module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.MeasureTheory.Measure.Haar.Extension | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 54
} | {
"line": 264,
"column": 55
} | [
{
"pp": "A : Type u_1\nB : Type u_2\nC : Type u_3\ninst✝¹⁷ : Group A\ninst✝¹⁶ : Group B\ninst✝¹⁵ : Group C\ninst✝¹⁴ : TopologicalSpace A\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace C\nφ : A →* B\nψ : B →* C\nH : IsSES φ ψ\ninst✝¹¹ : IsTopologicalGroup A\ninst✝¹⁰ : IsTopologicalGroup B\ninst✝⁹ : Me... | [
"A : Type u_1\nB : Type u_2\nC : Type u_3\ninst✝¹⁷ : Group A\ninst✝¹⁶ : Group B\ninst✝¹⁵ : Group C\ninst✝¹⁴ : TopologicalSpace A\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace C\nφ : A →* B\nψ : B →* C\nH : IsSES φ ψ\ninst✝¹¹ : IsTopologicalGroup A\ninst✝¹⁰ : IsTopologicalGroup B\ninst✝⁹ : MeasurableSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | {
"line": 644,
"column": 26
} | {
"line": 644,
"column": 60
} | {
"line": 644,
"column": 61
} | [
{
"pp": "Ω : Type u_1\ninst✝³ : PseudoMetricSpace Ω\ninst✝² : MeasurableSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\ninst✝ : SeparableSpace Ω\nP : ProbabilityMeasure Ω\nε : ℝ\nε_pos : ε > 0\nthird_ε_pos : 0 < ε / 3\nthird_ε_pos' : 0 < ENNReal.ofReal (ε / 3)\nEs : ℕ → Set Ω\nEs_mble : ∀ (n : ℕ), MeasurableSet (Es n... | [
"Ω : Type u_1\ninst✝³ : PseudoMetricSpace Ω\ninst✝² : MeasurableSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\ninst✝ : SeparableSpace Ω\nP : ProbabilityMeasure Ω\nε : ℝ\nε_pos : ε > 0\nthird_ε_pos : 0 < ε / 3\nthird_ε_pos' : 0 < ENNReal.ofReal (ε / 3)\nEs : ℕ → Set Ω\nEs_mble : ∀ (n : ℕ), MeasurableSet (Es n)\nEs_bdd : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.IntegralCharFun | {
"line": 166,
"column": 95
} | {
"line": 175,
"column": 31
} | {
"line": 177,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\nmE : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\nμ : Measure E\ninst✝ : IsProbabilityMeasure μ\na : E\nr : ℝ\nhr : 0 < r\n⊢ μ.real {x | r < |⟪a, x⟫|} ≤ 2⁻¹ * r * ‖∫ (t : ℝ) in -2 * r⁻¹..2 * r⁻¹, 1 - charFun μ (t • ... | [] | by
have : IsProbabilityMeasure (μ.map (fun x ↦ ⟪a, x⟫)) :=
Measure.isProbabilityMeasure_map (by fun_prop)
convert! measureReal_abs_gt_le_integral_charFun (μ := μ.map (fun x ↦ ⟪a, x⟫)) hr with x
· rw [map_measureReal_apply (by fun_prop)]
· simp
· exact MeasurableSet.preimage measurableSet_Ioi (by fun_p... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls | {
"line": 174,
"column": 2
} | {
"line": 177,
"column": 36
} | {
"line": 178,
"column": 2
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\np : ℝ\nhp : 1 ≤ p\nh₁ : 0 < p\nthis✝ : (ENNReal.ofReal p).toReal = p\nh₂ : ∀ (x : ι → ℝ), 0 ≤ ∑ i, |x i| ^ p\neq_norm : ∀ (x : ι → ℝ), ‖toLp (ENNReal.ofReal p) x‖ = (∑ i, |x i| ^ p) ^ (1 / p)\nthis : Fact (1 ≤ ENNReal.ofReal p)\neq_zero : ∀ (x : ι → ℝ), (∑ i, |x i| ^ p)... | [
"case e'_2\nι : Type u_1\ninst✝ : Fintype ι\np : ℝ\nhp : 1 ≤ p\nh₁ : 0 < p\nthis✝ : (ENNReal.ofReal p).toReal = p\nh₂ : ∀ (x : ι → ℝ), 0 ≤ ∑ i, |x i| ^ p\neq_norm : ∀ (x : ι → ℝ), ‖toLp (ENNReal.ofReal p) x‖ = (∑ i, |x i| ^ p) ^ (1 / p)\nthis : Fact (1 ≤ ENNReal.ofReal p)\neq_zero : ∀ (x : ι → ℝ), (∑ i, |x i| ^ p) ... | convert!
(measure_lt_one_eq_integral_div_gamma (volume : Measure (ι → ℝ)) (g := fun x =>
(∑ i, |x i| ^ p) ^ (1 / p)) nm_zero nm_neg nm_add (eq_zero _).mp (fun r x => nm_smul r x)
(by linarith : 0 < p)) using 4 | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 13
} | {
"line": 170,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : MeasurableSpace E\ninst✝³ : TopologicalSpace E\ninst✝² : T2Space E\ninst✝¹ : BorelSpace E\ninst✝ : CompactSpace E\n⊢ IsCompact (ProbabilityMeasure.toFiniteMeasure '' univ)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"MeasureTheory.FiniteMeasure.ins... | [
"E : Type u_1\ninst✝⁴ : MeasurableSpace E\ninst✝³ : TopologicalSpace E\ninst✝² : T2Space E\ninst✝¹ : BorelSpace E\ninst✝ : CompactSpace E\n⊢ IsCompact {μ | μ.mass = 1}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 25
} | {
"line": 184,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nC : ℝ≥0\nK : Set E\nhK : IsCompact K\nf : ↑K → E := Subtype.val\nhf : IsClosedEmbedding f\nrf : range f = K\nF : FiniteMeasure ↑K → FiniteMeasure E := fun μ ↦ μ.map f\nT : Set (FiniteMeasure... | [
"case h₁\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nC : ℝ≥0\nK : Set E\nhK : IsCompact K\nf : ↑K → E := ⋯\nhf : IsClosedEmbedding f\nrf : range f = K\nF : FiniteMeasure ↑K → FiniteMeasure E := ⋯\nT : Set (FiniteMeasure ↑K) := ⋯\n⊢ {μ | μ.mass ≤ ... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 238,
"column": 4
} | {
"line": 238,
"column": 43
} | {
"line": 238,
"column": 44
} | [
{
"pp": "E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nh : NormalSpace E ∨ Monotone K\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.r... | [
"E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nh : NormalSpace E ∨ Monotone K\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosedProd | {
"line": 121,
"column": 4
} | {
"line": 122,
"column": 41
} | {
"line": 123,
"column": 4
} | [
{
"pp": "case pos\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → Topol... | [
"case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → TopologicalSpace ... | · simp only [Set.mem_pi, mem_univ, forall_const] at hy
exact Finset.prod_eq_one (by simpa) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosedProd | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 43
} | {
"line": 123,
"column": 44
} | [
{
"pp": "case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → Topol... | [
"case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosedProd | {
"line": 128,
"column": 4
} | {
"line": 129,
"column": 41
} | {
"line": 130,
"column": 4
} | [
{
"pp": "case pos\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → Topol... | [
"case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → TopologicalSpace ... | · simp only [Set.mem_pi, mem_univ, forall_const] at hy
exact Finset.prod_eq_one (by simpa) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosedProd | {
"line": 130,
"column": 6
} | {
"line": 130,
"column": 43
} | {
"line": 130,
"column": 44
} | [
{
"pp": "case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → Topol... | [
"case neg\nι : Type u_1\nκ : Type u_2\nX : ι → Type u_5\nY : κ → Type u_6\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmY : (j : κ) → MeasurableSpace (Y j)\ninst✝⁵ : (j : κ) → TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.CurveIntegral.Poincare | {
"line": 351,
"column": 2
} | {
"line": 351,
"column": 27
} | {
"line": 352,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\na b : E\ns : Set E\nω : E → E →L[𝕜] F\ndω : E → E →L[ℝ] E →L[𝕜] F\nins... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\na b : E\ns : Set E\nω : E → E →L[𝕜] F\ndω : E → E →L[ℝ] E →L[𝕜] F\ninst✝ : Complet... | refine .const_add _ <| ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.Integral.CurveIntegral.Poincare | {
"line": 404,
"column": 4
} | {
"line": 404,
"column": 15
} | {
"line": 404,
"column": 16
} | [
{
"pp": "case hdω\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\ns : Set 𝕜\nhs : Convex ℝ s\nhf : DifferentiableOn 𝕜 f s\nthis : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ 𝕜 E\na : 𝕜\nha : a ∈ s\nx y : 𝕜... | [
"case hdω\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\ns : Set 𝕜\nhs : Convex ℝ s\nhf : DifferentiableOn 𝕜 f s\nthis : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ 𝕜 E\na : 𝕜\nha : a ∈ s\nx y : 𝕜\n⊢ x • y • ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.TightNormed | {
