module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.SymmetricAlgebra.Basic | {
"line": 248,
"column": 21
} | {
"line": 248,
"column": 32
} | [
{
"pp": "case add\nR : Type u_1\nM : Type u_2\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nA : Type u_3\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nf : M →ₗ[R] A\nh : IsSymmetricAlgebra f\nmotive : A → Prop\nalgebraMap : ∀ (r : R), motive ((Algebra.algebraMap R A) r)\nι : ∀ (x : M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.TensorProduct.Decomposition | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 13
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nM : Type u_3\nS : Type u_4\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nℳ : ι → Submodule R M\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : Decomposition ℳ\ni : ι\nx y : S ⊗[R] ↥(ℳ i)\nh : (Submodule.toBaseChange ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 143,
"column": 45
} | {
"line": 143,
"column": 70
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\ninst✝⁸ : CharZero R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\nP : RootPairing ι R M N\ninst✝³ : P.IsCrystallographic\ninst✝² : P.IsReduced\nb : P.Base\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 160,
"column": 28
} | {
"line": 160,
"column": 39
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁷ : CommRing R\ninst✝⁶ : CharZero R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\nP : RootPairing ι R M N\ninst✝¹ : P.IsCrystallographic\nb : P.Base\ninst✝ : Fintype ι\ni : ↥b.support\n_i : Invol... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 173,
"column": 4
} | {
"line": 173,
"column": 15
} | [
{
"pp": "case inl.inr\nι : Type u_1\nR : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\ninst✝⁸ : CharZero R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\nP : RootPairing ι R M N\ninst✝³ : P.IsCrystallographic\ninst✝² : P.IsReduced\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 15
} | [
{
"pp": "case inr\nι : Type u_1\nR : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\ninst✝⁸ : CharZero R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\nP : RootPairing ι R M N\ninst✝³ : P.IsCrystallographic\ninst✝² : P.IsReduced\nb :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 194,
"column": 6
} | {
"line": 194,
"column": 80
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 207,
"column": 4
} | {
"line": 207,
"column": 16
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | set μ := χ x | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 209,
"column": 39
} | {
"line": 209,
"column": 50
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Hydra | {
"line": 70,
"column": 4
} | {
"line": 71,
"column": 11
} | [
{
"pp": "case refine_1\nα : Type u_1\nr : α → α → Prop\ninst✝¹ : DecidableEq α\ninst✝ : Std.Irrefl r\ns t u : Multiset α\na : α\nhr : ∀ (a' : α), ¬r a' a → a' ∉ u\nb : α\nh : (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) b a\nhe : count b (s + {a}) = count b (t + u)\n⊢ count b s = count b t",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 219,
"column": 54
} | {
"line": 219,
"column": 65
} | [
{
"pp": "case h\nι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Hydra | {
"line": 81,
"column": 35
} | {
"line": 81,
"column": 58
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nx' x : α\nh✝ : r x' x\na : α\nh : a ∈ {x'}\n⊢ r a x",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Multiset",
"id",
"Multiset.instSingleton",
"Multiset.instMembership",
"Multiset.mem_singleton",
"If... | rwa [mem_singleton.1 h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Logic.Hydra | {
"line": 81,
"column": 35
} | {
"line": 81,
"column": 58
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nx' x : α\nh✝ : r x' x\na : α\nh : a ∈ {x'}\n⊢ r a x",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Multiset",
"id",
"Multiset.instSingleton",
"Multiset.instMembership",
"Multiset.mem_singleton",
"If... | rwa [mem_singleton.1 h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Hydra | {
"line": 81,
"column": 35
} | {
"line": 81,
"column": 58
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nx' x : α\nh✝ : r x' x\na : α\nh : a ∈ {x'}\n⊢ r a x",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Multiset",
"id",
"Multiset.instSingleton",
"Multiset.instMembership",
"Multiset.mem_singleton",
"If... | rwa [mem_singleton.1 h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 51
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Hydra | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 20
