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/Algebra/IndicatorFunction.lean | Set.mulIndicator_comp_right | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nι : Type ?u.20670\nM : Type u_2\nN : Type ?u.20676\ninst✝¹ : One M\ninst✝ : One N\ns✝ t : Set α\nf✝ g✝ : α → M\na : α\ns : Set α\nf : β → α\ng : α → M\nx : β\n⊢ (if x ∈ f ⁻¹' s then g (f x) else 1) = if f x ∈ s then g (f x) else 1",
"state_before": "α : Type u_1... | [
263,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.ediam_image_le | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nx y : α\nr : ℝ≥0∞\nhf : LipschitzWith K f\ns : Set α\n⊢ ∀ (x : β), x ∈ f '' s → ∀ (y : β), y ∈ f '' s → edist x y ≤ ↑K * diam ... | [
178,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.pow_mem_pow | [] | [
416,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_biUnion₀ | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.8654\nδ : Type ?u.8657\nι : Type ?u.8660\nR : Type ?u.8663\nR' : Type ?u.8666\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : Set β\nf : β → Set α\nhs : Set.Countable s\nhd : Set.Pairwise s (AEDisjoint μ on f)\nh : ∀ (b : β), b ∈ s →... | [
165,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Topology/Support.lean | hasCompactMulSupport_iff_eventuallyEq | [] | [
176,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.mul | [] | [
1387,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_upperSemicontinuousWithinAt_antitone | [] | [
862,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasStrictFDerivAt_pi | [] | [
390,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.sub_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_1\ninst✝¹ : Ring R\ninst✝ : OrderedSemiring S\nabv : AbsoluteValue R S\na b c : R\n⊢ ↑abv (a - c) ≤ ↑abv (a - b) + ↑abv (b - c)",
"tactic": "simpa [sub_eq_add_neg, add_assoc] using abv.add_le (a - b) (b - c)"
}
] | [
156,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
11
] |
Mathlib/Logic/Basic.lean | Imp.swap | [] | [
272,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasLimit_of_created | [] | [
163,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_dirac' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1688682\nγ : Type ?u.1688685\nδ : Type ?u.1688688\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSpace α\na : α\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ (∫⁻ (a : α), f a ∂dirac a) = f a",
"tactic": "simp [lintegral_congr_ae (... | [
1371,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_lt_add_of_le_of_lt | [] | [
717,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
11
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Mathlib/Topology/Order/Basic.lean | nhds_eq_order | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : Preorder α\nt : OrderTopology α\na : α\n⊢ (⨅ (s : Set α) (_ : s ∈ {s | a ∈ s ∧ s ∈ {s | ∃ a, s = Ioi a ∨ s = Iio a}}), 𝓟 s) =\n (⨅ (b : α) (_ : b ∈ Iio a), 𝓟 (Ioi b)) ⊓ ⨅ (b : α) (_ : b ∈ Ioi a), 𝓟 (Iio b)",
"st... | [
930,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Iio_iff | [] | [
574,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.coe_toSubalgebra | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Filter.Tendsto.mul_const | [] | [
139,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.dualProdDualEquivDual_apply | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Set/Function.lean | Set.surjective_iff_surjOn_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44646\nι : Sort ?u.44649\nπ : α → Type ?u.44654\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\n⊢ Surjective f ↔ SurjOn f univ univ",
"ta... | [
852,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Data/Int/Log.lean | Int.zpow_le_iff_le_log | [] | [
184,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_succ' | [
{
"state_after": "case zero\nα : Type u\nn : ℕ\nf✝ : Fin (succ n) → α\nf : Fin (succ zero) → α\n⊢ ofFn f = concat (ofFn fun i => f (↑Fin.castSucc i)) (f (Fin.last zero))\n\ncase succ\nα : Type u\nn✝ : ℕ\nf✝ : Fin (succ n✝) → α\nn : ℕ\nIH : ∀ (f : Fin (succ n) → α), ofFn f = concat (ofFn fun i => f (↑Fin.castSuc... | [
130,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.eqOn_set_closure | [] | [
