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.InnerProductSpace.Adjoint | {
"line": 573,
"column": 2
} | {
"line": 573,
"column": 37
} | [
{
"pp": "case h\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁹ : RCLike 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : FiniteDimensional... | refine ext_inner_left 𝕜 fun w => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 597,
"column": 2
} | {
"line": 597,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\nthis✝ : CompleteSpace E\nthis :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 604,
"column": 2
} | {
"line": 604,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\nthis✝ : CompleteSpace E\nthis :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 610,
"column": 2
} | {
"line": 610,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\nthis✝ : CompleteSpace E\nthis :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 613,
"column": 2
} | {
"line": 613,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\n⊢ (A ∘ₗ adjoint A).ker = (adjoi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 631,
"column": 2
} | {
"line": 631,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\n⊢ Function.Injective (⇑A ∘ ⇑(ad... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Basic | {
"line": 139,
"column": 2
} | {
"line": 140,
"column": 31
} | [
{
"pp": "case a\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nhx : x ∈ closedBall c f.rIn\n⊢ ‖(fun x ↦ f.rIn⁻¹ • (x - c)) x‖ ≤ 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NonAssocSemiring.toAddCommMon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | [
{
"pp": "G : Type u_4\nF : Type u_6\ninst✝⁴ : MeasurableSpace G\ninst✝³ : NormedAddCommGroup F\nμ : Measure G\ninst✝² : Group G\ninst✝¹ : MeasurableInv G\ninst✝ : μ.IsInvInvariant\nf : G → F\ns : Set G\nhf : IntegrableOn f s μ\nthis : s⁻¹ = ⇑(MeasurableEquiv.inv G) ⁻¹' s\n⊢ Integrable f ((map (⇑(MeasurableEquiv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 13
} | [
{
"pp": "G : Type u_4\nF : Type u_6\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : NormedAddCommGroup F\nμ : Measure G\ninst✝⁴ : PartialOrder G\ninst✝³ : CommGroup G\ninst✝² : IsOrderedMonoid G\ninst✝¹ : MeasurableInv G\ninst✝ : μ.IsInvInvariant\nc : G\nf : G → F\nhf : IntegrableOn f (Set.Ici c⁻¹) μ\n⊢ IntegrableOn (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 13
} | [
{
"pp": "G : Type u_4\nF : Type u_6\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : NormedAddCommGroup F\nμ : Measure G\ninst✝⁴ : PartialOrder G\ninst✝³ : CommGroup G\ninst✝² : IsOrderedMonoid G\ninst✝¹ : MeasurableInv G\ninst✝ : μ.IsInvInvariant\nc : G\nf : G → F\nhf : IntegrableOn f (Set.Iic c⁻¹) μ\n⊢ IntegrableOn (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 13
} | [
{
"pp": "G : Type u_4\nF : Type u_6\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : NormedAddCommGroup F\nμ : Measure G\ninst✝⁴ : PartialOrder G\ninst✝³ : CommGroup G\ninst✝² : IsOrderedMonoid G\ninst✝¹ : MeasurableInv G\ninst✝ : μ.IsInvInvariant\nc : G\nf : G → F\nhf : IntegrableOn f (Set.Ioi c⁻¹) μ\n⊢ IntegrableOn (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 13
} | [
{
"pp": "G : Type u_4\nF : Type u_6\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : NormedAddCommGroup F\nμ : Measure G\ninst✝⁴ : PartialOrder G\ninst✝³ : CommGroup G\ninst✝² : IsOrderedMonoid G\ninst✝¹ : MeasurableInv G\ninst✝ : μ.IsInvInvariant\nc : G\nf : G → F\nhf : IntegrableOn f (Set.Iio c⁻¹) μ\n⊢ IntegrableOn (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 640,
"column": 2
} | {
"line": 640,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nA : E →ₗ[𝕜] F\n⊢ (A ∘ₗ adjoint A).range = A.ra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.Integral | {
"line": 110,
"column": 27
} | {
"line": 110,
"column": 59
} | [
{
