module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 271,
"column": 2
} | {
"line": 271,
"column": 26
} | {
"line": 271,
"column": 27
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\nn : ℕ\n⊢ SuperpolynomialDecay l k (f * k ^ n) ↔ SuperpolynomialDecay l k f",
"ppTerm": "?m.2... | [
"α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\nn : ℕ\n⊢ SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Vitali | {
"line": 115,
"column": 6
} | {
"line": 115,
"column": 42
} | {
"line": 115,
"column": 43
} | [
{
"pp": "case inl\nα : Type u_1\nι : Type u_2\nB : ι → Set α\nt : Set ι\nδ : ι → ℝ\nτ : ℝ\nhτ : 1 < τ\nδnonneg : ∀ a ∈ t, 0 ≤ δ a\nR : ℝ\nδle : ∀ a ∈ t, δ a ≤ R\nhne : ∀ a ∈ t, (B a).Nonempty\nT : Set (Set ι) :=\n {u |\n u ⊆ t ∧\n u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c ∈ u,... | [
"case inl\nα : Type u_1\nι : Type u_2\nB : ι → Set α\nt : Set ι\nδ : ι → ℝ\nτ : ℝ\nhτ : 1 < τ\nδnonneg : ∀ a ∈ t, 0 ≤ δ a\nR : ℝ\nδle : ∀ a ∈ t, δ a ≤ R\nhne : ∀ a ∈ t, (B a).Nonempty\nT : Set (Set ι) :=\n {u |\n u ⊆ t ∧\n u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c ∈ u, (B a ∩ B c)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Hahn | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 64
} | {
"line": 91,
"column": 2
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto_nnreal_μ : ∀ (... | [
"α : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto_nnreal_μ : ∀ (s : Set α), ... | have he₂ : ∀ n, γ - (1 / 2) ^ n < d (e n) := fun n => (he n).2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.MeasureTheory.Integral.Average | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 52
} | {
"line": 206,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nhs : NullMeasurableSet s μ\nhs₀ : μ s ≠ 0\nhsc₀ : μ sᶜ ≠ 0\n⊢ ⨍⁻ (x : α), f x ∂μ ∈ openSegment ℝ≥0∞ (⨍⁻ (x : α) in s, f x ∂μ) (⨍⁻ (x : α) in sᶜ, f x ∂μ)",
"ppTerm": "?m.45",
"assigned": fals... | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nhs : NullMeasurableSet s μ\nhs₀ : μ s ≠ 0\nhsc₀ : μ sᶜ ≠ 0\n⊢ ⨍⁻ (x : α), f x ∂μ ∈ openSegment ℝ≥0∞ (⨍⁻ (x : α) in s, f x ∂μ) (⨍⁻ (x : α) in sᶜ, f x ∂μ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 13
} | {
"line": 262,
"column": 14
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\n⊢ ⨍⁻ (x : α), f x ∂μ ≤ essSup f μ",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\n⊢ ⨍⁻ (x : α), f x ∂μ ≤ essSup f μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 422,
"column": 2
} | {
"line": 422,
"column": 52
} | {
"line": 423,
"column": 4
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nf : α → E\ns : Set α\nhs : NullMeasurableSet s μ\nhs₀ : μ s ≠ 0\nhsc₀ : μ sᶜ ≠ 0\nhfi : Integrable f μ\n⊢ ⨍ (x : α), f x ∂μ ∈ openSegment ℝ (⨍ (x : α) i... | [
"α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nf : α → E\ns : Set α\nhs : NullMeasurableSet s μ\nhs₀ : μ s ≠ 0\nhsc₀ : μ sᶜ ≠ 0\nhfi : Integrable f μ\n⊢ ⨍ (x : α), f x ∂μ ∈ openSegment ℝ (⨍ (x : α) in s, f x ∂μ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 478,
"column": 2
} | {
"line": 478,
"column": 13
} | {
"line": 478,
"column": 14
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ\nhf : IntegrableOn f s μ\nhf₀ : 0 ≤ᵐ[μ.restrict s] f\n⊢ ENNReal.ofReal (⨍ (x : α) in s, f x ∂μ) = (∫⁻ (x : α) in s, ENNReal.ofReal (f x) ∂μ) / μ s",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"used... | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ\nhf : IntegrableOn f s μ\nhf₀ : 0 ≤ᵐ[μ.restrict s] f\n⊢ ENNReal.ofReal (⨍ (x : α) in s, f x ∂μ) = (∫⁻ (x : α) in s, ENNReal.ofReal (f x) ∂μ) / μ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 488,
"column": 2
} | {
"line": 488,
"column": 27
} | {
"line": 488,
"column": 28
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\nhf : AEMeasurable f (μ.restrict s)\nhf' : ∀ᵐ (x : α) ∂μ.restrict s, f x ≠ ∞\n⊢ (⨍⁻ (x : α) in s, f x ∂μ).toReal = ⨍ (x : α) in s, (f x).toReal ∂μ",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\nhf : AEMeasurable f (μ.restrict s)\nhf' : ∀ᵐ (x : α) ∂μ.restrict s, f x ≠ ∞\n⊢ (∫⁻ (x : α) in s, f x ∂μ).toReal / (μ s).toReal = ⨍ (x : α) in s, (f x).toReal ∂μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Sub | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 41
} | {
"line": 152,
"column": 42
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν ξ : Measure α\ninst✝ : IsFiniteMeasure ν\nh_le : ν ≤ μ\nh : μ - ν ≤ ξ\n⊢ μ ≤ ξ + ν",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm : MeasurableSpace α\nμ ν ξ : Measure α\ninst✝ : IsFiniteMeasure ν\nh_le : ν ≤ μ\nh : μ - ν ≤ ξ\n⊢ μ ≤ ξ + ν"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 129,
"column": 61
} | {
"line": 129,
"column": 100
} | {
"line": 131,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : μ.HaveLebesgueDecomposition ν\n⊢ ν.withDensity (μ.rnDeriv ν) + μ.singularPart ν = μ",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure... | [] | rw [add_comm, singularPart_add_rnDeriv] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 129,
"column": 61
} | {
"line": 129,
"column": 100
} | {
"line": 131,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : μ.HaveLebesgueDecomposition ν\n⊢ ν.withDensity (μ.rnDeriv ν) + μ.singularPart ν = μ",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure... | [] | rw [add_comm, singularPart_add_rnDeriv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 129,
"column": 61
} | {
"line": 129,
"column": 100
} | {
"line": 131,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : μ.HaveLebesgueDecomposition ν\n⊢ ν.withDensity (μ.rnDeriv ν) + μ.singularPart ν = μ",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure... | [] | rw [add_comm, singularPart_add_rnDeriv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 13
} | {
"line": 153,
"column": 14
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν μ' : Measure α\ninst✝¹ : μ.HaveLebesgueDecomposition ν\ninst✝ : μ'.HaveLebesgueDecomposition ν\nthis : ∀ (b : Bool), (bif b then μ else μ').HaveLebesgueDecomposition ν\n⊢ (μ + μ').HaveLebesgueDecomposition ν",
"ppTerm": "?m.20",
"assigned": false,
"u... | [