1237,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/Order/Bounds/Basic.lean | OrderBot.lowerBounds_univ | [] | [
822,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.coequalizer_preimage_image_eq_of_preimage_eq | [
{
"state_after": "X Y Z : Type u\nf g : X ⟶ Y\nπ : Y ⟶ Z\ne : f ≫ π = g ≫ π\nh : IsColimit (Cofork.ofπ π e)\nU : Set Y\nH : f ⁻¹' U = g ⁻¹' U\nlem : ∀ (x y : Y), CoequalizerRel f g x y → (x ∈ U ↔ y ∈ U)\n⊢ π ⁻¹' (π '' U) = U",
"state_before": "X Y Z : Type u\nf g : X ⟶ Y\nπ : Y ⟶ Z\ne : f ≫ π = g ≫ π\nh : I... | [
503,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.sup_left | [] | [
339,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | LinearMap.isometryOfInner_toLinearMap | [] | [
1300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_op_smul_set | [] | [
426,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.const_smul | [] | [
73,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.div2_succ | [
{
"state_after": "n : ℕ\n⊢ (match boddDiv2 n with\n | (false, m) => (true, m)\n | (true, m) => (false, succ m)).snd =\n bif (boddDiv2 n).fst then succ (boddDiv2 n).snd else (boddDiv2 n).snd",
"state_before": "n : ℕ\n⊢ div2 (succ n) = bif bodd n then succ (div2 n) else div2 n",
"tactic": "si... | [
125,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.isClosed_preimage | [] | [
150,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Matrix/Reflection.lean | Matrix.dotProductᵣ_eq | [
{
"state_after": "no goals",
"state_before": "l m✝ n : ℕ\nα : Type u_1\nβ : Type ?u.26440\ninst✝¹ : Mul α\ninst✝ : AddCommMonoid α\nm : ℕ\na b : Fin m → α\n⊢ dotProductᵣ a b = a ⬝ᵥ b",
"tactic": "simp_rw [dotProductᵣ, dotProduct, FinVec.sum_eq, FinVec.seq_eq, FinVec.map_eq,\n Function.comp_apply]"
... | [
138,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftr_coe_nat | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ shiftr ↑m ↑n = ↑(Nat.shiftr m n)",
"tactic": "cases n <;> rfl"
}
] | [
387,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Antitone.Iio | [] | [
97,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
11
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_sup | [] | [
200,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_self | [
{
"state_after": "no goals",
"state_before": "n i : ℕ\n⊢ testBit (lxor' n n) i = false",
"tactic": "simp"
}
] | [
239,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | ContinuousOn.cexp | [] | [
111,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_insert_right | [
{
"state_after": "α : Type u_3\nα' : Type ?u.38450\nβ : Type u_1\nβ' : Type ?u.38456\nγ : Type u_2\nγ' : Type ?u.38462\nδ : Type ?u.38465\nδ' : Type ?u.38468\nε : Type ?u.38471\nε' : Type ?u.38474\nζ : Type ?u.38477\nζ' : Type ?u.38480\nν : Type ?u.38483\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
195,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.self_trans_symm | [] | [
458,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Order/MinMax.lean | min_le_of_right_le | [] | [
104,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.isOpen_preimage | [] | [
146,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasurableSet.analyticSet | [
{
"state_after": "case intro.intro.intro.intro\nα✝ : Type ?u.62930\ninst✝³ : TopologicalSpace α✝\nι : Type ?u.62936\nα : Type u_1\nt : TopologicalSpace α\ninst✝² : PolishSpace α\ninst✝¹ : MeasurableSpace α\ninst✝ : BorelSpace α\ns : Set α\nhs : MeasurableSet s\nt' : TopologicalSpace α\nt't : t' ≤ t\nt'_polish :... | [
240,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.toSet_empty | [
{
"state_after": "no goals",
"state_before": "⊢ toSet ∅ = ∅",
"tactic": "simp [toSet]"
}
] | [
408,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_sign_of_nonzero | [
{
"state_after": "no goals",
"state_before": "z : Int\nhz : z ≠ 0\n⊢ natAbs (sign z) = 1",
"tactic": "rw [Int.natAbs_sign, if_neg hz]"
}
] | [
205,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
204,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.sup_limsup | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.164326\nι : Type ?u.164329\ninst✝¹ : CompleteDistribLattice α\nf : Filter β\np q : β → Prop\nu : β → α\ninst✝ : NeBot f\na : α\n⊢ (⨅ (i : Set β) (_ : i ∈ f), a ⊔ ⨆ (a : β) (_ : a ∈ i), u a) =\n ⨅ (s : Set β) (_ : s ∈ f), (⨆ (x : β) (_ : x ∈ s), a) ⊔ ⨆... | [