"line": 63,
"column": 61
} | {
"line": 63,
"column": 72
} | {
"line": 63,
"column": 73
} | [
{
"pp": "E : Type u_1\nmE : MeasurableSpace E\nS : Set (Measure E)\ninst✝¹ : PseudoMetricSpace E\ninst✝ : ProperSpace E\nx : E\nh✝ : ∀ ε > 0, ∃ N, ∀ n ≥ N, ⨆ μ ∈ S, μ (Metric.closedBall x n)ᶜ ≤ ε\nε : ℝ≥0∞\nhε : 0 < ε\nr : ℝ\nh : ∀ n ≥ r, ⨆ μ ∈ S, μ (Metric.closedBall x n)ᶜ ≤ ε\n⊢ ∀ μ ∈ S, μ (Metric.closedBall ... | [
"E : Type u_1\nmE : MeasurableSpace E\nS : Set (Measure E)\ninst✝¹ : PseudoMetricSpace E\ninst✝ : ProperSpace E\nx : E\nh✝ : ∀ ε > 0, ∃ N, ∀ n ≥ N, ⨆ μ ∈ S, μ (Metric.closedBall x n)ᶜ ≤ ε\nε : ℝ≥0∞\nhε : 0 < ε\nr : ℝ\nh : ∀ n ≥ r, ⨆ μ ∈ S, μ (Metric.closedBall x n)ᶜ ≤ ε\n⊢ ∀ μ ∈ S, μ (Metric.closedBall x r)ᶜ ≤ ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.TightNormed | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | {
"line": 115,
"column": 14
} | [
{
"pp": "E : Type u_1\nmE : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : BorelSpace E\ninst✝¹ : ProperSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : Tendsto (fun r ↦ limsup (fun n ↦ (μ n) {x | r < ‖x‖}) atTop) atTop (𝓝 0)\nn : ℕ\nh_tight : Tendsto (fun r ↦ ⨆ μ_1 ∈ {μ n}... | [
"E : Type u_1\nmE : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : BorelSpace E\ninst✝¹ : ProperSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : Tendsto (fun r ↦ limsup (fun n ↦ (μ n) {x | r < ‖x‖}) atTop) atTop (𝓝 0)\nn : ℕ\nh_tight : Tendsto (fun r ↦ ⨆ μ_1 ∈ {μ n}, μ_1 {x | r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.TightNormed | {
"line": 146,
"column": 26
} | {
"line": 146,
"column": 60
} | {
"line": 146,
"column": 61
} | [
{
"pp": "E : Type u_1\nmE : MeasurableSpace E\nS : Set (Measure E)\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_2\nι : Type u_3\ninst✝³ : RCLike 𝕜\ninst✝² : Fintype ι\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : FiniteDimensional 𝕜 E\nb : OrthonormalBasis ι 𝕜 E\nh : ∀ (i : ι), Tendsto (fun r ↦ ⨆ μ ∈ S, μ {x | r ... | [
"E : Type u_1\nmE : MeasurableSpace E\nS : Set (Measure E)\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_2\nι : Type u_3\ninst✝³ : RCLike 𝕜\ninst✝² : Fintype ι\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : FiniteDimensional 𝕜 E\nb : OrthonormalBasis ι 𝕜 E\nh : ∀ (i : ι), Tendsto (fun r ↦ ⨆ μ ∈ S, μ {x | r < ‖⟪b i, x⟫_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 373,
"column": 8
} | {
"line": 373,
"column": 19
} | {
"line": 373,
"column": 20
} | [
{
"pp": "case h₂\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nh : NormalSpace E ∨ Monotone K\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈... | [
"case h₂\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nh : NormalSpace E ∨ Monotone K\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.rang... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.TightNormed | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 21
} | {
"line": 224,
"column": 22
} | [
{
"pp": "E : Type u_1\nmE : MeasurableSpace E\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : FiniteDimensional 𝕜 E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : ∀ (y : E), Tendsto (fun r ↦ limsup (fun n ↦ (... | [
"E : Type u_1\nmE : MeasurableSpace E\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : FiniteDimensional 𝕜 E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : ∀ (y : E), Tendsto (fun r ↦ limsup (fun n ↦ (μ n) {x | r ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.TightNormed | {
"line": 272,
"column": 2
} | {
"line": 272,
"column": 52
} | {
"line": 272,
"column": 53
} | [
{
"pp": "E : Type u_1\nmE : MeasurableSpace E\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : FiniteDimensional 𝕜 E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : ∀ (y : E), ‖y‖ = 1 → Tendsto (fun r ↦ limsup ... | [
"E : Type u_1\nmE : MeasurableSpace E\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : FiniteDimensional 𝕜 E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsFiniteMeasure (μ i)\nh : ∀ (y : E), ‖y‖ = 1 → Tendsto (fun r ↦ limsup (fun n ↦ (μ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.LevyConvergence | {
"line": 112,
"column": 33
} | {
"line": 112,
"column": 44
} | {
"line": 112,
"column": 45
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsProbabilityMeasure (μ i)\nf : E → ℂ\nhf : ContinuousAt f 0\nh : ∀ (t : E), Tendsto (fun n ↦ charFun (μ ... | [
"E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsProbabilityMeasure (μ i)\nf : E → ℂ\nhf : ContinuousAt f 0\nh : ∀ (t : E), Tendsto (fun n ↦ charFun (μ n) t) atTop ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 400,
"column": 36
} | {
"line": 400,
"column": 47
} | {
"line": 400,
"column": 48
} | [
{
"pp": "E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjoi... | [
"E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjointed K i) = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 401,
"column": 31
} | {
"line": 401,
"column": 42
} | {
"line": 401,
"column": 43
} | [
{
"pp": "E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjoi... | [
"E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjointed K i) = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.MeasuredSets | {
"line": 120,
"column": 28
} | {
"line": 120,
"column": 39
} | {
"line": 120,
"column": 40
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nC : Set (Set α)\nhC : IsSetRing C\nh'C : ∃ D, D.Countable ∧ D ⊆ C ∧ μ (⋃₀ D)ᶜ = 0\nh : mα = generateFrom C\ns✝ : Set α\nhs✝ : MeasurableSet s✝\nε✝ : ℝ≥0∞\nhε : 0 < ε✝\ns : Set α\nhs : MeasurableSet s\nh's : ∀ (ε : ℝ≥0∞), 0 ... | [
"α : Type u_1\nmα : MeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nC : Set (Set α)\nhC : IsSetRing C\nh'C : ∃ D, D.Countable ∧ D ⊆ C ∧ μ (⋃₀ D)ᶜ = 0\nh : mα = generateFrom C\ns✝ : Set α\nhs✝ : MeasurableSet s✝\nε✝ : ℝ≥0∞\nhε : 0 < ε✝\ns : Set α\nhs : MeasurableSet s\nh's : ∀ (ε : ℝ≥0∞), 0 < ε → ∃ t ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 412,
"column": 10
} | {
"line": 412,
"column": 26
} | {
"line": 412,
"column": 27
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restri... | [
"case pos\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjoint... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 416,
"column": 10
} | {
"line": 416,
"column": 21
} | {
"line": 416,
"column": 22
} | [
{
"pp": "case neg\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restri... | [
"case neg\nE : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nu : ℕ → ℝ≥0\nK : ℕ → Set E\nC : ℝ≥0\nhu : Tendsto u atTop (𝓝 0)\nhK : ∀ (n : ℕ), IsCompact (K n)\nI :\n ∀ (μ : FiniteMeasure E) (n : ℕ),\n ∑ i ∈ Finset.range (n + 1), μ.restrict (disjoint... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.HasOuterApproxClosedProd | {
"line": 221,
"column": 2
} | {
"line": 221,
"column": 17
} | {
"line": 221,
"column": 18
} | [
{
"pp": "ι : Type u_1\nT : Type u_4\nX : ι → Type u_5\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmT : MeasurableSpace T\ninst✝⁵ : TopologicalSpace T\ninst✝⁴ : BorelSpace T\ninst✝³ : HasOu... | [
"ι : Type u_1\nT : Type u_4\nX : ι → Type u_5\nmX : (i : ι) → MeasurableSpace (X i)\ninst✝⁸ : (i : ι) → TopologicalSpace (X i)\ninst✝⁷ : ∀ (i : ι), BorelSpace (X i)\ninst✝⁶ : ∀ (i : ι), HasOuterApproxClosed (X i)\nmT : MeasurableSpace T\ninst✝⁵ : TopologicalSpace T\ninst✝⁴ : BorelSpace T\ninst✝³ : HasOuterApproxClo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.LevyConvergence | {
"line": 144,
"column": 8
} | {
"line": 144,
"column": 19
} | {
"line": 144,
"column": 20
} | [
{
