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.Analysis.Calculus.Monotone | {
"line": 128,
"column": 6
} | {
"line": 128,
"column": 45
} | [
{
"pp": "case h\nf : 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.rnDe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 528,
"column": 40
} | {
"line": 528,
"column": 82
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 545,
"column": 6
} | {
"line": 545,
"column": 86
} | [
{
"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.Analysis.Calculus.Monotone | {
"line": 161,
"column": 8
} | {
"line": 161,
"column": 19
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 597,
"column": 40
} | {
"line": 597,
"column": 82
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 607,
"column": 4
} | {
"line": 607,
"column": 84
} | [
{
"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.Analysis.Calculus.Monotone | {
"line": 187,
"column": 8
} | {
"line": 187,
"column": 19
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 718,
"column": 2
} | {
"line": 718,
"column": 56
} | [
{
"pp": "case h\nα : 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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 806,
"column": 44
} | {
"line": 806,
"column": 70
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.StarOrdered | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 11
} | [
{
"pp": "case h.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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.StarOrdered | {
"line": 92,
"column": 47
} | {
"line": 92,
"column": 58
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 826,
"column": 6
} | {
"line": 826,
"column": 45
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 835,
"column": 37
} | {
"line": 835,
"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 ... | ENNReal.add_halves | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Differentiation | {
"line": 860,
"column": 38
} | {
"line": 860,
"column": 77
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 41
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\nx y : α\nhx : x ∈ s\nhy : y ∈ s\nhxy : y ≤ x\nu : ℕ → α := fun n ↦ if n = 0 then y else x\nhu : Monotone u\nus : ∀ (i : ℕ), u i ∈ s\n⊢ edist (f x) (f y) ≤ eVariationOn f s",
"usedConstants": []
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 230,
"column": 2
} | {
"line": 231,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\ns : Set α\nf : α →ᵤ[singleton '' s] E\n⊢ ∀ x ∈ s, Tendsto (fun i ↦ id i x) (𝓝 f) (𝓝 (f x))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 498,
"column": 2
} | {
"line": 498,
"column": 34
} | [
{
"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 ∘ ⇑OrderDual.ofDual) (⇑OrderDual.ofDual ⁻¹' s)",
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.ofDual",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 526,
"column": 4
} | {
"line": 534,
"column": 40
} | [
{
"pp": "case h.inl.succ\nα : Type u_1\ninst✝³ : LinearOrder α\nE : Type u_2\ninst✝² : PseudoEMetricSpace E\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nf : α → E\ns : Set α\na : α\nh : (𝓝[s ∩ Iio a] a).NeBot\nh' : ContinuousWithinAt f (s ∩ Iic a) a\nu : ℕ → α\nn : ℕ\nu_mono : StrictMonoOn u (Iic (n ... | have : Tendsto (fun b ↦ edist (f b) (f (u n))
+ ∑ i ∈ Finset.range n, edist (f (u (i + 1))) (f (u i))) (𝓝[s ∩ Iio a] a)
(𝓝 (edist (f (u (n + 1))) (f (u n))
+ ∑ i ∈ Finset.range n, edist (f (u (i + 1))) (f (u i)))) := by
apply Tendsto.add_const
apply Tendsto.edist _ tendsto_const_nhds... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 73
} | [
{
"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... | 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
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 563,
"column": 4
} | {
"line": 563,
"column": 43
} | [
{
"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))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 588,