996,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Order/Lattice.lean | lt_sup_of_lt_right | [] | [
165,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_map_right_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.21466\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nf : γ → β\nx✝ : List α\n⊢ Forall₂ R x✝ (map f []) ↔ Forall₂ (fun a c => R a (f c)) x✝ []",
"tactic": "simp only [map, forall₂_nil_right_iff]... | [
134,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Init/Logic.lean | ExistsUnique.unique | [] | [
251,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Finset.prod_univ_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.45448\ninst✝³ : DecidableEq α\ninst✝² : Fintype α\ninst✝¹ : CommSemiring β\nδ : α → Type u_1\ninst✝ : (a : α) → DecidableEq (δ a)\nt : (a : α) → Finset (δ a)\nf : (a : α) → δ a → β\n⊢ ∏ a : α, ∑ b in t a, f a b = ∑ p in Fi... | [
194,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/NumberTheory/Liouville/Basic.lean | Liouville.irrational | [
{
"state_after": "case intro.mk'\na : ℤ\nb : ℕ\nbN0 : b ≠ 0\ncop : Nat.coprime (Int.natAbs a) b\nh : Liouville ↑(Rat.mk' a b)\n⊢ False",
"state_before": "x : ℝ\nh : Liouville x\n⊢ Irrational x",
"tactic": "rintro ⟨⟨a, b, bN0, cop⟩, rfl⟩"
},
{
"state_after": "case intro.mk'\na : ℤ\nb : ℕ\nbN0 : b... | [
72,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospan_right | [] | [
212,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.leftMulMatrix_apply | [] | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\n⊢ ((ρ_ X).inv ⊗ 𝟙 Y) ≫ (α_ X (𝟙_ C) Y).hom = 𝟙 X ⊗ (λ_ Y).inv",
"tactic": "coherence"
}
] | [
68,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Right.inv_le_one_iff | [
{
"state_after": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ a⁻¹ * a ≤ 1 * a ↔ 1 ≤ a",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 =>... | [
220,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/InformationTheory/Hamming.lean | swap_hammingDist | [
{
"state_after": "case h.h\nα : Type ?u.6729\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.6761\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y : (i : ι) → β i\n⊢ swap hammingDist x y = hammingDist x y",
"state_before": "α : Type ?u.6729\nι : Type u_1\n... | [
91,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/LocallyFinite.lean | WithTop.Ioc_coe_coe | [] | [
1133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.apply_ne | [
{
"state_after": "case intro.intro\nι : Type ?u.1651424\nα : Type u_1\nβ : Type ?u.1651430\nf g : Perm α\ns t : Set α\na b✝ x y : α\nhf : IsCycleOn f s\nhs : Set.Nontrivial s\nha : a ∈ s\nb : α\nhb : b ∈ s\nhba : b ≠ a\n⊢ ↑f a ≠ a",
"state_before": "ι : Type ?u.1651424\nα : Type u_1\nβ : Type ?u.1651430\nf ... | [
809,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
11
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_prod | [] | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.add_eq_union_left_of_le | [
{
"state_after": "ι : Type ?u.902858\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : DecidableEq α\nx y z : Multiset α\nh : y ≤ x\n⊢ z + x = z ∪ y ↔ z + x = z ∪ x ∧ x = y",
"state_before": "ι : Type ?u.902858\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α... | [
2102,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2092,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.Iic_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.295745\nγ : Type ?u.295748\nι : Sort u_2\nι' : Sort ?u.295754\nι₂ : Sort ?u.295757\nκ : ι → Sort ?u.295762\nκ₁ : ι → Sort ?u.295767\nκ₂ : ι → Sort ?u.295772\nκ' : ι' → Sort ?u.295777\ninst✝ : CompleteLattice α\nf : ι → α\nx✝ : α\n⊢ x✝ ∈... | [
2127,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2126,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.depthUB_le_two_depthLB | [] | [
65,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
63,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.nsmul_mem | [] | [
474,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_punit | [] | [