"pp": "case hbc.refine_1.refine_2\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsProbabilityMeasure (μ i)\nf : E → ℂ\nhf : ContinuousAt f 0\nh : ∀ (t : E), ... | [
"case hbc.refine_1.refine_2\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : ℕ → Measure E\ninst✝ : ∀ (i : ℕ), IsProbabilityMeasure (μ i)\nf : E → ℂ\nhf : ContinuousAt f 0\nh : ∀ (t : E), Tendsto (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.PreVariation | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 49
} | [
{
"pp": "X : Type u_1\ninst✝ : MeasurableSpace X\nf : Set X → ℝ≥0∞\ns : Set X\nhs : MeasurableSet s\nP : Finpartition ⟨s, hs⟩\n⊢ ∑ p ∈ P.parts, f ↑p ≤ preVariationFun f s",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"MeasurableSet",
... | [
"X : Type u_1\ninst✝ : MeasurableSpace X\nf : Set X → ℝ≥0∞\ns : Set X\nhs : MeasurableSet s\nP : Finpartition ⟨s, hs⟩\n⊢ ∀ (b : ℝ≥0∞), (∀ (i : Finpartition ⟨s, ⋯⟩), ∑ p ∈ i.parts, f ↑p ≤ b) → ∑ p ∈ P.parts, f ↑p ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.PreVariation | {
"line": 149,
"column": 44
} | {
"line": 149,
"column": 55
} | {
"line": 149,
"column": 56
} | [
{
"pp": "X : Type u_1\ninst✝ : MeasurableSpace X\nf : Set X → ℝ≥0∞\ns : Set X\nhs : MeasurableSet s\nh : preVariationFun f s ≠ ∞\nε : ℝ≥0\nhε : 0 < ↑ε\nh'ε : ↑ε < ∞\n⊢ 0 < ε",
"ppTerm": "?m.94",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝ : MeasurableSpace X\nf : Set X → ℝ≥0∞\ns : Set X\nhs : MeasurableSet s\nh : preVariationFun f s ≠ ∞\nε : ℝ≥0\nhε : 0 < ↑ε\nh'ε : ↑ε < ∞\n⊢ 0 < ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.LevyConvergence | {
"line": 166,
"column": 47
} | {
"line": 166,
"column": 58
} | {
"line": 166,
"column": 59
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\nE : Type u_3\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : PolishSpace E\ninst✝ : BorelSpace E\nι : Type u_4\n𝓕 : Filter ι\nμ : ι → ProbabilityMeasure E\nh_tight : IsTightMeasureSet {x | ∃ n, ↑(μ n) = x}\nμ₀ : ProbabilityMeasure E\nA : StarSubalg... | [
"𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\nE : Type u_3\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : PolishSpace E\ninst✝ : BorelSpace E\nι : Type u_4\n𝓕 : Filter ι\nμ : ι → ProbabilityMeasure E\nh_tight : IsTightMeasureSet {x | ∃ n, ↑(μ n) = x}\nμ₀ : ProbabilityMeasure E\nA : StarSubalgebra 𝕜 (E →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Support | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 62
} | {
"line": 75,
"column": 63
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : MeasurableSpace X\nμ : Measure X\ninst✝ : μ.IsOpenPosMeasure\n⊢ μ.support = Set.univ",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.to... | [
"X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : MeasurableSpace X\nμ : Measure X\ninst✝ : μ.IsOpenPosMeasure\n⊢ ∀ (x : X), ∀ U ∈ 𝓝 x, 0 < μ U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.ResolventTransform | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | {
"line": 70,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : MeasurableSpace 𝕜\na : A\ninst✝⁵ : OpensMeasurableSpace 𝕜\ninst✝⁴ : NormedRing A\ninst✝³ : NormedAlgebra 𝕜 A\ninst✝² : CompleteSpace A\ninst✝¹ : MeasurableSpace A\ninst✝ : BorelSpace A\nh1 : ContinuousOn (resolvent a) (resolv... | [
"𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : MeasurableSpace 𝕜\na : A\ninst✝⁵ : OpensMeasurableSpace 𝕜\ninst✝⁴ : NormedRing A\ninst✝³ : NormedAlgebra 𝕜 A\ninst✝² : CompleteSpace A\ninst✝¹ : MeasurableSpace A\ninst✝ : BorelSpace A\nh1 : ContinuousOn (resolvent a) (resolventSet 𝕜 a)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Support | {
"line": 141,
"column": 2
} | {
"line": 142,
"column": 9
} | {
"line": 142,
"column": 10
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : MeasurableSpace X\nμ : Measure X\nh : IsLindelof μ.supportᶜ\ns : X\nhs : s ∈ μ.supportᶜ\n⊢ ∃ t ∈ 𝓝[μ.supportᶜ] s, tᶜ ∈ ae μ",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"MeasureTheory.ae",
... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : MeasurableSpace X\nμ : Measure X\nh : IsLindelof μ.supportᶜ\ns : X\nhs : s ∈ μ.supportᶜ\n⊢ ∃ t ∈ 𝓝 s, μ t = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.LevyConvergence | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 46
} | {
"line": 195,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nι : Type u_2\n𝓕 : Filter ι\nμ₀ : ProbabilityMeasure E\nμ : ι → ProbabilityMeasure E\nh : ∀ (t : E), Tendsto (fun n ↦ charFun (↑(μ n)) t) 𝓕 (𝓝 (charFun (↑μ₀) t))\ng : E →ᵇ ℂ\... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nι : Type u_2\n𝓕 : Filter ι\nμ₀ : ProbabilityMeasure E\nμ : ι → ProbabilityMeasure E\nh : ∀ (t : E), Tendsto (fun n ↦ charFun (↑(μ n)) t) 𝓕 (𝓝 (charFun (↑μ₀) t))\ng : E →ᵇ ℂ\nw : AddMono... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.ResolventTransform | {
"line": 160,
"column": 10
} | {
"line": 160,
"column": 56
} | {
"line": 160,
"column": 57
} | [
{
"pp": "case hcd\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : HereditarilyLindelofSpace 𝕜\ninst✝⁵ : CompleteSpace 𝕜\ninst✝⁴ : MeasurableSpace 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : RCLike A\ninst✝¹ : NormedAlgebra 𝕜 A\nμ : Measure 𝕜\ninst✝ : IsFiniteMeasure μ\na : A\nha : a ∉ ⇑... | [
"case hcd\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : HereditarilyLindelofSpace 𝕜\ninst✝⁵ : CompleteSpace 𝕜\ninst✝⁴ : MeasurableSpace 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : RCLike A\ninst✝¹ : NormedAlgebra 𝕜 A\nμ : Measure 𝕜\ninst✝ : IsFiniteMeasure μ\na : A\nha : a ∉ ⇑(algebraMap ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.ResolventTransform | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 43
} | {
"line": 169,
"column": 44
} | [
{
"pp": "case right\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : HereditarilyLindelofSpace 𝕜\ninst✝⁵ : CompleteSpace 𝕜\ninst✝⁴ : MeasurableSpace 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : RCLike A\ninst✝¹ : NormedAlgebra 𝕜 A\nμ : Measure 𝕜\ninst✝ : IsFiniteMeasure μ\na : A\nha : a ∉... | [
"case right\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : HereditarilyLindelofSpace 𝕜\ninst✝⁵ : CompleteSpace 𝕜\ninst✝⁴ : MeasurableSpace 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : RCLike A\ninst✝¹ : NormedAlgebra 𝕜 A\nμ : Measure 𝕜\ninst✝ : IsFiniteMeasure μ\na : A\nha : a ∉ ⇑(algebraMa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 515,
"column": 35
} | {
"line": 515,
"column": 46
} | {
"line": 515,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nS : Set (ProbabilityMeasure E)\nhS : IsTightMeasureSet {x | ∃ μ ∈ S, ↑μ = x}\nu : ℕ → ℝ≥0\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nn : ℕ\nK : Set E\nK_comp : IsCompact K\... | [
"E : Type u_1\ninst✝³ : MeasurableSpace E\ninst✝² : TopologicalSpace E\ninst✝¹ : T2Space E\ninst✝ : BorelSpace E\nS : Set (ProbabilityMeasure E)\nhS : IsTightMeasureSet {x | ∃ μ ∈ S, ↑μ = x}\nu : ℕ → ℝ≥0\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nn : ℕ\nK : Set E\nK_comp : IsCompact K\nhK : ∀ μ ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.SeparableMeasure | {
"line": 233,
"column": 18
} | {
"line": 242,
"column": 60
} | {
"line": 243,
"column": 16
} | [
{
"pp": "case h₁\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\n𝒜 : Set (Set X)\ninst✝ : IsFiniteMeasure μ\nh𝒜 : IsSetAlgebra 𝒜\nhgen : m = MeasurableSpace.generateFrom 𝒜\ns : Set X\nf : ℕ → Set X\nhs✝ : ∀ (n : ℕ), MeasurableSet (f n)\nhf : ∀ (n : ℕ), MeasurableSet (f n) ∧ ∀ (ε : ℝ), 0 < ε → ∃ t ∈ 𝒜,... | [] | rw [measure_sdiff (h_fin := measure_ne_top _ _),
toReal_sub_of_le (ha := measure_ne_top _ _)]
· apply lt_of_le_of_lt (sub_le_dist ..)