"pp": "G : Type u_4\nE : Type u_5\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nμ : Measure G\ninst✝² : Group G\ninst✝¹ : MeasurableMul G\ninst✝ : μ.IsMulRightInvariant\nf : G → E\ng : G\n⊢ ∫ (x : G), f (x * g⁻¹) ∂μ = ∫ (x : G), f x ∂μ",
"usedConstants": [
"Di... | integral_mul_right_eq_self f g⁻¹ | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 714,
"column": 2
} | {
"line": 714,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nT : E →ₗ[𝕜] F\n⊢ (T ∘ₗ adjoint T).IsSymmetric"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 719,
"column": 2
} | {
"line": 719,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nT : E →ₗ[𝕜] E\nhT : T.IsSymmetric\nS : F →ₗ[𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nT : E →ₗ[𝕜] F\n⊢ (adjoint T ∘ₗ T).IsSymmetric"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 775,
"column": 2
} | {
"line": 775,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : FiniteDimensional 𝕜 E\nS T : E →ₗ[𝕜] E\nhS : IsStarProjection S\nhT : IsStarProjection T\nthis : CompleteSpace E\n⊢ S = T ↔ S.range = T.range",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 813,
"column": 4
} | {
"line": 813,
"column": 53
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\ninst✝⁶ : RCLike 𝕜\nH : Type u_5\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\nK : Type u_6\ninst✝² : NormedAddCommGroup K\ninst✝¹ : InnerProductSpace 𝕜 K\ninst✝ : CompleteSpace K\nu : H →L[𝕜] K\nh : ∀ (x y : H), ⟪u x, u y⟫_𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 902,
"column": 34
} | {
"line": 902,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : RCLike 𝕜\nH : Type u_5\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\nK : Type u_6\ninst✝² : NormedAddCommGroup K\ninst✝¹ : InnerProductSpace 𝕜 K\ninst✝ : CompleteSpace K\nf g : H ≃ₗᵢ[𝕜] K\nx✝ : ∃ y, y • 1 = ↑(↑g).symm ∘SL ↑↑f\ny : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 903,
"column": 48
} | {
"line": 903,
"column": 59
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝⁶ : RCLike 𝕜\nH : Type u_5\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\nK : Type u_6\ninst✝² : NormedAddCommGroup K\ninst✝¹ : InnerProductSpace 𝕜 K\ninst✝ : CompleteSpace K\nf g : H ≃ₗᵢ[𝕜] K\nx✝¹ : ∃ y, y • 1 = ↑(↑g).symm ∘SL ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 906,
"column": 15
} | {
"line": 907,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : RCLike 𝕜\nH : Type u_5\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\nK : Type u_6\ninst✝² : NormedAddCommGroup K\ninst✝¹ : InnerProductSpace 𝕜 K\ninst✝ : CompleteSpace K\nf g : H ≃ₗᵢ[𝕜] K\nx✝ : ∃ y, y • 1 = ↑(↑g).symm ∘SL ↑↑f\ny : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Adjoint | {
"line": 915,
"column": 34
} | {
"line": 915,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : RCLike 𝕜\nH : Type u_5\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\nK : Type u_6\ninst✝² : NormedAddCommGroup K\ninst✝¹ : InnerProductSpace 𝕜 K\ninst✝ : CompleteSpace K\nf g : H ≃ₗᵢ[𝕜] K\nx✝ : ∃ y, y • 1 = ↑(↑g).symm ∘SL ↑↑f\ny : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 211,
"column": 6
} | {
"line": 212,
"column": 13
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 167,
"column": 33
} | {
"line": 167,
"column": 73
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 240,
"column": 6
} | {
"line": 240,
"column": 51
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 105,
"column": 49
} | {
"line": 105,
"column": 60
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ENNReal.toReal 0\n⊢ Summable fun x ↦ 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 108,
"column": 49
} | {
"line": 108,
"column": 60
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\n⊢ Summable fun x ↦ 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 15
} | [
{