1929,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_eq | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Topology/Separation.lean | Embedding.t3Space | [] | [
1663,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1660,
11
] |
Mathlib/Data/List/AList.lean | AList.keys_replace | [] | [
197,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.bot_lt_mul | [] | [
262,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.coe_nnnorm_ae_le_snormEssSup | [] | [
730,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.Mon_tensor_mul_assoc | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nM N : Mon_ C\n⊢ ((tensor_μ C (M.X, N.X) (M.X, N.X) ⊗ 𝟙 (M.X ⊗ N.X)) ≫ ((M.mul ⊗ N.mul) ⊗ 𝟙 (M.X ⊗ N.X))) ≫\n tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) =\n (α_ (M.X ⊗ N.X) (M.X ⊗ N.X) (M... | [
445,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.sign_add_eq_of_sign_eq | [
{
"state_after": "this : 1 ≠ -1\n⊢ ∀ {m n : ℤ}, sign m = sign n → sign (m + n) = sign n",
"state_before": "⊢ ∀ {m n : ℤ}, sign m = sign n → sign (m + n) = sign n",
"tactic": "have : (1 : ℤ) ≠ -1 := by decide"
},
{
"state_after": "case ofNat.succ.ofNat.succ\nthis : 1 ≠ -1\nm n : ℕ\n⊢ sign (↑m + 1... | [
97,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Std/Data/List/Init/Lemmas.lean | List.length_eq_zero | [] | [
50,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
49,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.mkClasses_classes | [] | [
195,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | cmp_mul_pos_left | [] | [
961,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.paste_vert_iff | [] | [
544,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Std/Data/List/Lemmas.lean | List.get_cons_zero | [] | [
496,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
496,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Icc' | [] | [
2988,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2987,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_lt_lowerSemicontinuous_lintegral_ge | [
{
"state_after": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : WeaklyRegular μ\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : Measurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\n⊢ ∃ g, (∀ (x : α), ↑(f x) < g x) ∧ LowerSemicontinuous g ∧ (∫... | [
228,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.trans_isBigOWith | [
{
"state_after": "α : Type u_1\nβ : Type ?u.85733\nE : Type u_2\nF : Type u_3\nG : Type u_4\nE' : Type ?u.85745\nF' : Type ?u.85748\nG' : Type ?u.85751\nE'' : Type ?u.85754\nF'' : Type ?u.85757\nG'' : Type ?u.85760\nR : Type ?u.85763\nR' : Type ?u.85766\n𝕜 : Type ?u.85769\n𝕜' : Type ?u.85772\ninst✝¹² : Norm E... | [
486,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.inv_eq_zero | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type ?u.1713985\nk : Type u_2\ninst✝ : Field k\nφ : MvPowerSeries σ k\nh : φ⁻¹ = 0\n⊢ ↑(constantCoeff σ k) φ = 0",
"tactic": "simpa using congr_arg (constantCoeff σ k) h"
},
{
"state_after": "σ : Type u_1\nR : Type ?u.1713985\nk : T... | [
960,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.op_map_id_obj | [
{
"state_after": "no goals",
"state_before": "X Y Z : TopCat\nU : (Opens ↑X)ᵒᵖ\n⊢ (Functor.op (map (𝟙 X))).obj U = U",
"tactic": "simp"
}
] | [
182,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | lipschitzExtensionConstant_pos | [
{
"state_after": "𝕜 : Type u\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nF : Type w\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁸ : AddCommGroup F'\ninst✝⁷ : Module 𝕜 F'\ninst✝⁶ : TopologicalSpace F'\ninst✝⁵ :... | [
195,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/GroupTheory/Torsion.lean | ExponentExists.isTorsion | [
{
"state_after": "case intro.intro\nG : Type u_1\nH : Type ?u.170289\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : Group H\ng : G\nn : ℕ\nnpos : 0 < n\nhn : ∀ (g : G), g ^ n = 1\n⊢ IsOfFinOrder g",
"state_before": "G : Type u_1\nH : Type ?u.170289\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : Group H\nh : Exponen... | [
137,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.Compatible.restrict | [] | [