simp only [Finset.mem_range, Nat.lt_add_one_iff]
exact (dist_comm (α := ℝ) .. ▸ hN N (le_refl N))
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.SeparableMeasure | {
"line": 233,
"column": 18
} | {
"line": 242,
"column": 60
} | {
"line": 243,
"column": 16
} | [
{
"pp": "case h₁\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\n𝒜 : Set (Set X)\ninst✝ : IsFiniteMeasure μ\nh𝒜 : IsSetAlgebra 𝒜\nhgen : m = MeasurableSpace.generateFrom 𝒜\ns : Set X\nf : ℕ → Set X\nhs✝ : ∀ (n : ℕ), MeasurableSet (f n)\nhf : ∀ (n : ℕ), MeasurableSet (f n) ∧ ∀ (ε : ℝ), 0 < ε → ∃ t ∈ 𝒜,... | [] | rw [measure_sdiff (h_fin := measure_ne_top _ _),
toReal_sub_of_le (ha := measure_ne_top _ _)]
· apply lt_of_le_of_lt (sub_le_dist ..)
simp only [Finset.mem_range, Nat.lt_add_one_iff]
exact (dist_comm (α := ℝ) .. ▸ hN N (le_refl N))
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Typeclasses.ZeroOne | {
"line": 57,
"column": 2
} | {
"line": 65,
"column": 19
} | {
"line": 67,
"column": 0
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\nμ : Measure α\ninst✝ : IsZeroOneMeasure μ\n⊢ (∃ s, μ s = 1) ↔ μ univ = 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"False",
"MeasureTheory.Measure",
"congrArg",
"instIsBo... | [] | constructor
· rintro ⟨s, h⟩
rcases μ.zero_one univ with (h₀ | h₁)
· have := measure_mono (μ := μ) <| subset_univ s
rw [h] at this
simp_all
· exact h₁
· intro h
exact ⟨univ, h⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Typeclasses.ZeroOne | {
"line": 57,
"column": 2
} | {
"line": 65,
"column": 19
} | {
"line": 67,
"column": 0
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\nμ : Measure α\ninst✝ : IsZeroOneMeasure μ\n⊢ (∃ s, μ s = 1) ↔ μ univ = 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"False",
"MeasureTheory.Measure",
"congrArg",
"instIsBo... | [] | constructor
· rintro ⟨s, h⟩
rcases μ.zero_one univ with (h₀ | h₁)
· have := measure_mono (μ := μ) <| subset_univ s
rw [h] at this
simp_all
· exact h₁
· intro h
exact ⟨univ, h⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 569,
"column": 6
} | {
"line": 569,
"column": 73
} | {
"line": 569,
"column": 74
} | [
{
"pp": "case h\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝² : PseudoMetricSpace 𝓧\ninst✝¹ : OpensMeasurableSpace 𝓧\ninst✝ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\nU : ℕ → Set 𝓧\nO : ∀ (i : ℕ), IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (U i)\nCov : ⋃ i, U i = univ\... | [
"case h\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝² : PseudoMetricSpace 𝓧\ninst✝¹ : OpensMeasurableSpace 𝓧\ninst✝ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\nU : ℕ → Set 𝓧\nO : ∀ (i : ℕ), IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (U i)\nCov : ⋃ i, U i = univ\nhcomp : IsC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.SeparableMeasure | {
"line": 369,
"column": 6
} | {
"line": 376,
"column": 74
} | {
"line": 378,
"column": 0
} | [
{
"pp": "case refine_2\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\ninst✝¹ : CountablyGenerated X\ninst✝ : SigmaFinite μ\nh : (countableGeneratingSet X).Countable\nhgen : MeasurableSpace.generateFrom (countableGeneratingSet X) = m\n𝒜 : Set (Set X) := countableGeneratingSet X ∪ {x | ∃ n, μ.toFiniteSpann... | [] | induction hs with
| base t t_mem =>
rcases t_mem with t_mem | ⟨n, rfl⟩
· exact hgen ▸ measurableSet_generateFrom t_mem
· exact μ.toFiniteSpanningSetsIn.set_mem n
| empty => exact MeasurableSet.empty
| compl t _ t_mem => exact MeasurableSet.compl t_mem
| union t u _ _ t_me... | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.MeasureTheory.Measure.SeparableMeasure | {
"line": 369,
"column": 6
} | {
"line": 376,
"column": 74
} | {
"line": 378,
"column": 0
} | [
{
"pp": "case refine_2\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\ninst✝¹ : CountablyGenerated X\ninst✝ : SigmaFinite μ\nh : (countableGeneratingSet X).Countable\nhgen : MeasurableSpace.generateFrom (countableGeneratingSet X) = m\n𝒜 : Set (Set X) := countableGeneratingSet X ∪ {x | ∃ n, μ.toFiniteSpann... | [] | induction hs with
| base t t_mem =>
rcases t_mem with t_mem | ⟨n, rfl⟩
· exact hgen ▸ measurableSet_generateFrom t_mem
· exact μ.toFiniteSpanningSetsIn.set_mem n
| empty => exact MeasurableSet.empty
| compl t _ t_mem => exact MeasurableSet.compl t_mem
| union t u _ _ t_me... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.SeparableMeasure | {
"line": 369,
"column": 6
} | {
"line": 376,
"column": 74
} | {
"line": 378,
"column": 0
} | [
{
"pp": "case refine_2\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\ninst✝¹ : CountablyGenerated X\ninst✝ : SigmaFinite μ\nh : (countableGeneratingSet X).Countable\nhgen : MeasurableSpace.generateFrom (countableGeneratingSet X) = m\n𝒜 : Set (Set X) := countableGeneratingSet X ∪ {x | ∃ n, μ.toFiniteSpann... | [] | induction hs with
| base t t_mem =>
rcases t_mem with t_mem | ⟨n, rfl⟩
· exact hgen ▸ measurableSet_generateFrom t_mem
· exact μ.toFiniteSpanningSetsIn.set_mem n
| empty => exact MeasurableSet.empty
| compl t _ t_mem => exact MeasurableSet.compl t_mem
| union t u _ _ t_me... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 581,
"column": 8
} | {
"line": 581,
"column": 75
} | {
"line": 582,
"column": 12
} | [
{
"pp": "case h\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝² : PseudoMetricSpace 𝓧\ninst✝¹ : OpensMeasurableSpace 𝓧\ninst✝ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\nU : ℕ → Set 𝓧\nO : ∀ (i : ℕ), IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (U i)\nCov : ⋃ i, U i = univ\... | [
"case h\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝² : PseudoMetricSpace 𝓧\ninst✝¹ : OpensMeasurableSpace 𝓧\ninst✝ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\nU : ℕ → Set 𝓧\nO : ∀ (i : ℕ), IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (U i)\nCov : ⋃ i, U i = univ\nhcomp : IsC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.AddContent | {
"line": 39,
"column": 15
} | {
"line": 39,
"column": 26
} | {
"line": 39,
"column": 27
} | [
{
"pp": "α : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t\nh''m :... | [
"α : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t\nh''m : ∀ (s : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.AddContent | {
"line": 43,
"column": 6
} | {
"line": 43,
"column": 32
} | {
"line": 44,
"column": 6
} | [
{
"pp": "α : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t\nh''m :... | [
"α : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t\nh''m : ∀ (s : Set ... | simp only [← toReal_enorm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.VectorMeasure.AddContent | {
"line": 55,
"column": 16
} | {
"line": 55,
"column": 27
} | {
"line": 55,
"column": 28
} | [
{
"pp": "case zero\nα : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + ... | [
"case zero\nα : Type u_1\nhα : MeasurableSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\nμ : Measure α\nm : Set α → E\nhm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s\ninst✝ : IsFiniteMeasure μ\nh'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t\nh''m : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 632,