"α : Type u_1\nm : MeasurableSpace α\nμ ν μ' : Measure α\ninst✝¹ : μ.HaveLebesgueDecomposition ν\ninst✝ : μ'.HaveLebesgueDecomposition ν\nthis : ∀ (b : Bool), (bif b then μ else μ').HaveLebesgueDecomposition ν\n⊢ (μ + μ').HaveLebesgueDecomposition ν"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 519,
"column": 2
} | {
"line": 519,
"column": 37
} | {
"line": 519,
"column": 38
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ\nhμ : μ s ≠ 0\nhμ₁ : μ s ≠ ∞\nhf : IntegrableOn f s μ\n⊢ 0 < μ {x | x ∈ s ∧ ⨍ (a : α) in s, f a ∂μ ≤ f x}",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ\nhμ : μ s ≠ 0\nhμ₁ : μ s ≠ ∞\nhf : IntegrableOn f s μ\n⊢ 0 < μ {x | x ∈ s ∧ ⨍ (a : α) in s, f a ∂μ ≤ f x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 541,
"column": 2
} | {
"line": 541,
"column": 13
} | {
"line": 541,
"column": 14
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\n⊢ 0 < μ {x | f x ≤ ⨍ (a : α), f a ∂μ}",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\n⊢ 0 < μ {x | f x ≤ ⨍ (a : α), f a ∂μ}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 548,
"column": 2
} | {
"line": 548,
"column": 13
} | {
"line": 548,
"column": 14
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\n⊢ 0 < μ {x | ⨍ (a : α), f a ∂μ ≤ f x}",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\n⊢ 0 < μ {x | ⨍ (a : α), f a ∂μ ≤ f x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 37
} | {
"line": 574,
"column": 38
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, ⨍ (a : α), f a ∂μ ≤ f x",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, ⨍ (a : α), f a ∂μ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 585,
"column": 2
} | {
"line": 585,
"column": 40
} | {
"line": 586,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ 0 < μ {x | f x ≤ ∫ (a : α), f a ∂μ}",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ 0 < μ {x | f x ≤ ∫ (a : α), f a ∂μ}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 591,
"column": 2
} | {
"line": 591,
"column": 40
} | {
"line": 592,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ 0 < μ {x | ∫ (a : α), f a ∂μ ≤ f x}",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ 0 < μ {x | ∫ (a : α), f a ∂μ ≤ f x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 596,
"column": 2
} | {
"line": 596,
"column": 40
} | {
"line": 596,
"column": 41
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ ∃ x, f x ≤ ∫ (a : α), f a ∂μ",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ ∃ x, f x ≤ ∫ (a : α), f a ∂μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 600,
"column": 2
} | {
"line": 600,
"column": 40
} | {
"line": 600,
"column": 41
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ ∃ x, ∫ (a : α), f a ∂μ ≤ f x",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\n⊢ ∃ x, ∫ (a : α), f a ∂μ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 606,
"column": 2
} | {
"line": 606,
"column": 40
} | {
"line": 607,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, f x ≤ ∫ (a : α), f a ∂μ",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, f x ≤ ∫ (a : α), f a ∂μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 613,
"column": 2
} | {
"line": 613,
"column": 40
} | {
"line": 614,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, ∫ (a : α), f a ∂μ ≤ f x",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ\ninst✝ : IsProbabilityMeasure μ\nhf : Integrable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, ∫ (a : α), f a ∂μ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 627,
"column": 4
} | {
"line": 627,
"column": 83
} | {
"line": 627,
"column": 84
} | [
{
"pp": "case inl\nα : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\nhμ : μ s ≠ 0\nhμ₁ : μ s ≠ ∞\nhf : AEMeasurable f (μ.restrict s)\nh : ∫⁻ (a : α) in s, f a ∂μ = ∞\n⊢ 0 < μ {x | x ∈ s ∧ f x ≤ ⨍⁻ (a : α) in s, f a ∂μ}",
"ppTerm": "?inl",
"assigned": true,
"usedConstants"... | [
"case inl\nα : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nf : α → ℝ≥0∞\nhμ : μ s ≠ 0\nhμ₁ : μ s ≠ ∞\nhf : AEMeasurable f (μ.restrict s)\nh : ∫⁻ (a : α) in s, f a ∂μ = ∞\n⊢ ¬μ s = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 679,
"column": 2
} | {
"line": 679,
"column": 20
} | {
"line": 680,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nhμ : μ ≠ 0\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ 0 < μ {x | ⨍⁻ (a : α), f a ∂μ ≤ f x}",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nhμ : μ ≠ 0\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ 0 < μ {x | ⨍⁻ (a : α), f a ∂μ ≤ f x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 703,
"column": 2
} | {
"line": 703,
"column": 13
} | {
"line": 704,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : AEMeasurable f μ\n⊢ 0 < μ {x | f x ≤ ⨍⁻ (a : α), f a ∂μ}",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nhμ : μ ≠ 0\nhf : AEMeasurable f μ\n⊢ 0 < μ {x | f x ≤ ⨍⁻ (a : α), f a ∂μ}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 729,
"column": 2
} | {
"line": 729,
"column": 42
} | {
"line": 730,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\n⊢ 0 < μ {x | f x ≤ ∫⁻ (a : α), f a ∂μ}",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\n⊢ 0 < μ {x | f x ≤ ∫⁻ (a : α), f a ∂μ}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 735,
"column": 2
} | {
"line": 735,
"column": 42
} | {
"line": 736,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ 0 < μ {x | ∫⁻ (a : α), f a ∂μ ≤ f x}",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ 0 < μ {x | ∫⁻ (a : α), f a ∂μ ≤ f x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 405,
"column": 2
} | {
"line": 435,
"column": 91
} | {
"line": 437,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν s : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\nhs : s ⟂ₘ ν\nhadd : μ = s + ν.withDensity f\n⊢ s = μ.singularPart ν",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Eq.mpr",
"ENNReal.in... | [] | have : HaveLebesgueDecomposition μ ν := ⟨⟨⟨s, f⟩, hf, hs, hadd⟩⟩
obtain ⟨hmeas, hsing, hadd'⟩ := haveLebesgueDecomposition_spec μ ν
obtain ⟨⟨S, hS₁, hS₂, hS₃⟩, ⟨T, hT₁, hT₂, hT₃⟩⟩ := hs, hsing
rw [hadd'] at hadd
have hνinter : ν (S ∩ T)ᶜ = 0 := by
rw [compl_inter]
refine nonpos_iff_eq_zero.1 (le_trans (... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 405,
"column": 2
} | {
"line": 435,
"column": 91
} | {