"column": 4
} | {
"line": 588,
"column": 15
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"congrAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 610,
"column": 14
} | {
"line": 610,
"column": 29
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 168,
"column": 6
} | {
"line": 168,
"column": 86
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 291,
"column": 4
} | {
"line": 291,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 328,
"column": 8
} | {
"line": 328,
"column": 23
} | [
{
"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✝... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | {
"line": 338,
"column": 8
} | {
"line": 338,
"column": 88
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 125,
"column": 29
} | {
"line": 125,
"column": 57
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 18
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝¹³ : CommSemiring R\ninst✝¹² : StarRing R\ninst✝¹¹ : TopologicalSpace A\ninst✝¹⁰ : Semiring A\ninst✝⁹ : Algebra R A\ninst✝⁸ : StarRing A\ninst✝⁷ : StarModule R A\ninst✝⁶ : IsSemitopologicalSemiring A\ninst✝⁵ : ContinuousStar A\ninst✝⁴ : TopologicalSpace B\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 165,
"column": 4
} | {
"line": 165,
"column": 62
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝¹⁶ : CommSemiring R\ninst✝¹⁵ : StarRing R\ninst✝¹⁴ : TopologicalSpace A\ninst✝¹³ : Semiring A\ninst✝¹² : Algebra R A\ninst✝¹¹ : StarRing A\ninst✝¹⁰ : StarModule R A\ninst✝⁹ : IsSemitopologicalSemiring A\ninst✝⁸ : ContinuousStar A\ninst✝⁷ : TopologicalSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 230,
"column": 23
} | {
"line": 230,
"column": 34
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 250,
"column": 53
} | {
"line": 250,
"column": 64
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.StarSubalgebra | {
"line": 266,
"column": 25
} | {
"line": 266,
"column": 71
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝¹⁶ : CommSemiring R\ninst✝¹⁵ : StarRing R\ninst✝¹⁴ : TopologicalSpace A\ninst✝¹³ : Semiring A\ninst✝¹² : StarRing A\ninst✝¹¹ : IsSemitopologicalSemiring A\ninst✝¹⁰ : ContinuousStar A\ninst✝⁹ : Algebra R A\ninst✝⁸ : StarModule R A\ninst✝⁷ : TopologicalSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 877,
"column": 28
} | {
"line": 877,
"column": 39
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\nE : Type u_2\ninst✝¹ : PseudoEMetricSpace E\ninst✝ : CompleteSpace E\nhE : Nonempty E\nf : α → E\nhf : BoundedVariationOn f univ\n⊢ ∃ x, Tendsto f atTop (𝓝 x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 882,
"column": 28
} | {
"line": 882,
"column": 39
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\nE : Type u_2\ninst✝¹ : PseudoEMetricSpace E\ninst✝ : CompleteSpace E\nhE : Nonempty E\nf : α → E\nhf : BoundedVariationOn f univ\n⊢ ∃ x, Tendsto f atBot (𝓝 x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalAlgebra | {
"line": 147,
"column": 46
} | {
"line": 147,
"column": 57
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalAlgebra | {
"line": 177,
"column": 23
} | {
"line": 177,
"column": 34
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalStarAlgebra | {
"line": 159,
"column": 48
} | {
"line": 159,
"column": 59
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.NonUnitalStarAlgebra | {
"line": 189,
"column": 23
} | {
"line": 189,
"column": 34
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.EMetricSpace.BoundedVariation | {
"line": 1067,
"column": 53
} | {
"line": 1067,
"column": 64
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 544,
"column": 35
} | {
"line": 544,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 575,
"column": 2
} | {
"line": 575,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 655,
"column": 2
} | {
"line": 655,
"column": 41
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 656,