"column": 6
} | {
"line": 632,
"column": 17
} | {
"line": 632,
"column": 18
} | [
{
"pp": "case refine_1\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝³ : PseudoMetricSpace 𝓧\ninst✝² : OpensMeasurableSpace 𝓧\ninst✝¹ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\ninst✝ : CompleteSpace 𝓧\nhcomp : IsCompact (closure[ProbabilityMeasure.instTopologicalSpace] S)\nhnonempty : No... | [
"case refine_1\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝³ : PseudoMetricSpace 𝓧\ninst✝² : OpensMeasurableSpace 𝓧\ninst✝¹ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\ninst✝ : CompleteSpace 𝓧\nhcomp : IsCompact (closure[ProbabilityMeasure.instTopologicalSpace] S)\nhnonempty : Nonempty 𝓧\nD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | {
"line": 144,
"column": 6
} | {
"line": 144,
"column": 44
} | {
"line": 144,
"column": 45
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteS... | [
"case pos\nα : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | {
"line": 146,
"column": 36
} | {
"line": 146,
"column": 80
} | {
"line": 146,
"column": 81
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf ... | [
"α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf : α → E\na :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | {
"line": 153,
"column": 50
} | {
"line": 153,
"column": 61
} | {
"line": 153,
"column": 62
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf ... | [
"α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf : α → E\na :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | {
"line": 206,
"column": 6
} | {
"line": 206,
"column": 22
} | {
"line": 206,
"column": 23
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf ... | [
"α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf : α → E\nhf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Variation.Defs | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 57
} | {
"line": 48,
"column": 58
} | [
{
"pp": "X : Type u_1\nmX : MeasurableSpace X\nV : Type u_2\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : ℕ → { t // MeasurableSet t }\nhs : Pairwise (Function.onFun Disjoint (Subtype.val ∘ s))\nhmeas : ∀ (i : ℕ), MeasurableSet ↑(s i)\n⊢ (fun x ↦ ‖μ... | [
"X : Type u_1\nmX : MeasurableSpace X\nV : Type u_2\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : ℕ → { t // MeasurableSet t }\nhs : Pairwise (Function.onFun Disjoint (Subtype.val ∘ s))\nhmeas : ∀ (i : ℕ), MeasurableSet ↑(s i)\n⊢ ‖∑' (i : ℕ), μ ↑(s i)‖ₑ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | {
"line": 241,
"column": 6
} | {
"line": 241,
"column": 22
} | {
"line": 241,
"column": 23
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf ... | [
"α : Type u_1\ninst✝⁸ : LinearOrder α\ninst✝⁷ : DenselyOrdered α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : CompactIccSpace α\nhα : MeasurableSpace α\ninst✝² : BorelSpace α\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nf : α → E\nhf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Prokhorov | {
"line": 664,
"column": 4
} | {
"line": 664,
"column": 56
} | {
"line": 665,
"column": 4
} | [
{
"pp": "case inr.inr.refine_1\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝³ : PseudoMetricSpace 𝓧\ninst✝² : OpensMeasurableSpace 𝓧\ninst✝¹ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\ninst✝ : CompleteSpace 𝓧\nhcomp : IsCompact (closure[ProbabilityMeasure.instTopologicalSpace] S)\nhnonem... | [
"case inr.inr.refine_1\n𝓧 : Type u_1\nm𝓧 : MeasurableSpace 𝓧\ninst✝³ : PseudoMetricSpace 𝓧\ninst✝² : OpensMeasurableSpace 𝓧\ninst✝¹ : SecondCountableTopology 𝓧\nS : Set (ProbabilityMeasure 𝓧)\ninst✝ : CompleteSpace 𝓧\nhcomp : IsCompact (closure[ProbabilityMeasure.instTopologicalSpace] S)\nhnonempty : Nonemp... | refine Metric.totallyBounded_iff.mpr fun δ δpos ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 31
} | {
"line": 105,
"column": 4
} | [
{
"pp": "case refine_2\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\na : ℝ≥0∞\nha : a < preVariationFun (fun x ↦ ‖μ x‖ₑ) s\nP : Finpartition ⟨s, hs⟩\nhP : a < ∑ p ∈ P.p... | [
"case refine_2\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\na : ℝ≥0∞\nha : a < preVariationFun (fun x ↦ ‖μ x‖ₑ) s\nP : Finpartition ⟨s, hs⟩\nhP : a < ∑ p ∈ P.parts, (fun x... | rcases hi with ⟨h'i, i_mem⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 107,
"column": 34
} | {
"line": 107,
"column": 45
} | {
"line": 107,
"column": 46
} | [
{
"pp": "X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\na : ℝ≥0∞\nha : a < preVariationFun (fun x ↦ ‖μ x‖ₑ) s\nP : Finpartition ⟨s, hs⟩\nhP : a < ∑ p ∈ P.parts, (fun x ↦ ... | [
"X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\na : ℝ≥0∞\nha : a < preVariationFun (fun x ↦ ‖μ x‖ₑ) s\nP : Finpartition ⟨s, hs⟩\nhP : a < ∑ p ∈ P.parts, (fun x ↦ ‖μ x‖ₑ) ↑p\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 31
} | {
"line": 130,
"column": 4
} | [
{
"pp": "case refine_2\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\nε : ℝ≥0∞\nhε : 0 < ε\nhμ : preVariationFun (fun x ↦ ‖μ x‖ₑ) s ≠ ∞\nP : Finpartition ⟨s, hs⟩\nhP : p... | [
"case refine_2\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\nε : ℝ≥0∞\nhε : 0 < ε\nhμ : preVariationFun (fun x ↦ ‖μ x‖ₑ) s ≠ ∞\nP : Finpartition ⟨s, hs⟩\nhP : preVariationF... | rcases hi with ⟨h'i, i_mem⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 132,
"column": 34
} | {
"line": 132,
"column": 45
} | {
"line": 132,
"column": 46
} | [
{
"pp": "X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\nε : ℝ≥0∞\nhε : 0 < ε\nhμ : preVariationFun (fun x ↦ ‖μ x‖ₑ) s ≠ ∞\nP : Finpartition ⟨s, hs⟩\nhP : preVariationFun ... | [
"X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nhs : MeasurableSet s\nε : ℝ≥0∞\nhε : 0 < ε\nhμ : preVariationFun (fun x ↦ ‖μ x‖ₑ) s ≠ ∞\nP : Finpartition ⟨s, hs⟩\nhP : preVariationFun (fun x ↦ ‖μ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 49
} | {
"line": 179,
"column": 50
} | [
{
"pp": "X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nm : Measure X\nhs : MeasurableSet s\nh : ∀ (E : Set X), MeasurableSet E → E ⊆ s → ‖μ E‖ₑ ≤ m E\ni : Finpartition ⟨s, ⋯⟩\na : Subtype Mea... | [
"X : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝² : TopologicalSpace V\ninst✝¹ : ENormedAddCommMonoid V\ninst✝ : T2Space V\nμ : VectorMeasure X V\ns : Set X\nm : Measure X\nhs : MeasurableSet s\nh : ∀ (E : Set X), MeasurableSet E → E ⊆ s → ‖μ E‖ₑ ≤ m E\ni : Finpartition ⟨s, ⋯⟩\na : Subtype MeasurableSet\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 39
} | {
"line": 202,
"column": 6
} | [
{
"pp": "case insert\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝³ : TopologicalSpace V\ninst✝² : ENormedAddCommMonoid V\ninst✝¹ : T2Space V\ninst✝ : ContinuousAdd V\nι : Type u_3\nμ : ι → VectorMeasure X V\ni : ι\ns : Finset ι\nhis : i ∉ s\nih : (∑ i ∈ s, μ i).variation ≤ ∑ i ∈ s, (μ i).variation... | [
"case insert\nX : Type u_1\nV : Type u_2\nmX : MeasurableSpace X\ninst✝³ : TopologicalSpace V\ninst✝² : ENormedAddCommMonoid V\ninst✝¹ : T2Space V\ninst✝ : ContinuousAdd V\nι : Type u_3\nμ : ι → VectorMeasure X V\ni : ι\ns : Finset ι\nhis : i ∉ s\nih : (∑ i ∈ s, μ i).variation ≤ ∑ i ∈ s, (μ i).variation\n⊢ (μ i + ∑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Variation.Semivariation | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 45