"pp": "case inr.inl.hf\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\nH : Summable fun x ↦ 1\n⊢ BddAbove (Set.range fun i ↦ ‖f i‖)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 27
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhp : 0 < p.toReal\nhp₁ : 0 < p\nhp₂ : p < ∞\nhf : Summable fun i ↦ ‖f i‖ ^ p.toReal\n⊢ ∀ (s : Finset α), ∑ i ∈ s, ‖f i‖ ^ p.toReal ≤ ∑' (i : α), ‖f i‖ ^ p.toReal",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 278,
"column": 6
} | {
"line": 278,
"column": 49
} | [
{
"pp": "case h\nα : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 214,
"column": 29
} | {
"line": 214,
"column": 60
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 283,
"column": 4
} | {
"line": 283,
"column": 69
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | refine contDiff_tsum (fun i => (hf i).of_le (mod_cast hm)) h'u ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 194,
"column": 17
} | {
"line": 194,
"column": 28
} | [
{
"pp": "α : Type u_3\nE : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nx : α → E\nhx : Memℓp x 1\n⊢ Summable fun a ↦ ‖x a‖",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Sqrt | {
"line": 57,
"column": 6
} | {
"line": 57,
"column": 17
} | [
{
"pp": "case inr.left\nx : ℝ\nhx✝ : x ≠ 0\nhx : 0 < x\nthis : 2 * √x ^ (2 - 1) ≠ 0\n⊢ HasStrictDerivAt (fun x ↦ √x) (1 / (2 * √x)) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Non... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 15
} | [
{
"pp": "case inr.inl.hf\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖(-f) i‖)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 15
} | [
{
"pp": "case inr.inr.hf\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖(-f) i‖ ^ p.toReal",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Sqrt | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 53
} | [
{
"pp": "f : ℝ → ℝ\ns : Set ℝ\nf' x : ℝ\nhf : HasDerivWithinAt f f' s x\nhx : f x ≠ 0\n⊢ HasDerivWithinAt (fun y ↦ √(f y)) (f' / (2 * √(f x))) s x",
"usedConstants": [
"HasDerivWithinAt.congr_simp",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHDiv",
"Non... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Sqrt | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 53
} | [
{
"pp": "f : ℝ → ℝ\nf' x : ℝ\nhf : HasDerivAt f f' x\nhx : f x ≠ 0\n⊢ HasDerivAt (fun y ↦ √(f y)) (f' / (2 * √(f x))) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Sqrt | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 53
} | [
{
"pp": "f : ℝ → ℝ\nf' x : ℝ\nhf : HasStrictDerivAt f f' x\nhx : f x ≠ 0\n⊢ HasStrictDerivAt (fun t ↦ √(f t)) (f' / (2 * √(f x))) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 223,
"column": 27
} | {
"line": 223,
"column": 38
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np : ℝ≥0∞\nf : (i : α) → E i\nhp : 0 < p.toReal\nhfq : Memℓp f 0\nhpq : 0 ≤ p\ni : α\nhi : i ∉ ⋯.toFinset\n⊢ f i = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 232,
"column": 4
} | {
"line": 232,
"column": 57
} | [
{
"pp": "case h\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nq : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhq : 0 < q.toReal\nhpq : q ≤ ∞\nA : ℝ\nhA : A ∈ upperBounds (Set.range fun i ↦ ‖f i‖ ^ q.toReal)\ni : α\nthis : 0 ≤ ‖f i‖ ^ q.toReal\n⊢ (fun i ↦ ‖f i‖) i ≤ A ^ q.toReal⁻¹",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 238,
"column": 8
} | {
"line": 238,
"column": 19
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np q : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhpq : q ≤ p\nhq : 0 < q.toReal\nleft✝ : 0 < p.toReal\nhpq' : q.toReal ≤ p.toReal\nhf' : Summable fun i ↦ ‖f i‖ ^ q.toReal\n⊢ {x | 1 ≤ ‖f x‖ ^ q.toReal}.Finite",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Ball.Homeomorph | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 40
} | [
{