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Irrefl r\ns : Multiset α\n⊢ ¬CutExpand r s 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"Relation.CutExpand",
"Multiset",
"id",
"Multiset.instMemb... | rw [cutExpand_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 55,
"column": 6
} | {
"line": 55,
"column": 66
} | [
{
"pp": "n m a : ℕ\nha : m - n ∣ a\np : ℕ\npp : Prime p\nhn : p ∣ n * a + 1\nhm : p ∣ m * a + 1\n⊢ p ∣ (m - n) * a",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 41
} | [
{
"pp": "n m a : ℕ\nha : m - n ∣ a\np : ℕ\npp : Prime p\nhn : p ∣ n * a + 1\nhm : p ∣ m * a + 1\nthis✝ : p ∣ (m - n) * a\nthis : p ∣ a\n⊢ p = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 29
} | [
{
"pp": "m : ℕ\na : Fin m → ℕ\ni : Fin m\nh₁ : a i < supOfSeq a\nh₂ : supOfSeq a ≤ (↑i + 1) * (supOfSeq a)! + 1\n⊢ a i < coprimes a i",
"usedConstants": [
"id",
"Nat",
"LT.lt",
"_private.Mathlib.Logic.Godel.GodelBetaFunction.0.Nat.coprimes",
"instLTNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 240,
"column": 6
} | {
"line": 240,
"column": 66
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 95,
"column": 10
} | {
"line": 95,
"column": 46
} | [
{
"pp": "m✝ m : ℕ\na : Fin m → ℕ\ni j : Fin m\nhij : i ≠ j\nltij : i < j\nhja : ↑j < supOfSeq a\n⊢ ↑j + 1 - (↑i + 1) ≤ supOfSeq a",
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 108,
"column": 8
} | {
"line": 108,
"column": 19
} | [
{
"pp": "m : ℕ\nl : List ℕ\n⊢ (↑Finset.univ).Pairwise (Function.onFun Coprime (coprimes fun x ↦ l[x]))",
"usedConstants": [
"Eq.mpr",
"Nat.Coprime",
"Finset.univ",
"Finset.coe_univ",
"Function.onFun",
"congrArg",
"Finset",
"Set.univ",
"id",
"Set.Pa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 38
} | [
{
"pp": "l : List ℕ\ni : Fin l.length\n⊢ (unbeta l).beta ↑i = l[i]",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Finset.univ",
"congrArg",
"Nat.unpair",
"Finset",
"Nat.beta",
"Nat.unbeta",
"Membership.mem",
"id",
"Nat.instMod",
"instHMod... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Godel.GodelBetaFunction | {
"line": 116,
"column": 10
} | {
"line": 116,
"column": 21
} | [
{
"pp": "l : List ℕ\ni : Fin l.length\n⊢ (↑Finset.univ).Pairwise (Function.onFun Coprime (coprimes fun x ↦ l[x]))",
"usedConstants": [
"Eq.mpr",
"Nat.Coprime",
"Finset.univ",
"Finset.coe_univ",
"Function.onFun",
"congrArg",
"Finset",
"Set.univ",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Hydra | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 20
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Irrefl r\np : α → Prop\nh : ∀ {a' a : α}, r a' a → p a → p a'\ns' s : Multiset α\n⊢ CutExpand r s' s → (∀ a ∈ s, p a) → ∀ a ∈ s', p a",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Classical.propDecidable",
"Membership.mem",
"Ex... | rw [cutExpand_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Logic.Hydra | {
"line": 164,
"column": 8
} | {
"line": 164,
"column": 23
} | [
{
"pp": "case cons\nα : Type u_1\nr : α → α → Prop\ninst✝ : Std.Irrefl r\na : α\ns : Multiset α\nihs : (∀ a ∈ s, Acc (CutExpand r) {a}) → Acc (CutExpand r) s\nhs : ∀ a_1 ∈ a ::ₘ s, Acc (CutExpand r) {a_1}\n⊢ Acc (CutExpand r) ({a} + s)",
"usedConstants": [
"congrArg",
"Membership.mem",
"Re... | forall_mem_cons | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 64
} | [
{
"pp": "case h.inl\nι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 247,
"column": 10
} | {
"line": 247,
"column": 81
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁹ : Field K\ninst✝⁸ : CharZero K\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module K M\ninst✝³ : AddCommGroup N\ninst✝² : Module K N\nP : RootPairing ι K M N\ninst✝¹ : P.IsRootSystem\ninst✝ : P.IsCrystallog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Cylinders | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 49
} | [
{
"pp": "ι : Type u_2\nα : ι → Type u_1\nC : (i : ι) → Set (Set (α i))\nhC : ∀ (i : ι), IsPiSystem (C i)\nhC_univ : ∀ (i : ι), univ ∈ C i\ns₁ : Finset ι\nt₁ : (i : ι) → Set (α i)\nh₁ : t₁ ∈ univ.pi C\ns₂ : Finset ι\nt₂ : (i : ι) → Set (α i)\nh₂ : t₂ ∈ univ.pi C\nhst_nonempty : ((↑s₁).pi t₁ ∩ (↑s₂).pi t₂).Nonemp... | refine ⟨s₁ ∪ s₂, fun i ↦ t₁' i ∩ t₂' i, ?_, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 281,
"column": 19
} | {
"line": 281,
"column": 36
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : Field K\ninst✝⁹ : CharZero K\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : Fintype ι\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module K M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module K N\nP : RootPairing ι K M N\ninst✝² : P.IsCrystallographic\nb : P.Base\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Cylinders | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 74