"line": 437,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν s : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\nhs : s ⟂ₘ ν\nhadd : μ = s + ν.withDensity f\n⊢ s = μ.singularPart ν",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Eq.mpr",
"ENNReal.in... | [] | have : HaveLebesgueDecomposition μ ν := ⟨⟨⟨s, f⟩, hf, hs, hadd⟩⟩
obtain ⟨hmeas, hsing, hadd'⟩ := haveLebesgueDecomposition_spec μ ν
obtain ⟨⟨S, hS₁, hS₂, hS₃⟩, ⟨T, hT₁, hT₂, hT₃⟩⟩ := hs, hsing
rw [hadd'] at hadd
have hνinter : ν (S ∩ T)ᶜ = 0 := by
rw [compl_inter]
refine nonpos_iff_eq_zero.1 (le_trans (... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Integral.Average | {
"line": 740,
"column": 2
} | {
"line": 740,
"column": 42
} | {
"line": 740,
"column": 43
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\n⊢ ∃ x, f x ≤ ∫⁻ (a : α), f a ∂μ",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\n⊢ ∃ x, f x ≤ ∫⁻ (a : α), f a ∂μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 744,
"column": 2
} | {
"line": 744,
"column": 42
} | {
"line": 745,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ ∃ x, ∫⁻ (a : α), f a ∂μ ≤ f x",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\n⊢ ∃ x, ∫⁻ (a : α), f a ∂μ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 751,
"column": 2
} | {
"line": 751,
"column": 42
} | {
"line": 752,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, f x ≤ ∫⁻ (a : α), f a ∂μ",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhf : AEMeasurable f μ\nhN : μ N = 0\n⊢ ∃ x ∉ N, f x ≤ ∫⁻ (a : α), f a ∂μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 758,
"column": 2
} | {
"line": 758,
"column": 42
} | {
"line": 759,
"column": 4
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\nhN : μ N = 0\n⊢ ∃ x ∉ N, ∫⁻ (a : α), f a ∂μ ≤ f x",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [... | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nN : Set α\nf : α → ℝ≥0∞\ninst✝ : IsProbabilityMeasure μ\nhint : ∫⁻ (a : α), f a ∂μ ≠ ∞\nhN : μ N = 0\n⊢ ∃ x ∉ N, ∫⁻ (a : α), f a ∂μ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Hahn | {
"line": 159,
"column": 4
} | {
"line": 159,
"column": 53
} | {
"line": 159,
"column": 54
} | [
{
"pp": "case refine_1\nα : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto... | [
"case refine_1\nα : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto_nnreal_μ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 790,
"column": 10
} | {
"line": 790,
"column": 59
} | {
"line": 790,
"column": 59
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0)\nf_int :... | [
"α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0)\nf_int : ∀ᶠ (i : ι) ... | ← integrableOn_iff_integrable_of_support_subset A | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 633,
"column": 2
} | {
"line": 633,
"column": 57
} | {
"line": 633,
"column": 58
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nν μ : Measure α\ninst✝¹ : IsFiniteMeasure ν\ninst✝ : ν.HaveLebesgueDecomposition μ\nr : ℝ≥0∞\nhr : r ≠ ∞\nh : (r.toNNReal • ν).rnDeriv μ =ᵐ[μ] r.toNNReal • ν.rnDeriv μ\n⊢ (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μ",
"ppTerm": "?m.53",
"assigned": false,
"us... | [
"α : Type u_1\nm : MeasurableSpace α\nν μ : Measure α\ninst✝¹ : IsFiniteMeasure ν\ninst✝ : ν.HaveLebesgueDecomposition μ\nr : ℝ≥0∞\nhr : r ≠ ∞\nh : (r.toNNReal • ν).rnDeriv μ =ᵐ[μ] r.toNNReal • ν.rnDeriv μ\n⊢ (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Hahn | {
"line": 170,
"column": 4
} | {
"line": 170,
"column": 53
} | {
"line": 170,
"column": 54
} | [
{
"pp": "case refine_2\nα : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto... | [
"case refine_2\nα : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s ↦ ↑(μ s).toNNReal - ↑(ν s).toNNReal\nc : Set ℝ := d '' {s | MeasurableSet s}\nγ : ℝ := sSup c\nhμ : ∀ (s : Set α), μ s ≠ ∞\nhν : ∀ (s : Set α), ν s ≠ ∞\nto_nnreal_μ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Hahn | {
"line": 184,
"column": 20
} | {
"line": 184,
"column": 31
} | {
"line": 184,
"column": 32
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nh : IsHahnDecomposition μ ν s\n⊢ μ.restrict sᶜᶜ ≤ ν.restrict sᶜᶜ",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure",
"compl_compl",
"congrArg",
"Compl.com... | [
"α : Type u_1\nmα : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nh : IsHahnDecomposition μ ν s\n⊢ μ.restrict s ≤ ν.restrict s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 55
} | {
"line": 100,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝ : SecondCountableTopology α\n⊢ ∀ᵐ (x : α) ∂μ, ∀ᶠ (a : Set α) in v.filterAt x, 0 < μ a",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"MeasureTheory.Measure",
"... | [
"α : Type u_1\ninst✝¹ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝ : SecondCountableTopology α\ns : Set α := {x | ¬∀ᶠ (a : Set α) in v.filterAt x, 0 < μ a}\nhs : s = {x | ¬∀ᶠ (a : Set α) in v.filterAt x, 0 < μ a}\n⊢ ∀ᵐ (x : α) ∂μ, ∀ᶠ (a : Set α) in v.filterAt x, 0 < μ a"
] | set s := {x | ¬∀ᶠ a in v.filterAt x, 0 < μ a} with hs | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 726,
"column": 59
} | {
"line": 726,
"column": 70
} | {
"line": 726,
"column": 71
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : ¬μ ⟂ₘ ν\nf : ℕ → Set α\nhf₁ : ∀ (n : ℕ), MeasurableSet (f n)\nhf₂ : ∀ (n : ℕ) (t : Set α), MeasurableSet t → ((1 / (↑n + 1)) • ν) (t ∩ f n) ≤ μ (t ∩ f n)\nhf₃ : ∀ (n : ℕ) (t : Set α), Measur... | [
"α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : ¬μ ⟂ₘ ν\nf : ℕ → Set α\nhf₁ : ∀ (n : ℕ), MeasurableSet (f n)\nhf₂ : ∀ (n : ℕ) (t : Set α), MeasurableSet t → ((1 / (↑n + 1)) • ν) (t ∩ f n) ≤ μ (t ∩ f n)\nhf₃ : ∀ (n : ℕ) (t : Set α), MeasurableSet t → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 820,
"column": 21
} | {
"line": 820,
"column": 32
} | {
"line": 820,
"column": 33
} | [
{
"pp": "case hbc\nα : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0... | [
"case hbc\nα : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0)\nf_int : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 753,
"column": 6
} | {
"line": 753,
"column": 22
} | {
"line": 753,
"column": 23
} | [
{