} | {
"line": 159,
"column": 4
} | [
{
"pp": "X : Type u_1\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nmX : MeasurableSpace X\nμ : VectorMeasure X E\nh : μ.semivariation univ = ∞\nt : Set X → Set X\nt_meas : ∀ (s : Set X), MeasurableSet s → μ.semivariation s = ∞ → MeasurableSet (t s)\nt_subs : ∀ (s : Set X), MeasurableSe... | [
"X : Type u_1\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nmX : MeasurableSpace X\nμ : VectorMeasure X E\nh : μ.semivariation univ = ∞\nt : Set X → Set X\nt_meas : ∀ (s : Set X), MeasurableSet s → μ.semivariation s = ∞ → MeasurableSet (t s)\nt_subs : ∀ (s : Set X), MeasurableSet s → μ.semi... | simp only [sdiff_le_iff, sup_eq_union, u] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.VectorMeasure.Variation.Semivariation | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 28
} | {
"line": 184,
"column": 29
} | [
{
"pp": "X : Type u_1\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nmX : MeasurableSpace X\nμ : VectorMeasure X E\ns : Set X\n⊢ ‖μ s‖ ≤ ↑μ.bound",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
... | [
"X : Type u_1\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nmX : MeasurableSpace X\nμ : VectorMeasure X E\ns : Set X\n⊢ ‖μ s‖₊ ≤ μ.bound"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 15
} | {
"line": 160,
"column": 16
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsSemilinearSet s) → IsSemilinearSet (⋃₀ s✝)\nhS' : IsSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsSemilinearSet a\n⊢ IsSemilinearSet (⋃₀ insert a✝¹ s✝)",
"ppTerm":... | [
"case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsSemilinearSet s) → IsSemilinearSet (⋃₀ s✝)\nhS' : IsSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsSemilinearSet a\n⊢ IsSemilinearSet (a✝¹ ∪ ⋃₀ s✝)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 40
} | {
"line": 265,
"column": 41
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ t ∈ s✝, IsLinearSet t) → IsSemilinearSet ↑(closure (⋃₀ s✝))\nhS' : IsLinearSet a✝¹ ∧ ∀ a ∈ s✝, IsLinearSet a\n⊢ IsSemilinearSet ↑(closure (⋃₀ insert a✝¹ s✝))",
... | [
"case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ t ∈ s✝, IsLinearSet t) → IsSemilinearSet ↑(closure (⋃₀ s✝))\nhS' : IsLinearSet a✝¹ ∧ ∀ a ∈ s✝, IsLinearSet a\n⊢ IsSemilinearSet (↑(closure a✝¹) + ↑(closure (⋃₀ s✝)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 264,
"column": 4
} | {
"line": 265,
"column": 69
} | {
"line": 267,
"column": 0
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ t ∈ s✝, IsLinearSet t) → IsSemilinearSet ↑(closure (⋃₀ s✝))\nhS' : ∀ t ∈ insert a✝¹ s✝, IsLinearSet t\n⊢ IsSemilinearSet ↑(closure (⋃₀ insert a✝¹ s✝))",
"ppTer... | [] | simp_rw [mem_insert_iff, forall_eq_or_imp] at hS'
simpa [closure_union, coe_sup] using hS'.1.closure.add (ih hS'.2) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 264,
"column": 4
} | {
"line": 265,
"column": 69
} | {
"line": 267,
"column": 0
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ t ∈ s✝, IsLinearSet t) → IsSemilinearSet ↑(closure (⋃₀ s✝))\nhS' : ∀ t ∈ insert a✝¹ s✝, IsLinearSet t\n⊢ IsSemilinearSet ↑(closure (⋃₀ insert a✝¹ s✝))",
"ppTer... | [] | simp_rw [mem_insert_iff, forall_eq_or_imp] at hS'
simpa [closure_union, coe_sup] using hS'.1.closure.add (ih hS'.2) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 324,
"column": 4
} | {
"line": 324,
"column": 15
} | {
"line": 324,
"column": 16
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsProperSemilinearSet s) → IsProperSemilinearSet (⋃₀ s✝)\nhS' : IsProperSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsProperSemilinearSet a\n⊢ IsProperSemilinearSet (⋃₀ ... | [
"case insert\nM : Type u_1\ninst✝ : AddCommMonoid M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsProperSemilinearSet s) → IsProperSemilinearSet (⋃₀ s✝)\nhS' : IsProperSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsProperSemilinearSet a\n⊢ IsProperSemilinearSet (a✝¹ ∪ ⋃₀ s✝)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 368,
"column": 24
} | {
"line": 368,
"column": 56
} | {
"line": 368,
"column": 56
} | [
{
"pp": "case a\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : IsCancelAdd M\na : M\nt : Finset M\nih : ∀ m < t.card, ∀ (a : M) (t : Finset M), t.card = m → IsProperSemilinearSet (a +ᵥ ↑(closure ↑t))\nt' : Finset M\nht' : t' ⊆ t\nf : M → ℕ\ni : M\nhi : i ∈ t'\nhfi : 0 < f i\nheq : ∑ x ∈ t', f x • x = ∑ x ∈ t ... | [
"case a\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : IsCancelAdd M\na : M\nt : Finset M\nih : ∀ m < t.card, ∀ (a : M) (t : Finset M), t.card = m → IsProperSemilinearSet (a +ᵥ ↑(closure ↑t))\nt' : Finset M\nht' : t' ⊆ t\nf : M → ℕ\ni : M\nhi : i ∈ t'\nhfi : 0 < f i\nheq : ∑ x ∈ t', f x • x = ∑ x ∈ t \\ t', f x •... | tsub_add_cancel_of_le (hfg j hj) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 407,
"column": 36
} | {
"line": 407,
"column": 72
} | {
"line": 407,
"column": 73
} | [
{
"pp": "S : Finset (Set ℕ)\nhS : ∀ t ∈ S, IsProperLinearSet t\na : ℕ\nt : Finset ℕ\nht : LinearIndepOn ℕ id ↑t\n⊢ t.card ≤ 1",
"ppTerm": "?m.165",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"S : Finset (Set ℕ)\nhS : ∀ t ∈ S, IsProperLinearSet t\na : ℕ\nt : Finset ℕ\nht : LinearIndepOn ℕ id ↑t\n⊢ t.card ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.SetIntegral | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 13
} | {
"line": 71,
"column": 14
} | [
{
"pp": "case intro\nι : Type u_1\nX : Type u_2\nE : Type u_3\nF : Type u_4\nmX : MeasurableSpace X\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\nμ : VectorMeasure X F\nf : X → E\ninst✝ : Finite ι\nt : ι → Set X\nht : ∀ (i : ι), MeasurableSet (t i)\nh't : ∀ (i : ι), μ.IntegrableOn f (t i)\nval✝... | [
"case intro\nι : Type u_1\nX : Type u_2\nE : Type u_3\nF : Type u_4\nmX : MeasurableSpace X\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\nμ : VectorMeasure X F\nf : X → E\ninst✝ : Finite ι\nt : ι → Set X\nht : ∀ (i : ι), MeasurableSet (t i)\nh't : ∀ (i : ι), μ.IntegrableOn f (t i)\nval✝ : Fintype ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | {
"line": 412,
"column": 30
} | {
"line": 412,
"column": 51
} | {
"line": 412,
"column": 52
} | [
{
"pp": "S : Finset (Set ℕ)\nhS : ∀ t ∈ S, IsProperLinearSet t\na b : ℕ\nht : LinearIndepOn ℕ id ↑{b}\n⊢ b ≠ 0",
"ppTerm": "?m.255",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
],
"usedFVars": [
"b"
],
"use... | [
"S : Finset (Set ℕ)\nhS : ∀ t ∈ S, IsProperLinearSet t\na b : ℕ\nht : LinearIndepOn ℕ id ↑{b}\n⊢ ¬b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.SetIntegral | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 89
} | {
"line": 124,
"column": 89
} | [
{
"pp": "X : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns t : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G\nB : E ... | [