} | [
{
"pp": "case h\nι : Type u_1\nα : ι → Type u_2\nh_nonempty : Nonempty ((i : ι) → α i)\nI J : Finset ι\nS : Set ((i : ↥I) → α ↑i)\nT : Set ((i : ↥J) → α ↑i)\nhJI : J ⊆ I\nf : (i : ↥I) → α ↑i\nh_eq :\n (I.restrict fun i ↦ if hi : i ∈ I then f ⟨i, hi⟩ else h_nonempty.some i) ∈ S ↔\n (J.restrict fun i ↦ if hi ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Projective | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 35
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → MeasurableSpace (α i)\nP : (J : Finset ι) → Measure ((j : ↥J) → α ↑j)\nh : IsEmpty ((i : ι) → α i)\nhP : IsProjectiveMeasureFamily P\nI : Finset ι\n⊢ P I = 0",
"usedConstants": [
"Exists",
"IsEmpty",
"isEmpty_pi",
"Iff.mp"
... | obtain ⟨i, hi⟩ := isEmpty_pi.mp h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.MeasureTheory.Constructions.Cylinders | {
"line": 366,
"column": 4
} | {
"line": 366,
"column": 19
} | [
{
"pp": "case a\nι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → MeasurableSpace (α i)\ni : ι\nx : Set ((i : ι) → α i)\n⊢ ∀ (x_1 : (i : ι) → Set (α i)),\n (∀ (i : ι), MeasurableSet (x_1 i)) → eval i ⁻¹' x_1 i = x → ∃ s S, MeasurableSet S ∧ x = cylinder s S",
"usedConstants": [
"Set"
]
}
] | rintro t ht rfl | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.MeasureTheory.Constructions.Projective | {
"line": 86,
"column": 4
} | {
"line": 88,
"column": 17
} | [
{
"pp": "case inl\nι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → MeasurableSpace (α i)\nP : (J : Finset ι) → Measure ((j : ↥J) → α ↑j)\nI J : Finset ι\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : ↥I) → α ↑i)\nT : Set ((i : ↥J) → α ↑i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J ⊆ ... | suffices ∀ I, P I univ = 0 by
simp only [Measure.measure_univ_eq_zero] at this
simp [this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.MeasureTheory.Constructions.Projective | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 15
} | [
{
"pp": "case inl\nι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → MeasurableSpace (α i)\nP : (J : Finset ι) → Measure ((j : ↥J) → α ↑j)\nI J : Finset ι\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : ↥I) → α ↑i)\nT : Set ((i : ↥J) → α ↑i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J ⊆ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Cylinders | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 13
} | [
{
"pp": "ι : Type u_2\nX : ι → Type u_3\nm : (i : ι) → MeasurableSpace (X i)\nΔ : Set ι\n⊢ cylinderEvents Δ ≤ MeasurableSpace.pi",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 315,
"column": 44
} | {
"line": 315,
"column": 61
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : Field K\ninst✝⁹ : CharZero K\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : Fintype ι\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module K M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module K N\nP : RootPairing ι K M N\ninst✝² : P.IsCrystallographic\nb : P.Base\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 316,
"column": 4
} | {
"line": 316,
"column": 37
} | [
{
"pp": "case h₀\nι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : Field K\ninst✝⁹ : CharZero K\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : Fintype ι\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module K M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module K N\nP : RootPairing ι K M N\ninst✝² : P.IsCrystallographic\nb : P.... | exact h fun k ↦ by simp [hωu, hU] | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 319,
"column": 6
} | {
"line": 319,
"column": 30
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹⁰ : Field K\ninst✝⁹ : CharZero K\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : Fintype ι\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module K M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module K N\nP : RootPairing ι K M N\ninst✝² : P.IsCrystallographic\nb : P.Base\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 339,
"column": 40
} | {
"line": 339,
"column": 72
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁸ : Field K\ninst✝⁷ : CharZero K\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module K M\ninst✝² : AddCommGroup N\ninst✝¹ : Module K N\nP : RootPairing ι K M N\ninst✝ : P.IsCrystallographic\nb : P.Base\nw : ↥... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 345,
"column": 4
} | {
"line": 346,
"column": 46
} | [
{