"pp": "case neg\nα : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : ¬μ ⟂ₘ ν\nf : ℕ → Set α\nhf₁ : ∀ (n : ℕ), MeasurableSet (f n)\nhf₂ : ∀ (n : ℕ) (t : Set α), MeasurableSet t → ((1 / (↑n + 1)) • ν) (t ∩ f n) ≤ μ (t ∩ f n)\nhf₃ : ∀ (n : ℕ) (t : Set ... | [
"case neg\nα : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : ¬μ ⟂ₘ ν\nf : ℕ → Set α\nhf₁ : ∀ (n : ℕ), MeasurableSet (f n)\nhf₂ : ∀ (n : ℕ) (t : Set α), MeasurableSet t → ((1 / (↑n + 1)) • ν) (t ∩ f n) ≤ μ (t ∩ f n)\nhf₃ : ∀ (n : ℕ) (t : Set α), Measurab... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.DensityTheorem | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 42
} | {
"line": 126,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx : α\nι : Type u_2\nl : Filter ι\nw : ι → α\nδ : ι → ℝ\nxmem : ∀ᶠ (j : ι) in l... | [
"α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx : α\nι : Type u_2\nl : Filter ι\nw : ι → α\nδ : ι → ℝ\nxmem : ∀ᶠ (j : ι) in l, x ∈ closed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Monotone | {
"line": 108,
"column": 6
} | {
"line": 108,
"column": 17
} | {
"line": 108,
"column": 18
} | [
{
"pp": "f : StieltjesFunction ℝ\nx : ℝ\nhx : Tendsto (fun a ↦ f.measure a / volume a) ((vitaliFamily volume 1).filterAt x) (𝓝 (f.measure.rnDeriv volume x))\nh'x : f.measure.rnDeriv volume x < ⊤\nh''x : ¬leftLim (↑f) x ≠ ↑f x\nL1 : Tendsto (fun y ↦ (↑f y - ↑f x) / (y - x)) (𝓝[>] x) (𝓝 (f.measure.rnDeriv volu... | [
"f : StieltjesFunction ℝ\nx : ℝ\nhx : Tendsto (fun a ↦ f.measure a / volume a) ((vitaliFamily volume 1).filterAt x) (𝓝 (f.measure.rnDeriv volume x))\nh'x : f.measure.rnDeriv volume x < ⊤\nh''x : ¬leftLim (↑f) x ≠ ↑f x\nL1 : Tendsto (fun y ↦ (↑f y - ↑f x) / (y - x)) (𝓝[>] x) (𝓝 (f.measure.rnDeriv volume x).toReal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 1006,
"column": 2
} | {
"line": 1006,
"column": 57
} | {
"line": 1006,
"column": 58
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nν μ : Measure α\ninst✝¹ : SigmaFinite ν\ninst✝ : SigmaFinite μ\nr : ℝ≥0∞\nhr : r ≠ ∞\nh : (r.toNNReal • ν).rnDeriv μ =ᵐ[μ] r.toNNReal • ν.rnDeriv μ\n⊢ (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μ",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
... | [
"α : Type u_1\nm : MeasurableSpace α\nν μ : Measure α\ninst✝¹ : SigmaFinite ν\ninst✝ : SigmaFinite μ\nr : ℝ≥0∞\nhr : r ≠ ∞\nh : (r.toNNReal • ν).rnDeriv μ =ᵐ[μ] r.toNNReal • ν.rnDeriv μ\n⊢ (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Monotone | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 45
} | {
"line": 126,
"column": 46
} | [
{
"pp": "f : StieltjesFunction ℝ\nx : ℝ\nhx : Tendsto (fun a ↦ f.measure a / volume a) ((vitaliFamily volume 1).filterAt x) (𝓝 (f.measure.rnDeriv volume x))\nh'x : f.measure.rnDeriv volume x < ⊤\nh''x : ¬leftLim (↑f) x ≠ ↑f x\nL1 : Tendsto (fun y ↦ (↑f y - ↑f x) / (y - x)) (𝓝[>] x) (𝓝 (f.measure.rnDeriv volu... | [
"f : StieltjesFunction ℝ\nx : ℝ\nhx : Tendsto (fun a ↦ f.measure a / volume a) ((vitaliFamily volume 1).filterAt x) (𝓝 (f.measure.rnDeriv volume x))\nh'x : f.measure.rnDeriv volume x < ⊤\nh''x : ¬leftLim (↑f) x ≠ ↑f x\nL1 : Tendsto (fun y ↦ (↑f y - ↑f x) / (y - x)) (𝓝[>] x) (𝓝 (f.measure.rnDeriv volume x).toReal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 439,
"column": 25
} | {
"line": 439,
"column": 41
} | {
"line": 440,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\np : ℝ≥0\ns : Set α\nh : s ⊆ {x | v.limRatioMe... | [] | by simp [(hρ A)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.Monotone | {
"line": 159,
"column": 8
} | {
"line": 159,
"column": 19
} | {
"line": 159,
"column": 20
} | [
{
"pp": "f : ℝ → ℝ\nhf : Monotone f\nx : ℝ\nhx :\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[<] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x).toReal) ∧\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[>] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDer... | [
"f : ℝ → ℝ\nhf : Monotone f\nx : ℝ\nhx :\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[<] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x).toReal) ∧\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[>] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Monotone | {
"line": 185,
"column": 8
} | {
"line": 185,
"column": 19
} | {
"line": 185,
"column": 20
} | [
{
"pp": "f : ℝ → ℝ\nhf : Monotone f\nx : ℝ\nhx :\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[<] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x).toReal) ∧\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[>] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDer... | [
"f : ℝ → ℝ\nhf : Monotone f\nx : ℝ\nhx :\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[<] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x).toReal) ∧\n Tendsto (fun b ↦ (↑hf.stieltjesFunction b - f x) / (b - x)) (𝓝[>] x)\n (𝓝 (hf.stieltjesFunction.measure.rnDeriv volume x)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.VariationOnFromTo | {
"line": 277,
"column": 53
} | {
"line": 277,
"column": 64
} | {
"line": 277,
"column": 65
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\nf : α → E\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nhf : BoundedVariationOn f univ\na x : α\nhx : ContinuousWithinAt f (Ici x) x\nthis : variationOnFromTo f univ a = fun y ↦ variationOnFromTo f univ a x + va... | [
"α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\nf : α → E\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nhf : BoundedVariationOn f univ\na x : α\nhx : ContinuousWithinAt f (Ici x) x\nthis : variationOnFromTo f univ a = fun y ↦ variationOnFromTo f univ a x + variationOnFro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 525,
"column": 40
} | {
"line": 525,
"column": 82
} | {
"line": 525,
"column": 83
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht ... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht : 1 < t\nt_n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.VariationOnFromTo | {
"line": 302,
"column": 4
} | {
"line": 302,
"column": 15
} | {
"line": 302,
"column": 16
} | [
{
"pp": "case hab\nα : Type u_1\ninst✝ : LinearOrder α\nf : α → ℝ\ns : Set α\nh : LocallyBoundedVariationOn f s\nc : α\ncs : c ∈ s\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≤ y\n⊢ variationOnFromTo f s c x + f x ≤ variationOnFromTo f s c y + f y",
"ppTerm": "?hab",
"assigned": false,
