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/Order/Filter/AtTopBot.lean | Filter.HasAntitoneBasis.tendsto | [] | [
1771,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1769,
11
] |
src/lean/Init/SizeOfLemmas.lean | Char.sizeOf | [
{
"state_after": "case mk\nval✝ : UInt32\nvalid✝ : UInt32.isValidChar val✝\n⊢ SizeOf.sizeOf { val := val✝, valid := valid✝ } = toNat { val := val✝, valid := valid✝ } + 3",
"state_before": "a : Char\n⊢ SizeOf.sizeOf a = toNat a + 3",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_... | [
30,
35
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
29,
9
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurable_derivWithin_Ici | [
{
"state_after": "F : Type u_1\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\ninst✝² : CompleteSpace F\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\ns : Set ((fun x => F) 1)\nhs : IsClosed s\n⊢ MeasurableSet ((fun x => derivWithin f (Ici x) x) ⁻¹' s)",
"state_before": "... | [
785,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Order/PartialSups.lean | partialSups_eq_biSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nf : ℕ → α\nn : ℕ\n⊢ ↑(partialSups f) n = ⨆ (i : ℕ) (_ : i ≤ n), f i",
"tactic": "simpa only [iSup_subtype] using partialSups_eq_ciSup_Iic f n"
}
] | [
177,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isWf_min_singleton | [] | [
633,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Fintype/Sort.lean | finSumEquivOfFinset_inl | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_eq_zero_of_nmem_periodicPts | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21228\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhx : ¬x ∈ periodicPts f\n⊢ minimalPeriod f x = 0",
"tactic": "simp only [minimalPeriod, dif_neg hx]"
}
] | [
306,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.sInf_mem | [] | [
160,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.coe_dualBasis | [
{
"state_after": "case h.h\nR : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : DecidableEq ι\nb : Basis ι R M\ninst✝ : _root_.Finite ι\ni : ι\nx : M\n⊢ ↑(↑(dualBasis b) i) x = ↑(coord b i) x",
"state_before": "R : Type u\... | [
449,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Algebra/Homology/ComplexShape.lean | ComplexShape.prev_eq' | [
{
"state_after": "ι : Type u_1\nc : ComplexShape ι\ni j : ι\nh : Rel c i j\n⊢ Rel c (prev c j) j",
"state_before": "ι : Type u_1\nc : ComplexShape ι\ni j : ι\nh : Rel c i j\n⊢ prev c j = i",
"tactic": "apply c.prev_eq _ h"
},
{
"state_after": "ι : Type u_1\nc : ComplexShape ι\ni j : ι\nh : Rel c... | [
163,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_add_iff_right | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\nh : k ∣ m\nd : Nat\nx✝ : k ∣ k * d + n\ne : Nat\nhe : k * d + n = k * e\n⊢ n = k * (e - d)",
"tactic": "rw [Nat.mul_sub_left_distrib, ← he, Nat.add_sub_cancel_left]"
}
] | [
674,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
670,
11
] |
Mathlib/LinearAlgebra/Determinant.lean | Basis.det_map | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁸ : CommRing R\nM : Type u_3\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nM' : Type u_4\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nι : Type u_1\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\ne : Basis ι R M\nA : Type ?u.2708089\ninst✝¹ :... | [
630,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto | [
{
"state_after": "case mp\nΩ : Type u_2\ninst✝² : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nnonzero : μ ≠ 0\n⊢ Tendsto (fun i => normalize (μs i)) F (𝓝 (normalize μ)) ∧ Tendsto (fun... | [
491,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_cons_of_neg | [] | [
2763,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2761,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.dual | [] | [
245,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
11
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisors_one | [
{
"state_after": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ divisors 1 ↔ a✝ ∈ {1}",
"state_before": "n : ℕ\n⊢ divisors 1 = {1}",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ divisors 1 ↔ a✝ ∈ {1}",
"tactic": "simp"
}
] | [
179,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.injective | [] | [
129,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_pempty | [] | [
877,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | isSimpleGroup_of_prime_card | [
{
"state_after": "α✝ : Type u\na : α✝\ninst✝² : Group α✝\nα : Type u\ninst✝¹ : Group α\ninst✝ : Fintype α\np : ℕ\nhp : Fact (Nat.Prime p)\nh : Fintype.card α = p\nh' : 1 < p\n⊢ Nontrivial α",
"state_before": "α✝ : Type u\na : α✝\ninst✝² : Group α✝\nα : Type u\ninst✝¹ : Group α\ninst✝ : Fintype α\np : ℕ\nhp ... | [
447,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.LEquiv.onFormula_symm | [] | [
983,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Std/Data/String/Lemmas.lean | String.offsetOfPosAux_of_valid | [
{