"pp": "case refine_1\nι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁸ : Field K\ninst✝⁷ : CharZero K\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module K M\ninst✝² : AddCommGroup N\ninst✝¹ : Module K N\nP : RootPairing ι K M N\ninst✝ : P.IsCrystallographic\nb ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 351,
"column": 32
} | {
"line": 351,
"column": 43
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝⁸ : Field K\ninst✝⁷ : CharZero K\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module K M\ninst✝² : AddCommGroup N\ninst✝¹ : Module K N\nP : RootPairing ι K M N\ninst✝ : P.IsCrystallographic\nb : P.Base\ni : ↥... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 70
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹³ : Field K\ninst✝¹² : CharZero K\ninst✝¹¹ : DecidableEq ι\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module K M\ninst✝⁷ : AddCommGroup N\ninst✝⁶ : Module K N\nP : RootPairing ι K M N\ninst✝⁵ : P.IsRootSystem\ninst✝⁴ : P.IsCryst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 375,
"column": 70
} | {
"line": 375,
"column": 81
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹³ : Field K\ninst✝¹² : CharZero K\ninst✝¹¹ : DecidableEq ι\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module K M\ninst✝⁷ : AddCommGroup N\ninst✝⁶ : Module K N\nP : RootPairing ι K M N\ninst✝⁵ : P.IsRootSystem\ninst✝⁴ : P.IsCryst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple | {
"line": 386,
"column": 34
} | {
"line": 386,
"column": 49
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nM : Type u_3\nN : Type u_4\ninst✝¹³ : Field K\ninst✝¹² : CharZero K\ninst✝¹¹ : DecidableEq ι\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module K M\ninst✝⁷ : AddCommGroup N\ninst✝⁶ : Module K N\nP : RootPairing ι K M N\ninst✝⁵ : P.IsRootSystem\ninst✝⁴ : P.IsCryst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 108,
"column": 12
} | {
"line": 108,
"column": 23
} | [
{
"pp": "case inr.a.inl.coe.top.inr.refine_1.h\nι : Type u_1\ninst✝¹ : Preorder ι\nts : TopologicalSpace ι\nht : OrderTopology ι\ninst✝ : SecondCountableTopology ι\nx₀ : ι\nc : Set ι\nc_count : c.Countable\nhc : ts = generateFrom {s | ∃ a ∈ c, s = Ioi a ∨ s = Iio a}\nc' : Set ι\nc'_count : c'.Countable\nhc' : D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 117,
"column": 62
} | {
"line": 117,
"column": 73
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : Preorder ι\nts : TopologicalSpace ι\nht : OrderTopology ι\ninst✝ : SecondCountableTopology ι\nx₀ : ι\nc : Set ι\nc_count : c.Countable\nhc : ts = generateFrom {s | ∃ a ∈ c, s = Ioi a ∨ s = Iio a}\nc' : Set ι\nc'_count : c'.Countable\nhc' : Dense c'\nx₁ : ι := if h : ∃ x, Ioi x = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 124,
"column": 12
} | {
"line": 124,
"column": 23
} | [
{
"pp": "case inr.a.inl.coe.coe.refine_1.coe.a\nι : Type u_1\ninst✝¹ : Preorder ι\nts : TopologicalSpace ι\nht : OrderTopology ι\ninst✝ : SecondCountableTopology ι\nx₀ : ι\nc : Set ι\nc_count : c.Countable\nhc : ts = generateFrom {s | ∃ a ∈ c, s = Ioi a ∨ s = Iio a}\nc' : Set ι\nc'_count : c'.Countable\nhc' : D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.SetAlgebra | {
"line": 227,
"column": 6
} | {
"line": 227,
"column": 17
} | [
{
"pp": "case h\nα : Type u_1\n𝒜 : Set (Set α)\nh : 𝒜.Countable\nℬ : Set (Set α) := {s | s ∈ 𝒜} ∪ {s | sᶜ ∈ 𝒜}\ns : Set α\n⊢ s ∈ compl '' 𝒜 ↔ s ∈ {s | sᶜ ∈ 𝒜}",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.compl",
"Set.mem_image._simp_1",
"setOf",
"Membership.mem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.AddContent | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 15
} | [
{
"pp": "case h_dis\nα : Type u_1\nC : Set (Set α)\nG : Type u_2\ninst✝ : AddCommMonoid G\nm : AddContent G C\nι : Type u_3\na : Finset ι\nf : ι → Set α\nhf : ∀ i ∈ a, f i ∈ C\nh_dis : (↑a).PairwiseDisjoint f\nh_mem : ⋃ i ∈ a, f i ∈ C\nA : ⋃ i ∈ a, f i = ⋃₀ ↑(Finset.image f a)\n⊢ (↑(Finset.image f a)).PairwiseD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.AddContent | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 57
} | [
{
"pp": "case convert_2\nα : Type u_1\nC : Set (Set α)\nG : Type u_2\ninst✝¹ : AddCommMonoid G\nm : AddContent G C\nι : Type u_3\ninst✝ : Fintype ι\nf : ι → Set α\nhf : ∀ (i : ι), f i ∈ C\nh_dis : Pairwise (Disjoint on f)\nh_mem : ⋃ i, f i ∈ C\n⊢ (↑Finset.univ).PairwiseDisjoint f",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 157,
"column": 72
} | {
"line": 157,
"column": 83
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : Preorder ι\nts : TopologicalSpace ι\nht : OrderTopology ι\ninst✝ : SecondCountableTopology ι\nx₀ : ι\nc : Set ι\nc_count : c.Countable\nhc : ts = generateFrom {s | ∃ a ∈ c, s = Ioi a ∨ s = Iio a}\nc' : Set ι\nc'_count : c'.Countable\nhc' : Dense c'\nx₁ : ι := if h : ∃ x, Ioi x = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 164,