"usedConst... | [
"case hab\nα : Type u_1\ninst✝ : LinearOrder α\nf : α → ℝ\ns : Set α\nh : LocallyBoundedVariationOn f s\nc : α\ncs : c ∈ s\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≤ y\n⊢ variationOnFromTo f s c x + f x ≤ variationOnFromTo f s c y + f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 542,
"column": 6
} | {
"line": 542,
"column": 86
} | {
"line": 543,
"column": 2
} | [
{
"pp": "case a\nα : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ... | [] | exact (measure_mono inter_subset_right).trans (v.measure_limRatioMeas_top hρ).le | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.EMetricSpace.VariationOnFromTo | {
"line": 306,
"column": 4
} | {
"line": 306,
"column": 15
} | {
"line": 306,
"column": 16
} | [
{
"pp": "case hab\nα : Type u_1\ninst✝ : LinearOrder α\nf : α → ℝ\ns : Set α\nh : LocallyBoundedVariationOn f s\nc : α\ncs : c ∈ s\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≤ y\n⊢ variationOnFromTo f s c x - f x ≤ variationOnFromTo f s c y - f y",
"ppTerm": "?hab",
"assigned": true,
"usedConsta... | [
"case hab\nα : Type u_1\ninst✝ : LinearOrder α\nf : α → ℝ\ns : Set α\nh : LocallyBoundedVariationOn f s\nc : α\ncs : c ∈ s\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≤ y\n⊢ variationOnFromTo f s c x ≤ variationOnFromTo f s c y - f y + f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 594,
"column": 40
} | {
"line": 594,
"column": 82
} | {
"line": 594,
"column": 83
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht ... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht : 1 < t\nt_n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 604,
"column": 4
} | {
"line": 604,
"column": 84
} | {
"line": 605,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Measure α\ninst✝ : IsLocallyFiniteMeasure ρ\nhρ : ρ ≪ μ\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht ... | [] | exact (measure_mono inter_subset_right).trans (v.measure_limRatioMeas_top hρ).le | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.ContinuousMap.StarOrdered | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 11
} | {
"line": 68,
"column": 12
} | [
{
"pp": "case h\nα : Type u_1\ninst✝⁸ : TopologicalSpace α\nR : Type u_2\ninst✝⁷ : PartialOrder R\ninst✝⁶ : NonUnitalSemiring R\ninst✝⁵ : StarRing R\ninst✝⁴ : StarOrderedRing R\ninst✝³ : TopologicalSpace R\ninst✝² : ContinuousStar R\ninst✝¹ : IsTopologicalSemiring R\ninst✝ : ContinuousSqrt R\nf g : C(α, R)\nh :... | [
"case h\nα : Type u_1\ninst✝⁸ : TopologicalSpace α\nR : Type u_2\ninst✝⁷ : PartialOrder R\ninst✝⁶ : NonUnitalSemiring R\ninst✝⁵ : StarRing R\ninst✝⁴ : StarOrderedRing R\ninst✝³ : TopologicalSpace R\ninst✝² : ContinuousStar R\ninst✝¹ : IsTopologicalSemiring R\ninst✝ : ContinuousSqrt R\nf g : C(α, R)\nh : ∀ (a : α), ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.StarOrdered | {
"line": 92,
"column": 47
} | {
"line": 92,
"column": 58
} | {
"line": 92,
"column": 59
} | [
{
"pp": "α : Type u_1\ninst✝¹⁰ : TopologicalSpace α\ninst✝⁹ : Zero α\nR : Type u_2\ninst✝⁸ : TopologicalSpace R\ninst✝⁷ : CommSemiring R\ninst✝⁶ : PartialOrder R\ninst✝⁵ : NoZeroDivisors R\ninst✝⁴ : StarRing R\ninst✝³ : StarOrderedRing R\ninst✝² : IsTopologicalSemiring R\ninst✝¹ : ContinuousStar R\ninst✝ : Star... | [
"α : Type u_1\ninst✝¹⁰ : TopologicalSpace α\ninst✝⁹ : Zero α\nR : Type u_2\ninst✝⁸ : TopologicalSpace R\ninst✝⁷ : CommSemiring R\ninst✝⁶ : PartialOrder R\ninst✝⁵ : NoZeroDivisors R\ninst✝⁴ : StarRing R\ninst✝³ : StarOrderedRing R\ninst✝² : IsTopologicalSemiring R\ninst✝¹ : ContinuousStar R\ninst✝ : StarOrderedRing ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 13
} | {
"line": 118,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nn : ℕ\nu : ℕ → α\nhu : MonotoneOn u (Iic n)\nus : ∀ i ≤ n, u i ∈ s\n⊢ ∑ i ∈ Finset.range n, edist (f (u (i + 1))) (f (u i)) ≤ eVariationOn f s",
"ppTerm": "?m.33",
"assigned": false,
"use... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nn : ℕ\nu : ℕ → α\nhu : MonotoneOn u (Iic n)\nus : ∀ i ≤ n, u i ∈ s\n⊢ ∑ i ∈ Finset.range n, edist (f (u (i + 1))) (f (u i)) ≤ eVariationOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 715,
"column": 2
} | {
"line": 715,
"column": 56
} | {
"line": 715,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝³ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\ns : Set α\nhs : MeasurableSet s\nthis : IsLocallyFiniteMeasure (μ.restrict s)\nx : α\nhx : Tendsto (fun a ↦... | [
"α : Type u_1\ninst✝³ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\ns : Set α\nhs : MeasurableSet s\nthis : IsLocallyFiniteMeasure (μ.restrict s)\nx : α\nhx : Tendsto (fun a ↦ (μ.restrict... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 803,
"column": 44
} | {
"line": 803,
"column": 70
} | {
"line": 803,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA ... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA : μ.FiniteSp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 823,
"column": 6
} | {
"line": 823,
"column": 45
} | {
"line": 823,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA ... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA : μ.FiniteSp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 832,
"column": 37
} | {
"line": 832,
"column": 55
} | {
"line": 832,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA ... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : Integrable f μ\nh'f : StronglyMeasurable f\nA : μ.FiniteSp... | ENNReal.add_halves | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 857,
"column": 38
} | {
"line": 857,
"column": 77
} | {
"line": 857,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : LocallyIntegrable f μ\nu : ℕ → Set α\nu_open :... | [
"α : Type u_1\ninst✝⁴ : PseudoMetricSpace α\nm0 : MeasurableSpace α\nμ : Measure α\nv : VitaliFamily μ\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nf : α → E\nhf : LocallyIntegrable f μ\nu : ℕ → Set α\nu_open : ∀ (n : ℕ), ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 73
} | {
"line": 124,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝¹⁹ : Semifield R\ninst✝¹⁸ : StarRing R\ninst✝¹⁷ : MetricSpace R\ninst✝¹⁶ : IsTopologicalSemiring R\ninst✝¹⁵ : ContinuousStar R\ninst✝¹⁴ : Semifield S\ninst✝¹³ : StarRing S\ninst✝¹² : MetricSpace S\ninst✝¹¹ : IsTopologicalSemiring S\ninst✝¹⁰... | [