"pp": "E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\nthis : 0 ∈ (univBall c r).source\n⊢ ↑(univBall c r).symm c = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Ball.Homeomorph | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\n⊢ Continuous ↑(univBall c r)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 268,
"column": 6
} | {
"line": 268,
"column": 17
} | [
{
"pp": "case pos\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf g : (i : α) → E i\nhf : Memℓp f p\nhg : Memℓp g p\nhp : 0 < p.toReal\nC : ℝ := if p.toReal < 1 then 1 else 2 ^ (p.toReal - 1)\ni : α\nh : p.toReal < 1\n⊢ (‖f i‖ + ‖g i‖) ^ p.toReal ≤ 1 * (‖f i‖ ^ p.toReal ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 271,
"column": 6
} | {
"line": 271,
"column": 37
} | [
{
"pp": "case neg\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf g : (i : α) → E i\nhf : Memℓp f p\nhg : Memℓp g p\nhp : 0 < p.toReal\nC : ℝ := if p.toReal < 1 then 1 else 2 ^ (p.toReal - 1)\ni : α\nF : Fin 2 → ℝ≥0 := ![‖f i‖₊, ‖g i‖₊]\nh : 1 ≤ p.toReal\n⊢ (‖f i‖ + ‖g i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 483,
"column": 2
} | {
"line": 483,
"column": 35
} | [
{
"pp": "case inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ ‖0‖ = 0",
"usedConstants": [
"CharP.cast_eq_zero",
"Norm.norm",
"False",
"Real",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"Finset",
"AddMonoid.toAddZe... | · simp [lp.norm_eq_card_dsupport] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 487,
"column": 4
} | {
"line": 487,
"column": 39
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < p.toReal\nhp' : 1 / p.toReal ≠ 0\n⊢ (∑' (i : α), ‖↑0 i‖ ^ p.toReal) ^ (1 / p.toReal) = 0",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real",
"Di... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 493,
"column": 42
} | {
"line": 493,
"column": 82
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E 0)\nh : ‖f‖ = 0\ni : α\n⊢ {i | ¬↑f i = 0} = ∅",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 498,
"column": 54
} | {
"line": 498,
"column": 69
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nh : ‖f‖ = 0\n_i : Nonempty α\n⊢ IsLUB (Set.range fun i ↦ ‖↑f i‖) 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 501,
"column": 4
} | {
"line": 501,
"column": 15
} | [
{
"pp": "case inr.inl.inr.h.h\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nh : ‖f‖ = 0\n_i : Nonempty α\nH : IsLUB (Set.range fun i ↦ ‖↑f i‖) 0\ni : α\nthis : ‖↑f i‖ = 0\n⊢ ↑f i = ↑0 i",
"usedConstants": [
"instAddCommGroupPreLp",
"AddCommGroup.toAd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 509,
"column": 6
} | {
"line": 509,
"column": 71
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E p)\nh : ‖f‖ = 0\nhp : 0 < p.toReal\nhf : (fun i ↦ ‖↑f i‖ ^ p.toReal) = 0\nthis : ∀ (i : α), 0 ≤ ‖↑f i‖ ^ p.toReal\ni : α\n⊢ ↑f i = 0 ∧ p.toReal ≠ 0",
"usedConstants": [
"Real",
"Real.instZer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 522,
"column": 4
} | {
"line": 522,
"column": 56
} | [
{
"pp": "case inr.inl.inr\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nh✝ : Nonempty α\n⊢ IsLUB (Set.range fun i ↦ ‖↑(-f) i‖) ‖f‖",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 526,
"column": 4
} | {
"line": 526,
"column": 63
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E p)\nhp : 0 < p.toReal\n⊢ HasSum (fun i ↦ ‖↑(-f) i‖ ^ p.toReal) (‖f‖ ^ p.toReal)",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"Real.instP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 614,
"column": 4
} | {
"line": 614,
"column": 28
} | [
{
"pp": "case inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nC : ℝ\nhC : 0 ≤ C\nhCf : ∀ (i : α), ‖↑f i‖ ≤ C\nh✝ : IsEmpty α\n⊢ ‖f‖ ≤ C",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 666,
"column": 46
} | {