"column": 12
} | {
"line": 164,
"column": 23
} | [
{
"pp": "case inr.a.inr.coe.coe.refine_1.coe.a\nι : Type u_1\ninst✝¹ : Preorder ι\nts : TopologicalSpace ι\nht : OrderTopology ι\ninst✝ : SecondCountableTopology ι\nx₀ : ι\nc : Set ι\nc_count : c.Countable\nhc : ts = generateFrom {s | ∃ a ∈ c, s = Ioi a ∨ s = Iio a}\nc' : Set ι\nc'_count : c'.Countable\nhc' : D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.LiminfLimsup | {
"line": 76,
"column": 60
} | {
"line": 76,
"column": 75
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nhs : ∀ (i : ℕ), IsClosed[PseudoMetricSpace.toUniformSpace... | iInf_eq_iInter, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.AddContent | {
"line": 268,
"column": 52
} | {
"line": 268,
"column": 67
} | [
{
"pp": "α : Type u_1\nC : Set (Set α)\ns t : Set α\nI✝ : Finset (Set α)\nG : Type u_2\ninst✝ : AddCommMonoid G\nm✝ m' m : AddContent G C\nhC : IsSetSemiring C\nI : Finset (Set α)\nhI : ↑I ⊆ _root_.supClosure C\nh'I : (↑I).PairwiseDisjoint id\nhh'I : ⋃₀ ↑I ∈ _root_.supClosure C\nJ : Set α → Finset (Set α)\nhJC ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.LiminfLimsup | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 17
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nhs : ∀ (i : ℕ), IsClosed[PseudoMetricSpace.toUn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.LiminfLimsup | {
"line": 112,
"column": 6
} | {
"line": 112,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nhs : ∀ (i : ℕ), IsClosed[PseudoMetricSpace.toUniformSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 15
} | [
{
"pp": "case inl\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : TopologicalSpace ι\ninst✝ : OrderTopology ι\nα : Type u_2\nf : Filter α\nx : α → WithTop ι\nh : IsEmpty ι\n⊢ Tendsto x f (𝓝 ⊤) ↔ ∀ (i : ι), ∀ᶠ (a : α) in f, ↑i < x a",
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"WithTop.inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.WithTop | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 15
} | [
{
"pp": "case inl\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : TopologicalSpace ι\ninst✝¹ : OrderTopology ι\ninst✝ : NoMaxOrder ι\nh : IsEmpty ι\n⊢ Tendsto some atTop (𝓝 ⊤)",
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"False",
"WithTop.instPartialOrder",
"congrArg",
"T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.AddContent | {
"line": 320,
"column": 4
} | {
"line": 320,
"column": 36
} | [
{
"pp": "case refine_4\nα : Type u_1\nC : Set (Set α)\ns t : Set α\nG : Type u_2\ninst✝² : AddCommMonoid G\nm : AddContent G C\ninst✝¹ : PartialOrder G\ninst✝ : CanonicallyOrderedAdd G\nhC : IsSetSemiring C\nhs : s ∈ C\nht : t ∈ C\nhst : s ⊆ t\nh : ∑ u ∈ {s}, m u ≤ m t\n⊢ m s ≤ m t",
"usedConstants": []
}... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 101,
"column": 10
} | {
"line": 101,
"column": 54
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.SetSemiring | {
"line": 580,
"column": 17
} | {
"line": 580,
"column": 28
} | [
{
"pp": "case singleton\nα : Type u_1\nC : Set (Set α)\nι : Type u_2\nhC : IsSetRing C\ns : ι → Set α\nS : Finset ι\na✝ : ι\nhs : ∀ n ∈ {a✝}, s n ∈ C\n⊢ ⋂ i ∈ {a✝}, s i ∈ C",
"usedConstants": [
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.iInter",
"Finset",
"Membership.mem",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 101,
"column": 10
} | {
"line": 101,
"column": 54
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 101,
"column": 10
} | {
"line": 101,
"column": 54
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.SetSemiring | {
"line": 590,
"column": 2
} | {
"line": 590,
"column": 13
} | [
{
"pp": "α : Type u_1\nC : Set (Set α)\nhC : IsSetRing C\nι : Type u_2\ns : ι → Set α\nt : Finset ι\nhs : ∀ i ∈ t, s i ∈ C\n⊢ t.sup s ∈ C",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Finset",
"F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.SetSemiring | {
"line": 595,
"column": 2
} | {
"line": 595,
"column": 51
} | [
{
"pp": "α : Type u_1\nC : Set (Set α)\nι : Type u_2\ninst✝¹ : Preorder ι\ninst✝ : LocallyFiniteOrderBot ι\nhC : IsSetRing C\ns : ι → Set α\nhs : ∀ (n : ι), s n ∈ C\nn : ι\n⊢ (partialSups s) n ∈ C",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toComplete... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 104,
"column": 6
} | {
"line": 104,
"column": 49
} | [
{
"pp": "case pos\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝¹ : SigmaFinite (μ.trim hm)\nthis✝ : s.indicator μ[... | · simp only [hx, hxs, Set.indicator_of_mem] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 111,