"R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝¹⁹ : Semifield R\ninst✝¹⁸ : StarRing R\ninst✝¹⁷ : MetricSpace R\ninst✝¹⁶ : IsTopologicalSemiring R\ninst✝¹⁵ : ContinuousStar R\ninst✝¹⁴ : Semifield S\ninst✝¹³ : StarRing S\ninst✝¹² : MetricSpace S\ninst✝¹¹ : IsTopologicalSemiring S\ninst✝¹⁰ : Continuou... | have := ContinuousFunctionalCalculus.compactSpace_spectrum (R := S) a | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 15
} | {
"line": 125,
"column": 16
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝¹⁹ : Semifield R\ninst✝¹⁸ : StarRing R\ninst✝¹⁷ : MetricSpace R\ninst✝¹⁶ : IsTopologicalSemiring R\ninst✝¹⁵ : ContinuousStar R\ninst✝¹⁴ : Semifield S\ninst✝¹³ : StarRing S\ninst✝¹² : MetricSpace S\ninst✝¹¹ : IsTopologicalSemiring S\ninst✝¹⁰... | [
"R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝¹⁹ : Semifield R\ninst✝¹⁸ : StarRing R\ninst✝¹⁷ : MetricSpace R\ninst✝¹⁶ : IsTopologicalSemiring R\ninst✝¹⁵ : ContinuousStar R\ninst✝¹⁴ : Semifield S\ninst✝¹³ : StarRing S\ninst✝¹² : MetricSpace S\ninst✝¹¹ : IsTopologicalSemiring S\ninst✝¹⁰ : Continuou... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 511,
"column": 2
} | {
"line": 511,
"column": 34
} | {
"line": 511,
"column": 35
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nhf : BoundedVariationOn f s\n⊢ BoundedVariationOn (f ∘ ⇑ofDual) (⇑ofDual ⁻¹' s)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nhf : BoundedVariationOn f s\n⊢ ¬eVariationOn f s = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 168,
"column": 6
} | {
"line": 168,
"column": 86
} | {
"line": 169,
"column": 8
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²¹ : Semifield R\ninst✝²⁰ : StarRing R\ninst✝¹⁹ : MetricSpace R\ninst✝¹⁸ : IsTopologicalSemiring R\ninst✝¹⁷ : ContinuousStar R\ninst✝¹⁶ : Semifield S\ninst✝¹⁵ : StarRing S\ninst✝¹⁴ : MetricSpace S\ninst✝¹³ : IsTopologicalSemiring S\ninst✝¹²... | [
"R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²¹ : Semifield R\ninst✝²⁰ : StarRing R\ninst✝¹⁹ : MetricSpace R\ninst✝¹⁸ : IsTopologicalSemiring R\ninst✝¹⁷ : ContinuousStar R\ninst✝¹⁶ : Semifield S\ninst✝¹⁵ : StarRing S\ninst✝¹⁴ : MetricSpace S\ninst✝¹³ : IsTopologicalSemiring S\ninst✝¹² : Continuou... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 291,
"column": 4
} | {
"line": 291,
"column": 15
} | {
"line": 291,
"column": 16
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²³ : Semifield R\ninst✝²² : StarRing R\ninst✝²¹ : MetricSpace R\ninst✝²⁰ : IsTopologicalSemiring R\ninst✝¹⁹ : ContinuousStar R\ninst✝¹⁸ : Field S\ninst✝¹⁷ : StarRing S\ninst✝¹⁶ : MetricSpace S\ninst✝¹⁵ : IsTopologicalRing S\ninst✝¹⁴ : Conti... | [
"R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²³ : Semifield R\ninst✝²² : StarRing R\ninst✝²¹ : MetricSpace R\ninst✝²⁰ : IsTopologicalSemiring R\ninst✝¹⁹ : ContinuousStar R\ninst✝¹⁸ : Field S\ninst✝¹⁷ : StarRing S\ninst✝¹⁶ : MetricSpace S\ninst✝¹⁵ : IsTopologicalRing S\ninst✝¹⁴ : ContinuousStar S\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 544,
"column": 35
} | {
"line": 544,
"column": 46
} | {
"line": 544,
"column": 47
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\nf : R → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 328,
"column": 8
} | {
"line": 328,
"column": 23
} | {
"line": 328,
"column": 24
} | [
{
"pp": "case pos\nR : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²⁵ : Semifield R\ninst✝²⁴ : StarRing R\ninst✝²³ : MetricSpace R\ninst✝²² : IsTopologicalSemiring R\ninst✝²¹ : ContinuousStar R\ninst✝²⁰ : Field S\ninst✝¹⁹ : StarRing S\ninst✝¹⁸ : MetricSpace S\ninst✝¹⁷ : IsTopologicalRing S\ninst✝... | [
"case pos\nR : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²⁵ : Semifield R\ninst✝²⁴ : StarRing R\ninst✝²³ : MetricSpace R\ninst✝²² : IsTopologicalSemiring R\ninst✝²¹ : ContinuousStar R\ninst✝²⁰ : Field S\ninst✝¹⁹ : StarRing S\ninst✝¹⁸ : MetricSpace S\ninst✝¹⁷ : IsTopologicalRing S\ninst✝¹⁶ : Continu... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 338,
"column": 8
} | {
"line": 338,
"column": 88
} | {
"line": 339,
"column": 10
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²⁵ : Semifield R\ninst✝²⁴ : StarRing R\ninst✝²³ : MetricSpace R\ninst✝²² : IsTopologicalSemiring R\ninst✝²¹ : ContinuousStar R\ninst✝²⁰ : Field S\ninst✝¹⁹ : StarRing S\ninst✝¹⁸ : MetricSpace S\ninst✝¹⁷ : IsTopologicalRing S\ninst✝¹⁶ : Conti... | [
"R : Type u_1\nS : Type u_2\nA : Type u_3\np q : A → Prop\ninst✝²⁵ : Semifield R\ninst✝²⁴ : StarRing R\ninst✝²³ : MetricSpace R\ninst✝²² : IsTopologicalSemiring R\ninst✝²¹ : ContinuousStar R\ninst✝²⁰ : Field S\ninst✝¹⁹ : StarRing S\ninst✝¹⁸ : MetricSpace S\ninst✝¹⁷ : IsTopologicalRing S\ninst✝¹⁶ : ContinuousStar S\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 125,
"column": 29
} | {
"line": 125,
"column": 57
} | {
"line": 125,
"column": 58
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\ninst✝³ : StarRing A\ninst✝² : StarModule R A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousStar A\ns : Subalgebra R A\nthis : ∀ (t : Subalgebra R ... | [
"R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\ninst✝³ : StarRing A\ninst✝² : StarModule R A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousStar A\ns : Subalgebra R A\nthis : ∀ (t : Subalgebra R A), (star t)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 655,
"column": 2
} | {
"line": 655,
"column": 41
} | {
"line": 656,
"column": 4
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\na : A\nr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 656,
"column": 68
} | {
"line": 656,
"column": 79
} | {
"line": 656,
"column": 80
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\na : A\nr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 660,
"column": 2
} | {
"line": 660,
"column": 13
} | {
"line": 660,
"column": 14
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\na : A\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 669,
"column": 4
} | {
"line": 669,
"column": 43
} | {
"line": 669,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\nε : ℝ≥0∞\ns : Set α\nh : ε < eVariationOn f s\n⊢ ∃ n u, (Monotone u ∧ ∀ (i : ℕ), u i ∈ s) ∧ ε < ∑ x ∈ Finset.range n, edist (f (u (x + 1))) (f (u x))",