"line": 666,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np q : ℝ≥0∞\ninst✝⁶ : (i : α) → NormedAddCommGroup (E i)\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : (i : α) → Module 𝕜 (E i)\ninst✝² : (i : α) → Module 𝕜' (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\ninst✝ : ∀ (i : α)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 725,
"column": 68
} | {
"line": 725,
"column": 79
} | [
{
"pp": "α : Type u_3\nE : Type u_5\ninst✝ : NormedAddCommGroup E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun a ↦ ‖‖↑f a‖‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"congrArg",
"SummationFilter",
"PseudoMetricSpace.toUni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 738,
"column": 34
} | {
"line": 738,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summabl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 738,
"column": 74
} | {
"line": 738,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summabl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 741,
"column": 55
} | {
"line": 741,
"column": 66
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nc : 𝕜\nf : ↥(lp (fun x ↦ E) 1)\n⊢ S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 742,
"column": 18
} | {
"line": 742,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ ‖{ toFun ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 777,
"column": 4
} | {
"line": 777,
"column": 15
} | [
{
"pp": "case inr.inl.hf\nα : Type u_3\nE : α → Type u_4\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖star f i‖)",
"usedConstants": [
"norm_star",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 779,
"column": 4
} | {
"line": 779,
"column": 15
} | [
{
"pp": "case inr.inr.hf\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖star f i‖ ^ p.toReal",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 875,
"column": 24
} | {
"line": 879,
"column": 66
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\nI : Type u_5\nB : I → Type u_6\ninst✝³ : (i : I) → NonUnitalNormedRing (B i)\ninst✝² : (i : I) → StarRing (B i)\ninst✝¹ : ∀ (i : I), NormedStarGroup (B i)\ninst✝ : ∀ (i : I), CStarRin... | by
rw [← sq, ← Real.le_sqrt (norm_nonneg _) (norm_nonneg _)]
refine lp.norm_le_of_forall_le ‖star f * f‖.sqrt_nonneg fun i => ?_
rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CStarRing.norm_star_mul_self]
exact lp.norm_apply_le_norm ENNReal.top_ne_zero (star f * f) i | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1077,
"column": 2
} | {
"line": 1077,
"column": 39
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : (i : α) → E i\ns : Finset α\nh : ∀ i ∉ s, ‖if i ∈ s then f i else 0‖ ^ p.toReal = 0\nh' : ∀ i ∈ s, ‖f i‖ ^ p.toReal = ‖if i ∈ s then f i else 0‖ ^ p.toReal\n⊢ HasSum (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1093,
"column": 39
} | {
"line": 1093,
"column": 50
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np✝ : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\ni : α\nx : E i\nthis : Nonempty α\np : ℝ≥0\nhp : 0 < ↑p\n⊢ 0 < (↑p).toReal",
"usedConstants": [
"Eq.mpr",
"Real",
"ENNReal.ofNNReal",
"Preorder.toLT",
"Real.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1135,
"column": 6
} | {
"line": 1136,
"column": 38
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : ↥(lp E p)\ns : Finset α\nF : α → ℝ := fun i ↦ ‖↑f i‖ ^ p.toReal - ‖↑(f - ∑ i ∈ s, lp.single p i (↑f i)) i‖ ^ p.toReal\ni : α\nhi : i ∉ s\nthis : ‖↑f i‖ ^ p.toReal - ‖↑f i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1166,
"column": 4
} | {
"line": 1167,
"column": 38
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : DecidableEq α\ninst✝ : Fact (1 ≤ p)\nhp : p ≠ ∞\nf : ↥(lp E p)\nhp₀ : 0 < p\nhp' : 0 < p.toReal\nthis :\n ∀ ε > 0,\n ∀ᶠ (x : Finset α) in (SummationFilter.unconditional α).filter,\n dist (∑ b ∈ x, ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 381,
"column": 51
} | {
"line": 381,
"column": 77
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1252,