"column": 8
} | {
"line": 111,
"column": 52
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 111,
"column": 8
} | {
"line": 111,
"column": 52
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 111,
"column": 8
} | {
"line": 111,
"column": 52
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhf_int : Integrable f μ\nhs : MeasurableSet s\nhm : m ≤ m0\nhμm this✝ : SigmaFinite (μ.trim hm)\nthis : s.indicator... | rw [Set.indicator_indicator, Set.inter_self] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 86
} | [
{
"pp": "case refine_1\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nf : α → E\ns : Set α\nhm : m ≤ m0\ninst✝ : SigmaFinite (μ.trim hm)\nhs_m : MeasurableSet s\nhf_int : Integrable f μ\nthis : SigmaFinite ... | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.AddContent | {
"line": 471,
"column": 48
} | {
"line": 471,
"column": 59
} | [
{
"pp": "α : Type u_1\nC : Set (Set α)\ns t : Set α\nI✝ : Finset (Set α)\nG✝ : Type u_2\ninst✝² : AddCommMonoid G✝\nm m' : AddContent G✝ C\ninst✝¹ : LinearOrder α\nG : Type u_3\ninst✝ : AddCommGroup G\nf : α → G\nn : ℕ\nih :\n ∀ (I : Finset (Set α)),\n ↑I ⊆ {s | ∃ u v, u ≤ v ∧ s = Set.Ioc u v} →\n (↑I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalLExpectation | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 57
} | [
{
"pp": "case pos\nΩ : Type u_1\nmΩ₀ mΩ : MeasurableSpace Ω\nP : Measure Ω\nX : Ω → ℝ≥0∞\nhm : mΩ ≤ mΩ₀\n⊢ Measurable P⁻[X|mΩ]",
"usedConstants": [
"le_refl",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"ENNReal.measurableSpace",
"MeasurableSpace",
"Mea... | exact (measurable_condLExp _ _ _).mono hm (le_refl _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Function.ConditionalLExpectation | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 57
} | [
{
"pp": "case pos\nΩ : Type u_1\nmΩ₀ mΩ : MeasurableSpace Ω\nP : Measure Ω\nX : Ω → ℝ≥0∞\nhm : mΩ ≤ mΩ₀\n⊢ Measurable P⁻[X|mΩ]",
"usedConstants": [
"le_refl",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"ENNReal.measurableSpace",
"MeasurableSpace",
"Mea... | exact (measurable_condLExp _ _ _).mono hm (le_refl _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.ConditionalLExpectation | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 57
} | [
{
"pp": "case pos\nΩ : Type u_1\nmΩ₀ mΩ : MeasurableSpace Ω\nP : Measure Ω\nX : Ω → ℝ≥0∞\nhm : mΩ ≤ mΩ₀\n⊢ Measurable P⁻[X|mΩ]",
"usedConstants": [
"le_refl",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"ENNReal.measurableSpace",
"MeasurableSpace",
"Mea... | exact (measurable_condLExp _ _ _).mono hm (le_refl _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.ConditionalExpectation.CondJensen | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 29
} | [
{
"pp": "case h\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : CompleteSpace E\nα : Type u_2\nf : α → E\nφ : E → ℝ\nm mα : MeasurableSpace α\nμ : Measure α\ns : Set E\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : HereditarilyLindelofSpace E\nhm : m ≤ mα\nhφ_cvx : ConvexOn ℝ s φ\nhφ_cont... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator | {
"line": 166,
"column": 10
} | {
"line": 166,
"column": 25
} | [
{
"pp": "α : Type u_1\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : CompleteSpace E\nf : α → E\ns : Set α\nm m₂ m0 : MeasurableSpace α\nμ : Measure α\nhm : m ≤ m0\nhm₂ : m₂ ≤ m0\ninst✝¹ : SigmaFinite (μ.trim hm)\ninst✝ : SigmaFinite (μ.trim hm₂)\nhs_m : MeasurableSet s\nhs : ∀... | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Function.ConditionalLExpectation | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 35
} | [
{
"pp": "Ω : Type u_1\nmΩ₀ mΩ : MeasurableSpace Ω\nhm : mΩ ≤ mΩ₀\nP : Measure Ω\nhσ : SigmaFinite (P.trim hm)\nX : Ω → ℝ≥0∞\n⊢ ∫⁻ (ω : Ω), P⁻[X|mΩ] ω ∂P = ∫⁻ (ω : Ω), X ω ∂P",
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"Set.univ",
"MeasureTheory.Measure.r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.CondJensen | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 51
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nα : Type u_2\nf : α → E\nm mα : MeasurableSpace α\nμ : Measure α\nhm : m ≤ mα\nhμm : ¬SigmaFinite (μ.trim hm)\n⊢ (fun x ↦ ‖μ[f | m] x‖) ≤ᶠ[ae μ] μ[fun x ↦ ‖f x‖ | m]",
"usedConstants": [
... | simp [condExp_of_not_sigmaFinite hm hμm]; aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.ConditionalExpectation.CondJensen | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 51