"state_after": "l r : List Char\nn : Nat\n⊢ (if { byteIdx := utf8Len l } ≥ { byteIdx := utf8Len l + utf8Len [] } then n\n else\n if h : atEnd { data := l ++ [] ++ r } { byteIdx := utf8Len l } = true then n\n else\n let_fun this :=\n (_ :\n utf8ByteSize { data := l ++ []... | [
674,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
665,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.chaar_empty | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\neval : (Compacts G → ℝ) → ℝ := fun f => f ⊥\n⊢ chaar K₀ ⊥ = 0",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : P... | [
441,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_inter_eq_zero_of_restrict | [] | [
1668,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1667,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | refl_le_uniformity | [] | [
431,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.pi_def | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.281523\nγ : Type ?u.281526\nι : Sort ?u.281529\nι' : Sort ?u.281532\nι₂ : Sort ?u.281535\nκ : ι → Sort ?u.281540\nκ₁ : ι → Sort ?u.281545\nκ₂ : ι → Sort ?u.281550\nκ' : ι' → Sort ?u.281555\nπ : α → Type u_2\ni : Set α\ns : (a : α) → Set (π a)\nx✝ : (i : α) → π... | [
2021,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2019,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_union_of_not_mem_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.49319\nι : Type ?u.49322\nM : Type u_2\nN : Type ?u.49328\ninst✝ : MulOneClass M\ns t : Set α\nf✝ g : α → M\na : α\nh : ¬a ∈ s ∩ t\nf : α → M\n⊢ mulIndicator (s ∪ t) f a = mulIndicator s f a * mulIndicator t f a",
"tactic": "rw [← m... | [
387,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_eq_on_Ioc | [] | [
1216,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_one | [] | [
604,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Part.lean | Part.getOrElse_of_not_dom | [] | [
278,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/List/Basic.lean | List.map_id' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.133026\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\nh : ∀ (x : α), f x = x\nl : List α\n⊢ map f l = l",
"tactic": "simp [show f = id from funext h]"
}
] | [
1799,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Mathlib/Data/List/NodupEquivFin.lean | List.sublist_of_orderEmbedding_get?_eq | [
{
"state_after": "case nil\nα : Type u_1\nl l'✝ : List α\nf✝ : ℕ ↪o ℕ\nhf✝ : ∀ (ix : ℕ), get? l ix = get? l'✝ (↑f✝ ix)\nl' : List α\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), get? [] ix = get? l' (↑f ix)\n⊢ [] <+ l'\n\ncase cons\nα : Type u_1\nl l'✝ : List α\nf✝ : ℕ ↪o ℕ\nhf✝ : ∀ (ix : ℕ), get? l ix = get? l'✝ (↑f✝ ix)\nhd ... | [
141,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.continuousOn_tan | [] | [
159,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Std/Logic.lean | imp_congr | [] | [
139,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
139,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.comp_const | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_infs_infs_comm | [] | [
366,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Antitone.const_mul' | [] | [
1301,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.cos | [] | [
983,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.iff_eq_one | [] | [
91,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.unpair_lt | [
{
"state_after": "n : ℕ\nn1 : 1 ≤ n\ns : ℕ := sqrt n\n⊢ (unpair n).fst < n",
"state_before": "n : ℕ\nn1 : 1 ≤ n\n⊢ (unpair n).fst < n",
"tactic": "let s := sqrt n"
},
{
"state_after": "n : ℕ\nn1 : 1 ≤ n\ns : ℕ := sqrt n\n⊢ (if n - sqrt n * sqrt n < sqrt n then (n - sqrt n * sqrt n, sqrt n) else ... | [
104,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel.map_desc | [
{
"state_after": "case h\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝² : HasCokernel f✝\nX Y Z X' Y' Z' : C\nf : X ⟶ Y\ninst✝¹ : HasCokernel f\ng : Y ⟶ Z\nw : f ≫ g = 0\nf' : X' ⟶ Y'\ninst✝ : HasCokernel f'\ng' : Y' ⟶ Z'\nw' : f' ≫ g' = 0\np : X ⟶ X'\nq : Y ⟶ Y'\... | [
775,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | MonoidHom.ext_mint | [] | [
266,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27858\nγ : Type ?u.27861\nδ : Type ?u.27864\nδ' : Type ?u.27867\nι : Sort ?u.27870\ns✝ t u : Set α\nms : Set (MeasurableSpace α)\ns : Set α\n⊢ s ∈ ⋂₀ ((fun m => {t | MeasurableSet t}) '' ms) ↔ ∀ (m : MeasurableSpace α), m ∈ ms → Measura... | [
488,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Logic/Relation.lean | Relation.ReflTransGen.swap | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.26665\nγ : Type ?u.26668\nδ : Type ?u.26671\nr : α → α → Prop\na b c d : α\n⊢ ReflTransGen (Function.swap r) b b\n\ncase tail\nα : Type u_1\nβ : Type ?u.26665\nγ : Type ?u.26668\nδ : Type ?u.26671\nr : α → α → Prop\na b✝ c✝ d b c : α\na✝ : ReflTransGen r b✝... | [
575,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_subset_sUnion | [] | [
1071,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.cancel_right | [] | [