"column": 4
} | {
"line": 1252,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np✝ q✝ : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\np q r : ℝ≥0∞\ninst✝ : Fact (1 ≤ p)\ni : α\nx : ↥(lp E p)\nhp : p ≠ 0\n⊢ ‖(eva... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1287,
"column": 4
} | {
"line": 1287,
"column": 13
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_5\nl : Filter ι\ninst✝ : l.NeBot\n_i : Fact (1 ≤ p)\nhp : p ≠ ∞\nC : ℝ\nF : ι → ↥(lp E p)\nhCF : ∀ᶠ (k : ι) in l, ‖F k‖ ≤ C\nf : (a : α) → E a\nhf : Tendsto (id fun i ↦ ↑(F i)) l (𝓝 f)\ns : Finset α\nhp' ... | intro a _ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 42
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 13
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf' : ι → 𝕜 → G\nl' : Filter 𝕜\nhf' : UniformCauchySeqOnFilter f' l l'\nu : Set ((𝕜 →L[𝕜] G) × (𝕜 →L[𝕜] G))\nhu : u ∈ uniformity (𝕜 →L[𝕜] G)\n⊢ ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 497,
"column": 2
} | {
"line": 497,
"column": 42
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\ninst✝¹ : IsRCLikeNormedField 𝕜\ninst✝ : l.NeBot\ns : Set 𝕜\nhs : IsOpen[PseudoMetri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 32,
"column": 20
} | {
"line": 33,
"column": 9
} | [
{
"pp": "case monomial\nn : ℕ\nc : ℝ\n⊢ Tendsto (fun x ↦ eval x ((monomial n) c) / rexp x) atTop (𝓝 0)",
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Semiring.toModule",
"HMul.hMul",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 34,
"column": 21
} | {
"line": 34,
"column": 42
} | [
{
"pp": "case add\np q : ℝ[X]\nhp : Tendsto (fun x ↦ eval x p / rexp x) atTop (𝓝 0)\nhq : Tendsto (fun x ↦ eval x q / rexp x) atTop (𝓝 0)\n⊢ Tendsto (fun x ↦ eval x (p + q) / rexp x) atTop (𝓝 0)",
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Real",
"instHDiv",
"GroupWith... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 30,
"column": 93
} | {
"line": 34,
"column": 52
} | [
{
"pp": "p : ℝ[X]\n⊢ Tendsto (fun x ↦ eval x p / rexp x) atTop (𝓝 0)",
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HM... | by
induction p using Polynomial.induction_on' with
| monomial n c => simpa [exp_neg, div_eq_mul_inv, mul_assoc]
using tendsto_const_nhds.mul (tendsto_pow_mul_exp_neg_atTop_nhds_zero n)
| add p q hp hq => simpa [add_div] using hp.add hq | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 20
} | [
{
"pp": "p : ℝ[X]\n⊢ Tendsto (fun x ↦ Polynomial.eval x⁻¹ p * rexp (-x⁻¹)) (𝓝 0 ⊓ 𝓟 {x | ¬x ≤ 0}) (𝓝 0)",
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Real.instLE",
"Real",
"Preorder.toLT",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Real.instInv",... | simp only [not_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 13
} | [
{
"pp": "n : ℕ∞\n⊢ ContDiff ℝ (↑n) expNegInvGlue",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 42
} | [
{
"pp": "case inr\nx : ℝ\nhx : x < 1\n⊢ x.smoothTransition = 1 ↔ 1 ≤ x",
"usedConstants": [
"Eq.mpr",
"False",
"Real.instLE",
"Real",
"Preorder.toLT",
"eq_false",
"congrArg",
"PartialOrder.toPreorder",
"id",
"Real.smoothTransition.lt_one_of_lt_one"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 116,
"column": 8
} | {
"line": 116,
"column": 74
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 112,
"column": 4
} | {
"line": 118,
"column": 34
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α... | rcases subsingleton_or_nontrivial H with hH | hH
· have : Subsingleton (H →L[𝕜] E) := inferInstance
convert! hasFDerivAt_of_subsingleton _ x₀
· have : ¬(CompleteSpace (H →L[𝕜] E)) := by
simpa [SeparatingDual.completeSpace_continuousLinearMap_iff] using hE
simp only [integral, hE, ↓reduceDI... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 112,
"column": 4
} | {
"line": 118,
"column": 34
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α... | rcases subsingleton_or_nontrivial H with hH | hH