"ppTerm": "?m.64",
"assigned": false,
"usedCon... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\nε : ℝ≥0∞\ns : Set α\nh : ε < eVariationOn f s\n⊢ ∃ n u, (Monotone u ∧ ∀ (i : ℕ), u i ∈ s) ∧ ε < ∑ x ∈ Finset.range n, edist (f (u (x + 1))) (f (u x))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 13
} | {
"line": 664,
"column": 14
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\na : A\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 230,
"column": 23
} | {
"line": 230,
"column": 34
} | {
"line": 230,
"column": 35
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : StarRing A\ninst✝³ : IsSemitopologicalSemiring A\ninst✝² : ContinuousStar A\ninst✝¹ : Algebra R A\ninst✝ : StarModule R A\nx : A\n⊢ IsClosed[inst✝⁶] (Set.range Subtype.va... | [
"R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : StarRing A\ninst✝³ : IsSemitopologicalSemiring A\ninst✝² : ContinuousStar A\ninst✝¹ : Algebra R A\ninst✝ : StarModule R A\nx : A\n⊢ IsClosed[inst✝⁶] ↑(elemental R x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 250,
"column": 53
} | {
"line": 250,
"column": 64
} | {
"line": 250,
"column": 65
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : StarRing A\ninst✝³ : IsSemitopologicalSemiring A\ninst✝² : ContinuousStar A\ninst✝¹ : Algebra R A\ninst✝ : StarModule R A\nx y✝ : A\nhy✝ : y✝ ∈ elemental R x\nP : (u : A)... | [
"R : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Semiring A\ninst✝⁴ : StarRing A\ninst✝³ : IsSemitopologicalSemiring A\ninst✝² : ContinuousStar A\ninst✝¹ : Algebra R A\ninst✝ : StarModule R A\nx y✝ : A\nhy✝ : y✝ ∈ elemental R x\nP : (u : A) → u ∈ eleme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 694,
"column": 4
} | {
"line": 694,
"column": 15
} | {
"line": 694,
"column": 16
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\nL : Filter α\nhf : BoundedVariationOn f ∅\nhL : ∀ y ∈ ∅, ∅ ∩ Ici y ∈ L\n⊢ Tendsto (fun y ↦ eVariationOn f (∅ ∩ Ici y)) L (𝓝 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
... | [
"case inl\nα : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\nL : Filter α\nhf : BoundedVariationOn f ∅\nhL : ∀ y ∈ ∅, ∅ ∩ Ici y ∈ L\n⊢ Tendsto (fun y ↦ 0) L (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 704,
"column": 2
} | {
"line": 704,
"column": 13
} | {
"line": 704,
"column": 14
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\nf : R → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 707,
"column": 2
} | {
"line": 707,
"column": 13
} | {
"line": 707,
"column": 14
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁸ : CommSemiring R\ninst✝⁷ : StarRing R\ninst✝⁶ : MetricSpace R\ninst✝⁵ : IsTopologicalSemiring R\ninst✝⁴ : ContinuousStar R\ninst✝³ : TopologicalSpace A\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra R A\ninstCFC : ContinuousFunctionalCalculus R A p\nf : R → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 716,
"column": 14
} | {
"line": 716,
"column": 29
} | {
"line": 716,
"column": 30
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nhf : BoundedVariationOn f s\nL : Filter α\nhL : ∀ y ∈ s, s ∩ Ici y ∈ L\nx₀ : α\nhx₀ : x₀ ∈ s\nε : ℝ≥0∞\nεpos : ε > 0\nδ : ℝ≥0∞\nδpos : 0 < δ\nhδ : δ < ε\nH : ∃ᶠ (x : α) in L, ε ≤ eVariatio... | [
"case zero\nα : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nhf : BoundedVariationOn f s\nL : Filter α\nhL : ∀ y ∈ s, s ∩ Ici y ∈ L\nx₀ : α\nhx₀ : x₀ ∈ s\nε : ℝ≥0∞\nεpos : ε > 0\nδ : ℝ≥0∞\nδpos : 0 < δ\nhδ : δ < ε\nH : ∃ᶠ (x : α) in L, ε ≤ eVariationOn f (s ∩ I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalAlgebra | {
"line": 147,
"column": 46
} | {
"line": 147,
"column": 57
} | {
"line": 147,
"column": 58
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁷ : CommSemiring R\ninst✝⁶ : NonUnitalSemiring A\ninst✝⁵ : Module R A\ninst✝⁴ : IsScalarTower R A A\ninst✝³ : SMulCommClass R A A\ninst✝² : TopologicalSpace A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousConstSMul R A\nx : A\ns : NonUnitalSubalgebra R A\nhs ... | [
"R : Type u_1\nA : Type u_2\ninst✝⁷ : CommSemiring R\ninst✝⁶ : NonUnitalSemiring A\ninst✝⁵ : Module R A\ninst✝⁴ : IsScalarTower R A A\ninst✝³ : SMulCommClass R A A\ninst✝² : TopologicalSpace A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousConstSMul R A\nx : A\ns : NonUnitalSubalgebra R A\nhs : IsClosed ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalAlgebra | {
"line": 177,
"column": 23
} | {
"line": 177,
"column": 34
} | {
"line": 177,
"column": 35
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁷ : CommSemiring R\ninst✝⁶ : NonUnitalSemiring A\ninst✝⁵ : Module R A\ninst✝⁴ : IsScalarTower R A A\ninst✝³ : SMulCommClass R A A\ninst✝² : TopologicalSpace A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousConstSMul R A\nx : A\n⊢ IsClosed (Set.range Subtype.va... | [
"R : Type u_1\nA : Type u_2\ninst✝⁷ : CommSemiring R\ninst✝⁶ : NonUnitalSemiring A\ninst✝⁵ : Module R A\ninst✝⁴ : IsScalarTower R A A\ninst✝³ : SMulCommClass R A A\ninst✝² : TopologicalSpace A\ninst✝¹ : IsSemitopologicalSemiring A\ninst✝ : ContinuousConstSMul R A\nx : A\n⊢ IsClosed ↑(elemental R x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalStarAlgebra | {
"line": 159,
"column": 48
} | {
"line": 159,
"column": 59
} | {
"line": 159,
"column": 60
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : NonUnitalSemiring A\ninst✝⁸ : StarRing A\ninst✝⁷ : Module R A\ninst✝⁶ : IsScalarTower R A A\ninst✝⁵ : SMulCommClass R A A\ninst✝⁴ : StarModule R A\ninst✝³ : TopologicalSpace A\ninst✝² : IsSemitopologicalSemiring A\nins... | [
"R : Type u_1\nA : Type u_2\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : NonUnitalSemiring A\ninst✝⁸ : StarRing A\ninst✝⁷ : Module R A\ninst✝⁶ : IsScalarTower R A A\ninst✝⁵ : SMulCommClass R A A\ninst✝⁴ : StarModule R A\ninst✝³ : TopologicalSpace A\ninst✝² : IsSemitopologicalSemiring A\ninst✝¹ : Contin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalStarAlgebra | {
"line": 189,
"column": 23
} | {
"line": 189,
"column": 34
} | {
"line": 189,
"column": 35