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nα : Type u_2\nf : α → E\nm mα : MeasurableSpace α\nμ : Measure α\nhm : m ≤ mα\nhμm : ¬SigmaFinite (μ.trim hm)\n⊢ (fun x ↦ ‖μ[f | m] x‖) ≤ᶠ[ae μ] μ[fun x ↦ ‖f x‖ | m]",
"usedConstants": [
... | simp [condExp_of_not_sigmaFinite hm hμm]; aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 159,
"column": 91
} | {
"line": 160,
"column": 75
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf : ι → α → β\np : ℝ≥0∞\nhf : UnifIntegrable f p μ\nE : Set α\nε : ℝ\nhε : 0 < ε\nδ : ℝ\nhδ_pos : 0 < δ\nhδε :\n ∀ (i : ι) (s : Set α), MeasurableSet s → μ s ≤ ENNReal.ofReal δ → eLpNorm (s.in... | by
rw [eLpNorm_indicator_eq_eLpNorm_restrict hs, μ.restrict_restrict hs] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn | {
"line": 226,
"column": 8
} | {
"line": 226,
"column": 23
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\ni : Set α\nn m : ℕ\nh✝ : n ≠ m\nh : m < n\n⊢ s.restrictNonposSeq i n ∩ s.restrictNonposSeq i m = ∅",
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Set.instInter",
"Inter.inter",
"Set.inter_... | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 17
} | [
{
"pp": "Ω : Type u_1\nm mΩ : MeasurableSpace Ω\nμ : Measure Ω\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ℝ G\ninst✝¹ : CompleteSpace G\nB : F →L[... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 378,
"column": 8
} | {
"line": 378,
"column": 19
} | [
{
"pp": "case neg.h\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhp_one : 1 ≤ p\nhp_top : p ≠ ∞\nhf : MemLp f p μ\nhmeas : StronglyMeasurable f\nε : ℝ\nhε : 0 < ε\nM : ℝ\nhMpos : 0 < M\nhM : eLpNorm ({x | M ≤ ↑‖f x‖₊}.indicator f) p μ ≤ EN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 378,
"column": 8
} | {
"line": 378,
"column": 19
} | [
{
"pp": "case neg.h\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhp_one : 1 ≤ p\nhp_top : p ≠ ∞\nhf : MemLp f p μ\nhmeas : StronglyMeasurable f\nε : ℝ\nhε : 0 < ε\nM : ℝ\nhMpos : 0 < M\nhM : eLpNorm ({x | M ≤ ↑‖f x‖₊}.indicator f) p μ ≤ EN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Basic | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 34
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nM : Type u_4\ninst✝² : AddCommGroup M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nA : Set α\nhA : MeasurableSet A\n⊢ ↑v Aᶜ = ↑v univ - ↑v A",
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 414,
"column": 2
} | {
"line": 420,
"column": 73
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\ninst✝ : Subsingleton ι\nhp_one : 1 ≤ p\nhp_top : p ≠ ∞\nf : ι → α → β\nhf : ∀ (i : ι), MemLp (f i) p μ\n⊢ UnifIntegrable f p μ",
"usedConstants": [
"Eq.mpr",
"Real.pa... | intro ε hε
by_cases hι : Nonempty ι
· obtain ⟨i⟩ := hι
obtain ⟨δ, hδpos, hδ⟩ := (hf i).eLpNorm_indicator_le hp_one hp_top hε
refine ⟨δ, hδpos, fun j s hs hμs => ?_⟩
convert! hδ s hs hμs
· exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 414,
"column": 2
} | {
"line": 420,
"column": 73
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\ninst✝ : Subsingleton ι\nhp_one : 1 ≤ p\nhp_top : p ≠ ∞\nf : ι → α → β\nhf : ∀ (i : ι), MemLp (f i) p μ\n⊢ UnifIntegrable f p μ",
"usedConstants": [
"Eq.mpr",
"Real.pa... | intro ε hε
by_cases hι : Nonempty ι
· obtain ⟨i⟩ := hι
obtain ⟨δ, hδpos, hδ⟩ := (hf i).eLpNorm_indicator_le hp_one hp_top hε
refine ⟨δ, hδpos, fun j s hs hμs => ?_⟩
convert! hδ s hs hμs
· exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn | {
"line": 399,
"column": 4
} | {
"line": 401,
"column": 12
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nf : ℕ → ℝ\nleft✝ : Antitone f\nhf₂ : Tendsto f atTop (nhds (sInf s.measureOfNegatives))\nB : ℕ → Set α\nhB : ∀ (n : ℕ), B n ∈ {B | MeasurableSet B ∧ s ≤[B] 0} ∧ ↑s (B n) = f n\nhB₁ : ∀ (n : ℕ), MeasurableSet (B n)\nhB₂ : ∀ (n : ℕ), s ≤[B n] ... | rw [← hA₃,
of_union (Set.disjoint_of_subset_right (Set.Subset.trans hD hC₁) disjoint_compl_right) hA₁
hD₁] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.VectorMeasure.Basic | {
"line": 179,
"column": 50
} | {
"line": 179,
"column": 65
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nM : Type u_3\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\nv : VectorMeasure α M\ninst✝ : T2Space M\nA B : Set α\nhA : MeasurableSet A\nhB : MeasurableSet B\nh' : ↑v (B \\ A) = 0\n⊢ ↑v (A \\ B) + ↑v (B \\ A ∪ A ∩ B) = ↑v (A \\ B) + ↑v B",
"usedConstant... | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Function.UniformIntegrable | {
"line": 452,
"column": 2
} | {
"line": 452,
"column": 17
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\ninst✝ : Finite ι\nhp_one : 1 ≤ p\nhp_top : p ≠ ∞\nf : ι → α → β\nhf : ∀ (i : ι), MemLp (f i) p μ\nn : ℕ\nhn : Nonempty (ι ≃ Fin n)\nε : ℝ\nhε : 0 < ε\ng : Fin n → α → β := f ∘ ⇑hn.so... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Basic | {