"column": 68
} | {
"line": 656,
"column": 79
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 660,
"column": 2
} | {
"line": 660,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 704,
"column": 2
} | {
"line": 704,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 707,
"column": 2
} | {
"line": 707,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 814,
"column": 4
} | {
"line": 814,
"column": 53
} | [
{
"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",
"usedConstants": [
"Units.val",
"Eq.mpr",
"spectrum",
"Compl.compl",
"Membership.mem",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 820,
"column": 4
} | {
"line": 820,
"column": 53
} | [
{
"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",
"usedConstants": [
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 830,
"column": 15
} | {
"line": 830,
"column": 26
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 839,
"column": 15
} | {
"line": 839,
"column": 26
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 885,
"column": 34
} | {
"line": 885,
"column": 45
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 917,
"column": 4
} | {
"line": 917,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Polynomial.Bernstein | {
"line": 59,
"column": 2
} | {
"line": 60,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\n⊢ bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | norm_num [bernsteinPolynomial, choose]
ring | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Polynomial.Bernstein | {
"line": 59,
"column": 2
} | {
"line": 60,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\n⊢ bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | norm_num [bernsteinPolynomial, choose]
ring | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 944,
"column": 2
} | {
"line": 944,
"column": 29
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 955,
"column": 2
} | {
"line": 955,
"column": 29
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 960,
"column": 4
} | {
"line": 960,
"column": 15
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 966,
"column": 4
} | {
"line": 966,
"column": 15
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.Polynomial | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 61
} | [
{
"pp": "case h.mpr\na b : ℝ\nh : a < b\np : ℝ[X]\n⊢ ↑(toContinuousMapOnAlgHom (Set.Icc a b)) p ∈\n Subalgebra.comap (compRightAlgHom ℝ ℝ ↑(iccHomeoI a b h).symm) (polynomialFunctions I)",
"usedConstants": [
"Polynomial.C",
"Real",
"instHSMul",
"CommSemiring.toSemiring",
"Re... | let q := p.comp ((b - a) • Polynomial.X + Polynomial.C a) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 993,
"column": 2
} | {
"line": 993,
"column": 36
} | [
{
"pp": "R : 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\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 998,
"column": 2
} | {
"line": 998,
"column": 13
} | [
{
"pp": "R : 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\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1002,
"column": 2
} | {
"line": 1002,
"column": 13
} | [
{
"pp": "R : 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\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1006,
"column": 2
} | {
"line": 1006,
"column": 13
} | [
{
"pp": "R : 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\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1071,
"column": 2
} | {
"line": 1071,
"column": 13
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommRing R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalRing R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1076,
"column": 2
} | {
"line": 1076,
"column": 13
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommRing R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalRing R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1080,
"column": 2
} | {
"line": 1080,
"column": 13
