordering.casesOn (cmp (bit0 a... | [
185,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | StrictMonoOn.exists_deriv_lt_slope_aux | [
{
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1064,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | mul_self_zpow | [
{
"state_after": "α : Type ?u.125817\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✝ : Group G\nb : G\nm : ℤ\n⊢ b ^ 1 * b ^ m = b ^ (m + 1)",
"state_before": "α : Type ?u.125817\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\n... | [
229,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_right_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.81353\nα : Type u_1\nβ : Type ?u.81359\nπ : ι → Type ?u.81364\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ⇔ b ⇔ c = a ⇔ c ⇔ b",
"tactic": "simp_rw [bihimp_assoc, bihimp_comm]"
}
] | [
637,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean | Polynomial.exists_approx_polynomial_aux | [
{
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"state_before": "Fq : Ty... | [
101,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/CategoryTheory/Functor/Const.lean | CategoryTheory.Functor.const.unop_functor_op_obj_map | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.IsProj.eq_conj_prod_map' | [
{
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441,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.le_def | [] | [
60,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Computability/Reduce.lean | ComputablePred.computable_of_oneOneReducible | [] | [
147,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_image_preimage | [
{
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"tactic": "rw [image_preimage_eq_inter_range, preimage_inter_range]"
}
] | [
852,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.lsmul_apply | [] | [
398,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.Integrable.indicator | [] | [
273,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.zero_imK | [] | [
179,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
9
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zero_zpow | [
{
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"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nh : ↑n ≠ 0\n⊢ 0 ^ ↑n = 0",
"tactic": "rw [z... | [
92,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_univ | [] | [
1564,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
9
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_sup | [] | [
659,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | isUnit_exp_of_mem_ball | [] | [
304,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Deprecated/Subfield.lean | isSubfield_iUnion_of_directed | [] | [
158,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.equiv_relation | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : IsConnected J\nr : J → J → Prop\nhr : _root_.Equivalence r\nh : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → r j₁ j₂\nz : ∀ (j : J), r (Classical.arbitrary J) j\n⊢ ∀ (j₁ j₂ : J), r j₁ j₂",
"state_before": "J : Type u₁\ninst✝² : Cate... | [
306,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.coe_toLowerSet | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.sumToIter_Xr | [] | [
184,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.map_le_lfp | [] | [
76,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.le_def | [] | [
309,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.eq_of_le | [] | [
1005,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.mul_def | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Bool/Count.lean | List.Chain'.length_sub_one_le_two_mul_count_bool | [
{
"state_after": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ length l - 1 ≤ if Even (length l) then length l else if (some b == head? l) = true then length l + 1 else length l - 1",
"state_before": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ length l - 1 ≤ 2 * cou... | [
126,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.ite | [] | [
624,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
11
] |
Mathlib/Order/Zorn.lean | zorn_subset | [] | [
192,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.trans_refl | [
{
"state_after": "case h.h\nF : Type ?u.83017\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.83026\nδ : Type ?u.83029\ninst✝² : LE α\ninst✝¹ : LE β\ninst✝ : LE γ\ne : α ≃o β\nx : α\n⊢ ↑(trans e (refl β)) x = ↑e x",
"state_before": "F : Type ?u.83017\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.83026\nδ : Type ?u.8302... | [
918,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/GroupTheory/Solvable.lean | derivedSeries_le_map_derivedSeries | [
{
"state_after": "case zero\nG : Type u_1\nG' : Type u_2\ninst✝¹ : Group G\ninst✝ : Group G'\nf : G →* G'\nhf : Function.Surjective ↑f\n⊢ derivedSeries G' Nat.zero ≤ map f (derivedSeries G Nat.zero)\n\ncase succ\nG : Type u_1\nG' : Type u_2\ninst✝¹ : Group G\ninst✝ : Group G'\nf : G →* G'\nhf : Function.Surject... | [
92,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_nonpos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.6857\nα : Type u_1\nβ : Type ?u.6863\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\n⊢ a⁻¹ ≤ 0 ↔ a ≤ 0",
"tactic": "simp only [← not_lt, inv_pos]"
}
] | [
72,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Order/Invertible.lean | invOf_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedSemiring α\na : α\ninst✝ : Invertible a\n⊢ 0 < a * ⅟a",
"tactic": "simp only [mul_invOf_self, zero_lt_one]"
}
] | [
24,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_multiset_sum | [] | [
266,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_smul_set_iff_inv_smul_mem | [] | [
886,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Topology/Support.lean | HasCompactMulSupport.comp_left | [] | [
205,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.ofReal_norm_sub_eq_lintegral | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1306428\nδ : Type ?u.1306431\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf g : { x // x ∈ Lp β 1 }\n⊢ (∫⁻ (x : α), edist (↑↑(f - g) x) 0 ∂μ) = ∫⁻ (x : α), edist (↑↑f x ... | [
1338,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | LinearMap.hasStrictDerivAt | [] | [
91,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_comp_perm_smul_le_sum_smul | [
{
"state_after": "case h.e'_3\nι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : LinearOrderedRing α\ninst✝² : LinearOrderedAddCommGroup β\ninst✝¹ : Module α β\ninst✝ : OrderedSMul α β\ns : Finset ι\nσ : Perm ι\nf : ι → α\ng : ι → β\nhfg : MonovaryOn f g ↑s\nhσ : {x | ↑σ x ≠ x} ⊆ ↑s\n⊢ ∑ i in s, f (↑σ i) • g i... | [
158,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toLp_toSimpleFunc | [] | [
635,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
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