1351,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.map_pow | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.89298\ndec : DecidableEq α\na b : α\nf : α → β\nP : RegularExpression α\n⊢ 1 = map f P ^ 0",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.89298\ndec : DecidableEq α\na b : α\nf : α → β\nP : RegularExpression α\n⊢ map f (P ^ 0) = map f P ^... | [
422,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
11
] |
Mathlib/Algebra/Squarefree.lean | squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommMonoidWithZero R\ninst✝ : WfDvdMonoid R\nr : R\nhr : ∃ x, Irreducible x\n⊢ Squarefree r ↔ (r = 0 ∧ ¬∃ x, Irreducible x) ∨ Squarefree r",
"state_before": "R : Type u_1\ninst✝¹ : CommMonoidWithZero R\ninst✝ : WfDvdMonoid R\nr : R\nhr : ∃ x, Irreducible x\n⊢ Squaref... | [
182,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Set/MulAntidiagonal.lean | Set.MulAntidiagonal.finite_of_isWf | [] | [
141,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | Polynomial.smul_eq_map | [
{
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43,
92
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Mathlib/Algebra/Group/Basic.lean | div_mul_div_comm | [
{
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}
] | [
595,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
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Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.apply_of_ne_none | [
{
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] | [
190,
75
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189,
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Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.of_fst | [] | [
209,
6
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208,
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Mathlib/Order/LiminfLimsup.lean | Filter.IsBoundedUnder.bddAbove_range | [
{
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158,
38
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155,
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Mathlib/Algebra/Order/Group/Abs.lean | abs_max_le_max_abs_abs | [] | [
343,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Mathlib/Order/Filter/Basic.lean | Filter.frequently_map | [] | [
1825,
10
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1824,
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideEqualizer.condition | [] | [
604,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.rightInverse_symm | [] | [
437,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_bot | [] | [
577,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
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Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.exists_s_b_of_part_denom | [
{
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75,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Lattice.lean | Set.image2_iUnion_right | [
{
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1881,
54
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1879,
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Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.image_of_monotoneOn | [] | [
428,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.Measure.ofMeasurable_apply | [] | [
129,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Continuous.aestronglyMeasurable | [] | [
1267,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_mono | [] | [
1400,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_pow_id | [
{
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2036,
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioi_eq_bot_iff | [
{
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1634,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | subset_balancedCore | [
{
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215,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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src/lean/Init/Core.lean | PSigma.eta | [
{
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1056,
12
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1052,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.const_smul' | [] | [
1338,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
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Mathlib/Data/Fin/Basic.lean | Fin.castLE_castLE | [
{
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"tactic": "simp only [coe_castLE]"
}
] | [
1051,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.gen_empty_right | [] | [
81,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_biUnion_finset_le | [
{
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"state_before": "α : Type u_2\nβ ... | [
250,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.val_multiset_prod | [] | [
102,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_mk | [] | [
259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_id' | [] | [
234,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_zero_zero | [
{
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"tactic": "ext a... | [
76,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | IsOpen.measurableSet | [] | [