"X : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns t : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G\nB : E →L[ℝ] F →L[ℝ... | integral_add_vectorMeasure (hfs.mono hs inter_subset_left) (hfs.mono hs sdiff_subset) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.VectorMeasure.WithDensityVec | {
"line": 77,
"column": 35
} | {
"line": 77,
"column": 69
} | {
"line": 77,
"column": 70
} | [
{
"pp": "X : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf g : X → E\nB : E →L[ℝ] F →L[... | [
"X : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf g : X → E\nB : E →L[ℝ] F →L[ℝ] G\nh : f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.SetIntegral | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 59
} | {
"line": 174,
"column": 60
} | [
{
"pp": "case neg\nX : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G... | [
"case neg\nX : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G\nB : E →L[ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.WithDensityVec | {
"line": 133,
"column": 8
} | {
"line": 133,
"column": 66
} | {
"line": 134,
"column": 4
} | [
{
"pp": "case inr\nX : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf : X → E\nB : E →L... | [] | apply mul_le_of_le_one_left (by positivity) mul_inv_le_one | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.MeasureTheory.VectorMeasure.WithDensityVec | {
"line": 137,
"column": 12
} | {
"line": 137,
"column": 23
} | {
"line": 137,
"column": 24
} | [
{
"pp": "X : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf : X → E\nB : E →L[ℝ] F →L[ℝ... | [
"X : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf : X → E\nB : E →L[ℝ] F →L[ℝ] G\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 13
} | {
"line": 246,
"column": 14
} | [
{
"pp": "case e_a\nM : Type u_1\ninst✝ : AddCommMonoid M\na : M\nt : Set M\nht : t.Finite\nx : M\n⊢ x ∈ t ↔ x ∈ ⇑(closure (insert a t)).subtype '' ⇑(closure (insert a t)).subtype ⁻¹' t",
"ppTerm": "?e_a✝",
"assigned": true,
"usedConstants": [
"AddSubmonoid.subtype",
"Eq.mpr",
"Iff.... | [
"case e_a\nM : Type u_1\ninst✝ : AddCommMonoid M\na : M\nt : Set M\nht : t.Finite\nx : M\n⊢ x ∈ t → x ∈ closure (insert a t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.SetIntegral | {
"line": 343,
"column": 63
} | {
"line": 344,
"column": 53
} | {
"line": 346,
"column": 0
} | [
{
"pp": "X : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\nμ : VectorMeasure X F\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedSpace ℝ G\nB : E →L[ℝ] F →L[ℝ] G\ninst✝¹... | [] | by
rw [integral_indicator s_meas, ← setIntegral_const] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 311,
"column": 4
} | {
"line": 311,
"column": 15
} | {
"line": 311,
"column": 16
} | [
{
"pp": "case insert\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : AddMonoid.FG M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsSemilinearSet s) → IsSemilinearSet (⋂₀ s✝)\nhS' : IsSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsSemilinearSet a\n⊢ IsSemilinearSet (⋂₀ inser... | [
"case insert\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : AddMonoid.FG M\nS : Set (Set M)\na✝¹ : Set M\ns✝ : Set (Set M)\na✝ : a✝¹ ∉ s✝\nhs✝ : s✝.Finite\nih : (∀ s ∈ s✝, IsSemilinearSet s) → IsSemilinearSet (⋂₀ s✝)\nhS' : IsSemilinearSet a✝¹ ∧ ∀ a ∈ s✝, IsSemilinearSet a\n⊢ IsSemilinearSet (a✝¹ ∩ ⋂₀ s✝)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 24
} | {
"line": 354,
"column": 25
} | [
{
"pp": "ι : Type u_3\nx y : ι → ℕ\nh : toRatVec x = toRatVec y\ni : ι\n⊢ x i = y i",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_3\nx y : ι → ℕ\nh : toRatVec x = toRatVec y\ni : ι\n⊢ x i = y i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 378,
"column": 4
} | {
"line": 378,
"column": 15
} | {
"line": 378,
"column": 16
} | [
{
"pp": "ι : Type u_3\ns : Set (ι → ℕ)\nt : Finset (ι → ℕ)\nf : (ι → ℕ) → ℤ\nht : ↑t ⊆ s\nhf : ∀ i ∉ t, f i = 0\nheq : ∑ i ∈ t, f i • toRatVec i = 0\ni : ι → ℕ\nhs : (Int.toNat ∘ f) i = (Int.toNat ∘ (fun x ↦ -x) ∘ f) i\nhi : i ∈ t\n⊢ (f i).toNat = (-f i).toNat",
"ppTerm": "?m.167",
"assigned": false,
... | [
"ι : Type u_3\ns : Set (ι → ℕ)\nt : Finset (ι → ℕ)\nf : (ι → ℕ) → ℤ\nht : ↑t ⊆ s\nhf : ∀ i ∉ t, f i = 0\nheq : ∑ i ∈ t, f i • toRatVec i = 0\ni : ι → ℕ\nhs : (Int.toNat ∘ f) i = (Int.toNat ∘ (fun x ↦ -x) ∘ f) i\nhi : i ∈ t\n⊢ (f i).toNat = (-f i).toNat"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 498,
"column": 4
} | {
"line": 498,
"column": 57
} | {
"line": 498,
"column": 58
} | [
{
"pp": "case mem\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx y✝ : ι → ℕ\ni : ↑hs.basisSet\nt : Set (ι → ℕ)\nht : t ⊆ hs.basisSet\nhi : ↑i ∉ t\ny : ι → ℕ\nhy : y ∈ t\n⊢ (hs.basis.repr (hs.basis ⟨y, ⋯⟩)) i = 0",
"ppTerm": "?mem",
"assigned": true,
"usedConstants": [
... | [
"case mem\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx y✝ : ι → ℕ\ni : ↑hs.basisSet\nt : Set (ι → ℕ)\nht : t ⊆ hs.basisSet\nhi : ↑i ∉ t\ny : ι → ℕ\nhy : y ∈ t\n⊢ ¬y = ↑i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 646,
"column": 8
} | {
"line": 646,
"column": 37
} | {
"line": 646,
"column": 38
} | [
{
"pp": "case mp.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : hs.floor x i < 0\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ↑j ∈ hs.basisSet \\ {↑i}",
"ppTerm": "?mp.refine_2",
"assigned": true,
... | [
"case mp.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : hs.floor x i < 0\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ¬j = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 648,
"column": 8
} | {
"line": 648,
"column": 37
} | {
"line": 648,
"column": 38
} | [
{
"pp": "case mp.refine_3\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : hs.floor x i < 0\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ↑j ∈ hs.basisSet \\ {↑i}",
"ppTerm": "?mp.refine_3",
"assigned": true,
... | [
"case mp.refine_3\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : hs.floor x i < 0\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ¬j = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 672,
"column": 8
} | {
"line": 672,
"column": 25
} | {
"line": 672,
"column": 26
} | [
{
"pp": "case mpr.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\ni : ↑hs.basisSet\nz : ι → ℕ\nhz : z ∈ closure (hs.basisSet \\ {↑i})\nz' : ι → ℕ\nhz' : z' ∈ closure (hs.basisSet \\ {↑i})\nn : ℕ\nheq : hs.floor x i = -↑(n + 1)\n⊢ hs.floor x i < 0",
"ppTerm": "... | [
"case mpr.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\ni : ↑hs.basisSet\nz : ι → ℕ\nhz : z ∈ closure (hs.basisSet \\ {↑i})\nz' : ι → ℕ\nhz' : z' ∈ closure (hs.basisSet \\ {↑i})\nn : ℕ\nheq : hs.floor x i = -↑(n + 1)\n⊢ -1 < ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 709,
"column": 8
} | {
"line": 709,
"column": 37
} | {
"line": 709,
"column": 38
} | [
{
"pp": "case mp.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : ↑i ∉ hs.periods\nhi' : 0 < hs.floor x i\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ↑j ∈ hs.basisSet \\ {↑i}",
"ppTerm": "?mp.refine_2",
... | [
"case mp.refine_2\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : ↑i ∉ hs.periods\nhi' : 0 < hs.floor x i\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ¬j = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | {
"line": 711,