178,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion | [
{
"state_after": "α : Type u_2\nβ : Type ?u.742871\nγ : Type ?u.742874\nδ : Type ?u.742877\nι✝ : Type ?u.742880\nR : Type ?u.742883\nR' : Type ?u.742886\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nι : Type u_1\ninst✝¹ : Mea... | [
3622,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3608,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15791\nR : Type ?u.15794\nR' : Type ?u.15797\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\ns : ℕ → Set α\nh_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)\nh0 : (∑' (k : ℕ), ↑m (s (k + 1) \\ s k)) ≠ ⊤\ninst✝ : (i : ℕ) → DecidablePred fun x => x ∈ s i\n⊢ Tendsto (fun k => ↑m (... | [
217,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_zero' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.923765\nF : Type u_2\nG : Type ?u.923771\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\n⊢ snorm (fun x => 0) p μ = 0",
"tactic... | [
214,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.esymm_eq_sum_subtype | [] | [
183,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_div_right' | [] | [
885,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.restrict | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nh : IsPartition π\nhJ : J ≤ I\n⊢ Prepartition.iUnion (restrict π J) = ↑J",
"tactic": "simp [h.iUnion_eq, hJ]"
}
] | [
773,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
11
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.aux | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\nu a : Finset α\nhuv : ∀ (x : α), x ∈ u → ∃ y, y ∈ ∅ ∧ IsCompressed (erase u x) (erase ∅ y) 𝒜\n⊢ u = ∅",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\nu v a : Finset α\nhuv : ∀ (x : α), x ∈ u → ∃ y... | [
319,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
9
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.continuous_re | [] | [
262,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_sInf | [] | [
671,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.sup | [
{
"state_after": "α : Type ?u.284505\nβ : Type ?u.284508\nγ : Type ?u.284511\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\nH : IsNormal f\nι : Type u\ng : ι → Ordinal\ninst✝ : Nonempty ι\na : Ordinal\n⊢ f (Ordinal.sup g) ≤ a ↔ ∀ (i : ι), (f ∘ g) i ≤ a",
"state_before": "α : T... | [
1306,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_smul_vsub_vadd_left | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.178003\nP : Type u_3\nP' : Type ?u.178009\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\np₁ p₂ x :... | [
356,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Std/Logic.lean | and_iff_left_of_imp | [] | [
199,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
198,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | HasStrictFDerivAt.star | [] | [
41,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.fin_map | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.137971\nβ : Type ?u.137974\nγ : Type ?u.137977\nn : ℕ\ns : Finset ℕ\n⊢ map Fin.valEmbedding (Finset.fin n s) = filter (fun x => x < n) s",
"tactic": "simp [Finset.fin, Finset.map_map]"
}
] | [
742,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convexHull_diam | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.41107\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns✝ t s : Set E\n⊢ diam (↑(convexHull ℝ).toOrderHom s) = diam s",
"tactic": "simp only [Metric.diam, convexHull_ediam]"
}
] | [
117,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.comap_eq_lift' | [] | [
414,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.toOrderIso_eq_coe | [] | [
415,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapSMul_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.593102\nγ : Type ?u.593105\nι : Type ?u.593108\nM : Type u_2\nM' : Type ?u.593114\nN : Type ?u.593117\nP : Type ?u.593120\nG : Type u_3\nH : Type ?u.593126\nR : Type ?u.593129\nS : Type ?u.593132\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : AddCommMonoid M\ng : ... | [
1477,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1475,
1
] |
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