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommRing R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalRing R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | {
"line": 1084,
"column": 2
} | {
"line": 1084,
"column": 13
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁴ : CommRing R\ninst✝¹³ : PartialOrder R\ninst✝¹² : StarRing R\ninst✝¹¹ : MetricSpace R\ninst✝¹⁰ : IsTopologicalRing R\ninst✝⁹ : ContinuousStar R\ninst✝⁸ : ContinuousSqrt R\ninst✝⁷ : StarOrderedRing R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : Ring A\ninst✝⁴ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 373,
"column": 24
} | {
"line": 373,
"column": 39
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : Nontrivial R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Module R A... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Bernstein | {
"line": 201,
"column": 4
} | {
"line": 202,
"column": 11
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nf : C(↑I, E)\nthis✝¹ : UniformSpace E := IsTopologicalAddGroup.rightUniformSpace E\nthis✝ : IsUniformAddGroup E\nU : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 381,
"column": 24
} | {
"line": 381,
"column": 39
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : Nontrivial R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Module R A... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Bernstein | {
"line": 239,
"column": 8
} | {
"line": 239,
"column": 23
} | [
{
"pp": "case h.hbc\nE : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nf : C(↑I, E)\nthis✝ : UniformSpace E := IsTopologicalAddGroup.rightUniformSpace E\nthis : IsUniformAddGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 436,
"column": 35
} | {
"line": 436,
"column": 46
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : Nontrivial R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Module R A\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 438,
"column": 31
} | {
"line": 438,
"column": 42
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : Nontrivial R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Module R A\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Bernstein | {
"line": 258,
"column": 8
} | {
"line": 259,
"column": 15
} | [
{
"pp": "case hbc.h.hbc\nE : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nf : C(↑I, E)\nthis✝ : UniformSpace E := ⋯\nthis : IsUniformAddGroup E\nU : Set E\nhU₀ : U ∈ 𝓝 0\nhUc :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 514,
"column": 2
} | {
"line": 514,
"column": 27
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : Nontrivial R\ninst✝⁹ : StarRing R\ninst✝⁸ : MetricSpace R\ninst✝⁷ : IsTopologicalSemiring R\ninst✝⁶ : ContinuousStar R\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Module R A\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 570,
"column": 24
} | {
"line": 570,
"column": 39
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹² : CommRing R\ninst✝¹¹ : Nontrivial R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : MetricSpace R\ninst✝⁸ : IsTopologicalRing R\ninst✝⁷ : ContinuousStar R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : Module R A\ninst✝... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 583,
"column": 34
} | {
"line": 583,
"column": 45
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹² : CommRing R\ninst✝¹¹ : Nontrivial R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : MetricSpace R\ninst✝⁸ : IsTopologicalRing R\ninst✝⁷ : ContinuousStar R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : Module R A\ninst✝² : IsScal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 587,
"column": 62
} | {
"line": 587,
"column": 82
} | [
{