306,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Std/Control/ForInStep/Lemmas.lean | ForInStep.run_done | [] | [
17,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
9
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_nnnorm_prod | [] | [
631,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.le_iff | [] | [
342,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_div_assoc | [
{
"state_after": "no goals",
"state_before": "a c d : Int\ncz : c = 0\n⊢ div (a * (c * d)) c = a * div (c * d) c",
"tactic": "simp [cz, Int.mul_zero]"
},
{
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"state_before": "a c d : Int\ncz : ¬c = 0\n⊢ div (a * (c * d)) c = a * div (c * d) c",
"tactic": "rw [Int... | [
715,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
712,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.lt_succ | [
{
"state_after": "n m : ℕ\na : Fin n\n⊢ ↑a < ↑a + 1",
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"tactic": "rw [castSucc, lt_iff_val_lt_val, coe_castAdd, val_succ]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\na : Fin n\n⊢ ↑a < ↑a + 1",
"tactic": "exact lt... | [
1317,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mul_apply_antidiagonal | [] | [
1525,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.div_lt_self' | [] | [
604,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_singleton | [] | [
399,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/GameAdd.lean | Sym2.GameAdd.snd | [] | [
187,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | IsHilbertSum.linearIsometryEquiv_symm_apply | [
{
"state_after": "no goals",
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337,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
11
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Mathlib/Data/Finset/Pointwise.lean | Finset.mem_div | [] | [
553,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coe_linearMapAt_of_mem | [
{
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244,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_Iic | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : (i : ι) → DecidableEq (α i)\ninst✝¹ : (i : ι) → CanonicallyOrderedAddMonoid (α i)\ninst✝ : (i : ι) → LocallyFiniteOrder (α i)\nf : Π₀ (i : ι), α i\n⊢ card (Iic f) = ∏ i in support f, card (Iic (↑f ... | [
209,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_prod_same_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.246243\nι : Type ?u.246246\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nx₁ x₂ : α\ny : β\n⊢ dist (x₁, y) (x₂, y) = dist x₁ x₂",
"tactic": "simp [Prod.dist_eq, dist_nonneg]"
}
] | [
1761,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1760,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_of_not_mem_closure | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.284702\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.284797\... | [
566,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_exp_comp_nhds_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx y z : ℝ\nl : Filter α\nf : α → ℝ\n⊢ Tendsto (fun x => exp (f x)) l (𝓝 0) ↔ Tendsto f l atBot",
"tactic": "simp_rw [←comp_apply (f := exp), ← tendsto_comap_iff, comap_exp_nhds_zero]"
}
] | [
345,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Ioc' | [] | [
2976,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2975,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.proof_of_subsumes | [] | [
122,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.liftp_iff' | [
{
"state_after": "P : PFunctor\nα : Type u\np : α → Prop\na : P.A\nf : B P a → α\n⊢ (∃ a_1 f_1, { fst := a, snd := f } = { fst := a_1, snd := f_1 } ∧ ∀ (i : B P a_1), p (f_1 i)) ↔ ∀ (i : B P a), p (f i)",
"state_before": "P : PFunctor\nα : Type u\np : α → Prop\na : P.A\nf : B P a → α\n⊢ Liftp p { fst := a, ... | [
206,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_range_comp | [] | [
1440,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1438,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cpow | [
{
"state_after": "a b : ℝ\nn : ℕ\nr : ℂ\nh : -1 < r.re ∨ r ≠ -1 ∧ ¬0 ∈ [[a, b]]\n⊢ (∫ (x : ℝ) in a..b, ↑x ^ r) = ↑b ^ (r + 1) / (r + 1) - ↑a ^ (r + 1) / (r + 1)",
"state_before": "a b : ℝ\nn : ℕ\nr : ℂ\nh : -1 < r.re ∨ r ≠ -1 ∧ ¬0 ∈ [[a, b]]\n⊢ (∫ (x : ℝ) in a..b, ↑x ^ r) = (↑b ^ (r + 1) - ↑a ^ (r + 1)) / (... | [
348,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
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] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformContinuous.inv | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : Group α\ninst✝¹ : UniformGroup α\ninst✝ : UniformSpace β\nf : β → α\nhf : UniformContinuous f\nthis : UniformContinuous fun x => 1 / f x\n⊢ UniformContinuous fun x => (f x)⁻¹",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝³... | [
93,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.hasFDerivAt | [
{
"state_after": "no goals",
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500,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
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