"column": 8
} | {
"line": 711,
"column": 37
} | {
"line": 711,
"column": 38
} | [
{
"pp": "case mp.refine_3\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : ↑i ∉ hs.periods\nhi' : 0 < hs.floor x i\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ↑j ∈ hs.basisSet \\ {↑i}",
"ppTerm": "?mp.refine_3",
... | [
"case mp.refine_3\nι : Type u_3\ns : Set (ι → ℕ)\nhs : IsProperLinearSet s\ninst✝ : Finite ι\nx : ι → ℕ\nhx : hs.fract x = hs.base\ni : ↑hs.basisSet\nhi : ↑i ∉ hs.periods\nhi' : 0 < hs.floor x i\nj : ↑hs.basisSet\nhj : j ∈ Finset.univ.erase i\n⊢ ¬j = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.SetIntegral | {
"line": 443,
"column": 55
} | {
"line": 443,
"column": 66
} | {
"line": 443,
"column": 67
} | [
{
"pp": "X : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G\nB : E →L... | [
"X : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\nmX : MeasurableSpace X\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedAddCommGroup G\nμ : VectorMeasure X F\nf : X → E\ns : Set X\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\ninst✝ : NormedSpace ℝ G\nB : E →L[ℝ] F →L[ℝ] ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.Arithmetic.Presburger.Definability | {
"line": 136,
"column": 4
} | {
"line": 136,
"column": 31
} | {
"line": 136,
"column": 32
} | [
{
"pp": "case e'_8\nα : Type u_1\nA : Set ℕ\ninst✝ : Finite α\nn✝ : ℕ\nthis : Fintype α\nn : ℕ\nφ : presburger[[↑A]].BoundedFormula α (n + 1)\ne : (α ⊕ Fin n) ⊕ Fin 1 ≃ α ⊕ Fin (n + 1) :=\n (Equiv.sumAssoc α (Fin n) (Fin 1)).trans ((_root_.Equiv.refl α).sumCongr finSumFinEquiv)\nih : IsSemilinearSet (⇑(LinearE... | [
"case e'_8.last\nα : Type u_1\nA : Set ℕ\ninst✝ : Finite α\nn✝ : ℕ\nthis : Fintype α\nn : ℕ\nφ : presburger[[↑A]].BoundedFormula α (n + 1)\ne : (α ⊕ Fin n) ⊕ Fin 1 ≃ α ⊕ Fin (n + 1) :=\n (Equiv.sumAssoc α (Fin n) (Fin 1)).trans ((_root_.Equiv.refl α).sumCongr finSumFinEquiv)\nih : IsSemilinearSet (⇑(LinearEquiv.fu... | cases i using Fin.lastCases | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.ModelTheory.Arithmetic.Presburger.Definability | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 52
} | {
"line": 168,
"column": 53
} | [
{
"pp": "A : Set ℕ\nhmul : A.Definable presburger {v | v 0 = v 1 * v 2}\nx✝ : Fin 1 → ℕ\n⊢ x✝ ∈ {x | x 0 ∈ {x | ∃ x_1, x_1 * x_1 = x}} ↔\n x✝ ∈ (fun g ↦ g ∘ ![0]) '' (fun g ↦ g ∘ ![0, 1, 1]) ⁻¹' {v | v 0 = v 1 * v 2}",
"ppTerm": "?m.137",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"A : Set ℕ\nhmul : A.Definable presburger {v | v 0 = v 1 * v 2}\nx✝ : Fin 1 → ℕ\n⊢ (∃ x, x * x = x✝ 0) ↔ ∃ a, x✝ 0 = a * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.ModelTheory.DirectLimit | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 31
} | {
"line": 70,
"column": 0
} | [
{
"pp": "case succ\nL : Language\nG' : ℕ → Type w\ninst✝ : (i : ℕ) → L.Structure (G' i)\nf' : (n : ℕ) → G' n ↪[L] G' (n + 1)\nm : ℕ\nx : G' m\nk : ℕ\nih : ∀ (h : m ≤ m + k), (natLERec f' m (m + k) h) x = Nat.leRecOn h (fun k ↦ ⇑(f' k)) x\nh : m ≤ m + (k + 1)\n⊢ (natLERec f' m (m + (k + 1)) h) x = Nat.leRecOn h ... | [] | rw [Nat.leRecOn_succ le_self_add, natLERec, Nat.leRecOn_succ le_self_add, ← natLERec,
Embedding.comp_apply, ih] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.ModelTheory.DirectLimit | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 31
} | {
"line": 70,
"column": 0
} | [
{
"pp": "case succ\nL : Language\nG' : ℕ → Type w\ninst✝ : (i : ℕ) → L.Structure (G' i)\nf' : (n : ℕ) → G' n ↪[L] G' (n + 1)\nm : ℕ\nx : G' m\nk : ℕ\nih : ∀ (h : m ≤ m + k), (natLERec f' m (m + k) h) x = Nat.leRecOn h (fun k ↦ ⇑(f' k)) x\nh : m ≤ m + (k + 1)\n⊢ (natLERec f' m (m + (k + 1)) h) x = Nat.leRecOn h ... | [] | rw [Nat.leRecOn_succ le_self_add, natLERec, Nat.leRecOn_succ le_self_add, ← natLERec,
Embedding.comp_apply, ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.ModelTheory.DirectLimit | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 31
} | {
"line": 70,
"column": 0
} | [
{
"pp": "case succ\nL : Language\nG' : ℕ → Type w\ninst✝ : (i : ℕ) → L.Structure (G' i)\nf' : (n : ℕ) → G' n ↪[L] G' (n + 1)\nm : ℕ\nx : G' m\nk : ℕ\nih : ∀ (h : m ≤ m + k), (natLERec f' m (m + k) h) x = Nat.leRecOn h (fun k ↦ ⇑(f' k)) x\nh : m ≤ m + (k + 1)\n⊢ (natLERec f' m (m + (k + 1)) h) x = Nat.leRecOn h ... | [] | rw [Nat.leRecOn_succ le_self_add, natLERec, Nat.leRecOn_succ le_self_add, ← natLERec,
Embedding.comp_apply, ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.VectorMeasure.Integral | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 14
} | [
{
"pp": "X : Type u_2\nE : Type u_4\nF : Type u_5\nG : Type u_6\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nB : E →L[ℝ] F →L[ℝ] G\ninst✝ ... | [
"X : Type u_2\nE : Type u_4\nF : Type u_5\nG : Type u_6\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nB : E →L[ℝ] F →L[ℝ] G\ninst✝ : Nontrivial... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.VectorMeasure.Integral | {
"line": 502,
"column": 4
} | {
"line": 502,
"column": 85
} | {
"line": 503,
"column": 6
} | [
{
"pp": "case pos\nX : Type u_2\nE : Type u_4\nF : Type u_5\nmX : MeasurableSpace X\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nf : X → E\nμ : VectorMeasure X F\nhf : μ.Integrable f\ns : Set X\nhs : MeasurableSet s\n⊢ (μ.restrict s).Integrable f",
"ppTerm": "?pos✝",
"assigned": true,
... | [
"case pos\nX : Type u_2\nE : Type u_4\nF : Type u_5\nmX : MeasurableSpace X\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nf : X → E\nμ : VectorMeasure X F\nhf : μ.Integrable f\ns : Set X\nhs : MeasurableSet s\n⊢ Integrable f (μ.variation.restrict s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CountableDenseLinearOrder | {
"line": 255,
"column": 6
} | {
"line": 255,
"column": 40
} | {
"line": 256,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹¹ : LinearOrder α\ninst✝¹⁰ : LinearOrder β\ninst✝⁹ : Countable α\ninst✝⁸ : DenselyOrdered α\ninst✝⁷ : NoMinOrder α\ninst✝⁶ : NoMaxOrder α\ninst✝⁵ : Nonempty α\ninst✝⁴ : Countable β\ninst✝³ : DenselyOrdered β\ninst✝² : NoMinOrder β\ninst✝¹ : NoMaxOrder β\ninst✝ : Nonemp... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹¹ : LinearOrder α\ninst✝¹⁰ : LinearOrder β\ninst✝⁹ : Countable α\ninst✝⁸ : DenselyOrdered α\ninst✝⁷ : NoMinOrder α\ninst✝⁶ : NoMaxOrder α\ninst✝⁵ : Nonempty α\ninst✝⁴ : Countable β\ninst✝³ : DenselyOrdered β\ninst✝² : NoMinOrder β\ninst✝¹ : NoMaxOrder β\ninst✝ : Nonempty β\nval✝¹ ... | rcases (F a).prop with ⟨f, hf, ha⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.VectorMeasure.WithDensityVec | {
"line": 353,
"column": 2
} | {
"line": 353,
"column": 45
} | {
"line": 354,
"column": 2
} | [
{
"pp": "case h₂\nX : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf : X → E\nB : E →L[... | [
"case h₂\nX : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nmX : MeasurableSpace X\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace ℝ G\nμ : VectorMeasure X F\nf : X → E\nB : E →L[ℝ] F →L[ℝ] G... | apply ContinuousLinearMap.opNNNorm_le_bound | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
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