"pp": "case h\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹² : CommRing R\ninst✝¹¹ : Nontrivial R\ninst✝¹⁰ : StarRing R\ninst✝⁹ : MetricSpace R\ninst✝⁸ : IsTopologicalRing R\ninst✝⁷ : ContinuousStar R\ninst✝⁶ : TopologicalSpace A\ninst✝⁵ : NonUnitalRing A\ninst✝⁴ : StarRing A\ninst✝³ : Module R A\ninst✝² ... | exact (cfcₙ_neg f a) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 623,
"column": 4
} | {
"line": 623,
"column": 15
} | [
{
"pp": "case mpr\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁹ : CommSemiring R\ninst✝¹⁸ : PartialOrder R\ninst✝¹⁷ : Nontrivial R\ninst✝¹⁶ : StarRing R\ninst✝¹⁵ : MetricSpace R\ninst✝¹⁴ : IsTopologicalSemiring R\ninst✝¹³ : ContinuousStar R\ninst✝¹² : ContinuousSqrt R\ninst✝¹¹ : StarOrderedRing R\ninst✝¹⁰ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 646,
"column": 2
} | {
"line": 646,
"column": 30
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁹ : CommSemiring R\ninst✝¹⁸ : PartialOrder R\ninst✝¹⁷ : Nontrivial R\ninst✝¹⁶ : StarRing R\ninst✝¹⁵ : MetricSpace R\ninst✝¹⁴ : IsTopologicalSemiring R\ninst✝¹³ : ContinuousStar R\ninst✝¹² : ContinuousSqrt R\ninst✝¹¹ : StarOrderedRing R\ninst✝¹⁰ : NoZeroDi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 652,
"column": 4
} | {
"line": 652,
"column": 15
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁸ : CommSemiring R\ninst✝¹⁷ : PartialOrder R\ninst✝¹⁶ : Nontrivial R\ninst✝¹⁵ : StarRing R\ninst✝¹⁴ : MetricSpace R\ninst✝¹³ : IsTopologicalSemiring R\ninst✝¹² : ContinuousStar R\ninst✝¹¹ : ContinuousSqrt R\ninst✝¹⁰ : StarOrderedRing R\ninst✝⁹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 662,
"column": 4
} | {
"line": 662,
"column": 15
} | [
{
"pp": "case pos\nR : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁸ : CommSemiring R\ninst✝¹⁷ : PartialOrder R\ninst✝¹⁶ : Nontrivial R\ninst✝¹⁵ : StarRing R\ninst✝¹⁴ : MetricSpace R\ninst✝¹³ : IsTopologicalSemiring R\ninst✝¹² : ContinuousStar R\ninst✝¹¹ : ContinuousSqrt R\ninst✝¹⁰ : StarOrderedRing R\ninst✝⁹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 687,
"column": 22
} | {
"line": 687,
"column": 37
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : PartialOrder R\ninst✝¹⁷ : Nontrivial R\ninst✝¹⁶ : StarRing R\ninst✝¹⁵ : MetricSpace R\ninst✝¹⁴ : IsTopologicalRing R\ninst✝¹³ : ContinuousStar R\ninst✝¹² : ContinuousSqrt R\ninst✝¹¹ : StarOrderedRing R\ninst✝¹⁰ : NoZeroDivisors R... | cfcₙ_apply g a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 797,
"column": 15
} | {
"line": 797,
"column": 65
} | [
{
"pp": "R : Type u_1\nA : Type u_2\np : A → Prop\ninst✝⁹ : Semifield R\ninst✝⁸ : StarRing R\ninst✝⁷ : MetricSpace R\ninst✝⁶ : IsTopologicalSemiring R\ninst✝⁵ : ContinuousStar R\ninst✝⁴ : Ring A\ninst✝³ : StarRing A\ninst✝² : TopologicalSpace A\ninst✝¹ : Algebra R A\ninst✝ : ContinuousFunctionalCalculus R A p\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.StoneWeierstrass | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 61
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nL : Set C(X, ℝ)\nnA : L.Nonempty\ninf_mem : ∀ f ∈ L, ∀ g ∈ L, f ⊓ g ∈ L\nsup_mem : ∀ f ∈ L, ∀ g ∈ L, f ⊔ g ∈ L\nsep : ∀ (v : X → ℝ) (x y : X), ∃ f ∈ L, f x = v x ∧ f y = v y\nf : C(X, ℝ)\nε : ℝ\npos : 0 < ε\nnX : Nonempty X\ng... | let U : X → X → Set X := fun x y => {z | f z - ε < g x y z} | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 137,
"column": 6
} | {
"line": 138,
"column": 33
} | [
{
"pp": "case inl\nX : Type u_1\ninst✝⁵ : TopologicalSpace X\nA : Type u_2\ninst✝⁴ : Ring A\ninst✝³ : StarRing A\ninst✝² : Algebra ℝ A\ninst✝¹ : TopologicalSpace A\ninst✝ : IsSemitopologicalRing A\nφ : C(X, ℝ≥0) →⋆ₐ[ℝ≥0] A\nr : ℝ≥0\n⊢ φ ((algebraMap ℝ C(X, ℝ)) ↑r).toNNReal - φ (-(algebraMap ℝ C(X, ℝ)) ↑r).toNNR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 142,
"column": 6
} | {
"line": 143,
"column": 67
} | [
{
"pp": "case inr\nX : Type u_1\ninst✝⁵ : TopologicalSpace X\nA : Type u_2\ninst✝⁴ : Ring A\ninst✝³ : StarRing A\ninst✝² : Algebra ℝ A\ninst✝¹ : TopologicalSpace A\ninst✝ : IsSemitopologicalRing A\nφ : C(X, ℝ≥0) →⋆ₐ[ℝ≥0] A\nr✝ : ℝ\nr : ℝ≥0\n⊢ φ ((algebraMap ℝ C(X, ℝ)) (-↑r)).toNNReal - φ ((algebraMap ℝ C(X, ℝ))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 13