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : NonUnitalSemiring A\ninst✝⁸ : StarRing A\ninst✝⁷ : Module R A\ninst✝⁶ : IsScalarTower R A A\ninst✝⁵ : SMulCommClass R A A\ninst✝⁴ : StarModule R A\ninst✝³ : TopologicalSpace A\ninst✝² : IsSemitopologicalSemiring A\nins... | [
"R : Type u_1\nA : Type u_2\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : NonUnitalSemiring A\ninst✝⁸ : StarRing A\ninst✝⁷ : Module R A\ninst✝⁶ : IsScalarTower R A A\ninst✝⁵ : SMulCommClass R A A\ninst✝⁴ : StarModule R A\ninst✝³ : TopologicalSpace A\ninst✝² : IsSemitopologicalSemiring A\ninst✝¹ : Contin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 814,
"column": 4
} | {
"line": 814,
"column": 53
} | {
"line": 814,
"column": 54
} | [
{
"pp": "R : Type u_3\nA : Type u_4\ninst✝⁴ : Semifield R\ninst✝³ : Ring A\ninst✝² : TopologicalSpace R\ninst✝¹ : ContinuousInv₀ R\ninst✝ : Algebra R A\na : Aˣ\n⊢ spectrum R ↑a ⊆ {0}ᶜ",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"spectrum",
... | [
"R : Type u_3\nA : Type u_4\ninst✝⁴ : Semifield R\ninst✝³ : Ring A\ninst✝² : TopologicalSpace R\ninst✝¹ : ContinuousInv₀ R\ninst✝ : Algebra R A\na : Aˣ\n⊢ 0 ∉ spectrum R ↑a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 820,
"column": 4
} | {
"line": 820,
"column": 53
} | {
"line": 820,
"column": 54
} | [
{
"pp": "R : Type u_3\nA : Type u_4\ninst✝⁵ : Semifield R\ninst✝⁴ : Ring A\ninst✝³ : TopologicalSpace R\ninst✝² : ContinuousInv₀ R\ninst✝¹ : Algebra R A\ninst✝ : ContinuousMul R\na : Aˣ\nn : ℤ\n⊢ spectrum R ↑a ⊆ {0}ᶜ",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Units.val",
... | [
"R : Type u_3\nA : Type u_4\ninst✝⁵ : Semifield R\ninst✝⁴ : Ring A\ninst✝³ : TopologicalSpace R\ninst✝² : ContinuousInv₀ R\ninst✝¹ : Algebra R A\ninst✝ : ContinuousMul R\na : Aˣ\nn : ℤ\n⊢ 0 ∉ spectrum R ↑a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 839,
"column": 15
} | {
"line": 839,
"column": 26
} | {
"line": 839,
"column": 27
} | [
{
"pp": "case ofNat\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁰ : Semifield R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ : Ring A\ninst✝³ : StarRing A\ninst✝² : Algebra R A\ninst✝¹ : ContinuousFunctionalCa... | [
"case ofNat\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁰ : Semifield R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ : Ring A\ninst✝³ : StarRing A\ninst✝² : Algebra R A\ninst✝¹ : ContinuousFunctionalCalculus R A p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 885,
"column": 34
} | {
"line": 885,
"column": 45
} | {
"line": 885,
"column": 46
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁹ : CommRing R\ninst✝⁸ : StarRing R\ninst✝⁷ : MetricSpace R\ninst✝⁶ : IsTopologicalRing R\ninst✝⁵ : ContinuousStar R\ninst✝⁴ : TopologicalSpace A\ninst✝³ : Ring A\ninst✝² : StarRing A\ninst✝¹ : Algebra R A\ninst✝ : ContinuousFunctionalCalculus R A p\nf : R... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁹ : CommRing R\ninst✝⁸ : StarRing R\ninst✝⁷ : MetricSpace R\ninst✝⁶ : IsTopologicalRing R\ninst✝⁵ : ContinuousStar R\ninst✝⁴ : TopologicalSpace A\ninst✝³ : Ring A\ninst✝² : StarRing A\ninst✝¹ : Algebra R A\ninst✝ : ContinuousFunctionalCalculus R A p\nf : R → R\na : A\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 831,
"column": 57
} | {
"line": 831,
"column": 76
} | {
"line": 831,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝ : TopologicalSpace α := Preorder.topology α\nthis : OrderTopology α\nha : ¬IsBot a\n⊢ ∃ a_1, a_1 < a",
"ppTe... | [
"α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝ : TopologicalSpace α := Preorder.topology α\nthis : OrderTopology α\nha : ¬IsBot a\n⊢ ∃ a_1, a_1 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 835,
"column": 4
} | {
"line": 835,
"column": 33
} | {
"line": 835,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝¹ : TopologicalSpace α := ⋯\nthis✝ : OrderTopology α\nha : ¬IsBot a\nthis : (𝓝[<] a).NeBot\n⊢ Tendsto f (𝓝[univ... | [
"α : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝¹ : TopologicalSpace α := Preorder.topology α\nthis✝ : OrderTopology α\nha : ¬IsBot a\nthis : (𝓝[<] a).NeBot\n⊢ Tendsto f (�... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 917,
"column": 4
} | {
"line": 917,
"column": 15
} | {
"line": 917,
"column": 16
} | [
{
"pp": "case mpr\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵... | [
"case mpr\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 836,
"column": 2
} | {
"line": 836,
"column": 13
} | {
"line": 836,
"column": 14
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝² : TopologicalSpace α := Preorder.topology α\nthis✝¹ : OrderTopology α\nha : ¬IsBot a\nthis✝ : (𝓝[<] ... | [
"case neg\nα : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : DenselyOrdered α\nf : α → E\na : α\nhf : BoundedVariationOn f univ\nthis✝² : TopologicalSpace α := Preorder.topology α\nthis✝¹ : OrderTopology α\nha : ¬IsBot a\nthis✝ : (𝓝[<] a).NeBot\nth... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 944,
"column": 2
} | {
"line": 944,
"column": 29
} | {
"line": 944,
"column": 30
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ : St... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 955,
"column": 2
} | {
"line": 955,
"column": 29
} | {
"line": 955,
"column": 30
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\... | [
"R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalSemiring R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ : St... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 960,
"column": 4
} | {
"line": 960,
"column": 15
} | {
"line": 960,
"column": 16
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹³ : CommSemiring R\ninst✝¹² : PartialOrder R\ninst✝¹¹ : StarRing R\ninst✝¹⁰ : MetricSpace R\ninst✝⁹ : IsTopologicalSemiring R\ninst✝⁸ : ContinuousStar R\ninst✝⁷ : ContinuousSqrt R\ninst✝⁶ : StarOrderedRing R\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ ... | [
"case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹³ : CommSemiring R\ninst✝¹² : PartialOrder R\ninst✝¹¹ : StarRing R\ninst✝¹⁰ : MetricSpace R\ninst✝⁹ : IsTopologicalSemiring R\ninst✝⁸ : ContinuousStar R\ninst✝⁷ : ContinuousSqrt R\ninst✝⁶ : StarOrderedRing R\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ : Ring A\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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