· have : Subsingleton (H →L[𝕜] E) := inferInstance
convert! hasFDerivAt_of_subsingleton _ x₀
· have : ¬(CompleteSpace (H →L[𝕜] E)) := by
simpa [SeparatingDual.completeSpace_continuousLinearMap_iff] using hE
simp only [integral, hE, ↓reduceDI... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\n⊢ HasDerivWithinAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 44
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\nx : ℝ\n⊢ HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g x⟫) x",
"usedConstants": [
"No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nn : WithTop ℕ∞\nx : E\nhx : x ≠ 0\nthis : ‖id x‖ ^ 2 ≠ 0\n⊢ ContDiffAt ℝ n Norm.norm x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 13
} | [
{
"pp": "F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\nx : ℝ\nhf : HasDerivAt f f' x\n⊢ HasDerivAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 13
} | [
{
"pp": "F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\n⊢ HasDerivWithinAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 226,
"column": 4
} | {
"line": 227,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : ... | refine (convex_ball _ _).lipschitzOnWith_of_nnnorm_hasFDerivWithin_le
(fun x x_in ↦ (ha_deriv x (hε x_in)).hasFDerivWithinAt) fun x x_in ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 29
} | [
{
"pp": "F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (x * a) = |a⁻¹| • ∫ (y : ℝ), g y",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
"instHSMul",
"NonUnitalCommRing.t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 29
} | [
{
"pp": "F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (x * a⁻¹) = |a| • ∫ (y : ℝ), g y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 180,
"column": 4
} | {
"line": 182,
"column": 49
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\nthis : ∀ {g : E → F}, Integrabl... | refine ⟨fun hf => ?_, fun hf => this hf hR⟩
convert! this hf (inv_ne_zero hR)
rw [← mul_smul, mul_inv_cancel₀ hR, one_smul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 180,
"column": 4
} | {
"line": 182,
"column": 49
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\nthis : ∀ {g : E → F}, Integrabl... | refine ⟨fun hf => ?_, fun hf => this hf hR⟩
convert! this hf (inv_ne_zero hR)
rw [← mul_smul, mul_inv_cancel₀ hR, one_smul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 64
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\ng : E → F\nhg : Integrable g μ\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 197,
"column": 2
} | {
"line": 197,
"column": 32
} | [
{
"pp": "F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (R * x)) volume ↔ Integrable g volume",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 29
} | [
{
"pp": "F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (x * R)) volume ↔ Integrable g volume",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"NonUnit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 278,
"column": 4
} | {
"line": 278,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace 𝕜 E\nbound : α → ℝ\nF : 𝕜 → α → E\nx₀ : 𝕜\ns : Set 𝕜\nF' : α → E\nhs : s ∈ 𝓝 x₀\nhF_meas : ∀ᶠ (x : 𝕜) in 𝓝 x₀, AE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 281,
"column": 4
} | {
"line": 281,
"column": 30
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace 𝕜 E\nbound : α → ℝ\nF : 𝕜 → α → E\nx₀ : 𝕜\ns : Set 𝕜\nF' : α → E\nhs : s ∈ 𝓝 x₀\nhF_meas : ∀ᶠ (x : 𝕜) in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 283,
"column": 2
} | {
"line": 283,
"column": 78
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace 𝕜 E\nbound : α → ℝ\nF : 𝕜 → α → E\nx₀ : 𝕜\ns : Set 𝕜\nF' : α → E\nhs : s ∈ 𝓝 x₀\nhF_meas : ∀ᶠ (x : 𝕜) in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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