} | [
{
"pp": "case h\nX : Type u_1\ninst✝³ : TopologicalSpace X\nA : Type u_2\ninst✝² : Ring A\ninst✝¹ : StarRing A\ninst✝ : Algebra ℝ A\nφ ψ : C(X, ℝ≥0) →⋆ₐ[ℝ≥0] A\nh : φ.realContinuousMapOfNNReal = ψ.realContinuousMapOfNNReal\nf : C(X, ℝ≥0)\n⊢ φ f = ψ f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | {
"line": 866,
"column": 4
} | {
"line": 866,
"column": 36
} | [
{
"pp": "R : 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 : Ring A\ninst✝⁴ : StarRing A\ninst✝³ : TopologicalSpace A\ninst✝² : Algebra R A\ninst✝¹ : ContinuousFunctionalCalculus R A p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 253,
"column": 4
} | {
"line": 253,
"column": 48
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : Zero X\nr : ℝ≥0\nf : C(X, ℝ)₀\nx : X\nh : 0 ≤ f x\n⊢ ↑((r • f).toNNReal x) = ↑((r • f.toNNReal) x)",
"usedConstants": [
"NNReal.instTopologicalSpace",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 254,
"column": 4
} | {
"line": 255,
"column": 11
} | [
{
"pp": "case neg\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : Zero X\nr : ℝ≥0\nf : C(X, ℝ)₀\nx : X\nh : f x < 0\n⊢ ↑((r • f).toNNReal x) = ↑((r • f.toNNReal) x)",
"usedConstants": [
"NNReal.instTopologicalSpace",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 265,
"column": 2
} | {
"line": 266,
"column": 9
} | [
{
"pp": "case a\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : Zero X\nf g : C(X, ℝ)₀\n⊢ ↑((f * g).toNNReal + (-f).toNNReal * g.toNNReal + f.toNNReal * (-g).toNNReal) =\n ↑((-(f * g)).toNNReal + f.toNNReal * g.toNNReal + (-f).toNNReal * (-g).toNNReal)",
"usedConstants": [
"NNReal.instTopologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 272,
"column": 2
} | {
"line": 273,
"column": 9
} | [
{
"pp": "case a\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : Zero X\nf g : C(X, ℝ)₀\n⊢ ↑((f + g).toNNReal + (-f).toNNReal + (-g).toNNReal) = ↑((-(f + g)).toNNReal + f.toNNReal + g.toNNReal)",
"usedConstants": [
"NNReal.instTopologicalSpace",
"Eq.mpr",
"NonAssocSemiring.toAddCommMono... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Unitization | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NonUnitalNormedRing A\ninst✝³ : NormedSpace 𝕜 A\ninst✝² : IsScalarTower 𝕜 A A\ninst✝¹ : SMulCommClass 𝕜 A A\ninst✝ : RegularNormedAlgebra 𝕜 A\nx : Unitization 𝕜 A\n⊢ ‖(addEquiv 𝕜 A) x‖ ≤ 2 * ‖x‖",
"usedConstants": [
... | rw [norm_eq_sup, Prod.norm_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Normed.Algebra.Unitization | {
"line": 166,
"column": 8
} | {
"line": 166,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NonUnitalNormedRing A\ninst✝³ : NormedSpace 𝕜 A\ninst✝² : IsScalarTower 𝕜 A A\ninst✝¹ : SMulCommClass 𝕜 A A\ninst✝ : RegularNormedAlgebra 𝕜 A\nx : Unitization 𝕜 A\na✝ : Nontrivial A\n⊢ ‖(mul 𝕜 A) x.toProd.2‖ ≤ ‖(algebraMap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | {
"line": 348,
"column": 2
} | {
"line": 348,
"column": 13
} | [
{
"pp": "case h\nX : Type u_1\ninst✝⁴ : TopologicalSpace X\ninst✝³ : Zero X\nA : Type u_2\ninst✝² : NonUnitalRing A\ninst✝¹ : StarRing A\ninst✝ : Module ℝ A\nφ ψ : C(X, ℝ≥0)₀ →⋆ₙₐ[ℝ≥0] A\nh : φ.realContinuousMapZeroOfNNReal = ψ.realContinuousMapZeroOfNNReal\nf : C(X, ℝ≥0)₀\n⊢ φ f = ψ f",
"usedConstants": []... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Unitization | {
"line": 247,
"column": 17
} | {
"line": 248,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NonUnitalNormedRing A\ninst✝³ : NormedSpace 𝕜 A\ninst✝² : IsScalarTower 𝕜 A A\ninst✝¹ : SMulCommClass 𝕜 A A\ninst✝ : RegularNormedAlgebra 𝕜 A\n⊢ ‖1‖ = 1",
"usedConstants": [
"NormedCommRing.toNormedRing",
"No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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