"line": 246,
"column": 65
} | {
"line": 246,
"column": 76
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nM : Type u_4\ninst✝³ : AddCommGroup M\ninst✝² : TopologicalSpace M\ninst✝¹ : T2Space M\ninst✝ : ContinuousSub M\nv : VectorMeasure α M\ns : ℕ → Set α\nhm : Antitone s\nhs : ∀ (i : ℕ), MeasurableSet (s i)\nI : ∀ (n : ℕ), ↑v (s n) = ↑v univ - ↑v (s n)ᶜ\nJ : ↑v (⋂ n, s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Basic | {
"line": 414,
"column": 40
} | {
"line": 414,
"column": 51
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nM : Type u_3\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : MeasurableSpace β\nx✝ : β\nv✝ : M\ns : Set β\nx : β\nv : M\nf : ℕ → Set β\nf_meas : ∀ (i : ℕ), MeasurableSet (f i)\nf_disj : Pairwise (Disjoint on f)\nhx : x ∈ ⋃ i, f i\nthis ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym | {
"line": 41,
"column": 6
} | {
"line": 41,
"column": 39
} | [
{
"pp": "case h.hf\nα : Type u_1\nm : MeasurableSpace α\ns : SignedMeasure α\nμ : Measure α\ninst✝ : SigmaFinite μ\nh : s.toJordanDecomposition.posPart ≪ μ ∧ s.toJordanDecomposition.negPart ≪ μ\ni : Set α\nhi : MeasurableSet i\n⊢ Integrable (fun x ↦ (s.toJordanDecomposition.posPart.rnDeriv μ x).toReal) (μ.restr... | refine Integrable.integrableOn ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym | {
"line": 41,
"column": 6
} | {
"line": 41,
"column": 39
} | [
{
"pp": "case h.hg\nα : Type u_1\nm : MeasurableSpace α\ns : SignedMeasure α\nμ : Measure α\ninst✝ : SigmaFinite μ\nh : s.toJordanDecomposition.posPart ≪ μ ∧ s.toJordanDecomposition.negPart ≪ μ\ni : Set α\nhi : MeasurableSet i\n⊢ Integrable (fun x ↦ (s.toJordanDecomposition.negPart.rnDeriv μ x).toReal) (μ.restr... | refine Integrable.integrableOn ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue | {
"line": 282,
"column": 2
} | {
"line": 284,
"column": 72
} | [
{
"pp": "case e_a.e_μ\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ns t : SignedMeasure α\nf : α → ℝ\nhf : Measurable f\nhfi : Integrable f μ\nhtμ : t.toJordanDecomposition.posPart ⟂ₘ μ ∧ t.toJordanDecomposition.negPart ⟂ₘ μ\nhadd : s = t + μ.withDensityᵥ f\nhtμ' : t ⟂ᵥ μ.toENNRealVectorMeasure\n⊢ t.toJo... | · have hfpos : Measurable fun x => ENNReal.ofReal (f x) := by fun_prop
refine eq_singularPart hfpos htμ.1 ?_
rw [toJordanDecomposition_eq_of_eq_add_withDensity hf hfi htμ' hadd] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue | {
"line": 395,
"column": 2
} | {
"line": 399,
"column": 44
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns t : SignedMeasure α\nμ : Measure α\ninst✝² : s.HaveLebesgueDecomposition μ\ninst✝¹ : t.HaveLebesgueDecomposition μ\ninst✝ : (s + t).HaveLebesgueDecomposition μ\n⊢ μ.withDensityᵥ ((s + t).rnDeriv μ) = μ.withDensityᵥ (s.rnDeriv μ + t.rnDeriv μ)",
"usedConstants"... | rw [← add_right_inj ((s + t).singularPart μ), singularPart_add_withDensity_rnDeriv_eq,
withDensityᵥ_add (integrable_rnDeriv _ _) (integrable_rnDeriv _ _), singularPart_add,
add_assoc, add_comm (t.singularPart μ), add_assoc, add_comm _ (t.singularPart μ),
singularPart_add_withDensity_rnDeriv_eq, ← add_assoc,... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosed | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 62
} | [
{
"pp": "case refine_1\nΩ : Type u_1\ninst✝⁴ : TopologicalSpace Ω\ninst✝³ : MeasurableSpace Ω\ninst✝² : OpensMeasurableSpace Ω\nι : Type u_2\nL : Filter ι\ninst✝¹ : L.IsCountablyGenerated\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nfs : ι → Ω →ᵇ ℝ≥0\nc : ℝ≥0\nfs_le_const : ∀ᶠ (i : ι) in L, ∀ᵐ (ω : Ω) ∂μ, (fs i) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosed | {
"line": 69,
"column": 4
} | {
"line": 69,
"column": 63
} | [
{
"pp": "case refine_2\nΩ : Type u_1\ninst✝⁴ : TopologicalSpace Ω\ninst✝³ : MeasurableSpace Ω\ninst✝² : OpensMeasurableSpace Ω\nι : Type u_2\nL : Filter ι\ninst✝¹ : L.IsCountablyGenerated\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nfs : ι → Ω →ᵇ ℝ≥0\nc : ℝ≥0\nfs_le_const : ∀ᶠ (i : ι) in L, ∀ᵐ (ω : Ω) ∂μ, (fs i) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosed | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 13
} | [
{
"pp": "Ω : Type u_2\nmΩ : MeasurableSpace Ω\ninst✝² : PseudoEMetricSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nF : Set Ω\nδ : ℝ\nδ_pos : 0 < δ\nx : Ω\n⊢ ‖↑((thickenedIndicator δ_pos F) x)‖ ≤ 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instL... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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