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.Distribution.TemperateGrowth | {
"line": 287,
"column": 12
} | {
"line": 287,
"column": 39
} | [
{
"pp": "case zero\nR : Type u_3\nE : Type u_5\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedRing R\ninst✝ : NormedAlgebra ℝ R\nf : E → R\nhf : HasTemperateGrowth f\n⊢ HasTemperateGrowth (f ^ 0)",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Real",
"Normed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 376,
"column": 29
} | {
"line": 376,
"column": 44
} | [
{
"pp": "H : Type u_8\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℝ H\nr : ℝ\nt : Set ℝ := {y | 1 / 2 < y}\nht : (Set.range fun x ↦ 1 + ‖x‖ ^ 2) ⊆ t\nhdiff : ContDiffOn ℝ ∞ (fun x ↦ x ^ r) t\nhunique : UniqueDiffOn ℝ t\nN k : ℕ\nhk : max r ((↑N - r) * Real.log 2 / Real.log (3 / 2)) ≤ ↑k\nhk₁ : r ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 382,
"column": 27
} | {
"line": 382,
"column": 38
} | [
{
"pp": "H : Type u_8\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℝ H\nr : ℝ\nt : Set ℝ := {y | 1 / 2 < y}\nht : (Set.range fun x ↦ 1 + ‖x‖ ^ 2) ⊆ t\nhdiff : ContDiffOn ℝ ∞ (fun x ↦ x ^ r) t\nhunique : UniqueDiffOn ℝ t\nN k : ℕ\nhk : max r ((↑N - r) * Real.log 2 / Real.log (3 / 2)) ≤ ↑k\nhk₁ : r ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 393,
"column": 6
} | {
"line": 393,
"column": 17
} | [
{
"pp": "case e_a\nH : Type u_8\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℝ H\nr : ℝ\nt : Set ℝ := {y | 1 / 2 < y}\nht : (Set.range fun x ↦ 1 + ‖x‖ ^ 2) ⊆ t\nhdiff : ContDiffOn ℝ ∞ (fun x ↦ x ^ r) t\nhunique : UniqueDiffOn ℝ t\nN k : ℕ\nhk : max r ((↑N - r) * Real.log 2 / Real.log (3 / 2)) ≤ ↑k\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 436,
"column": 2
} | {
"line": 436,
"column": 42
} | [
{
"pp": "E : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : MeasurableSpace E\nμ : Measure E\nh : μ.HasTemperateGrowth\n⊢ Integrable (fun x ↦ (1 + ‖x‖) ^ (-↑μ.integrablePower)) μ",
"usedConstants": [
"zpow_natCast",
"dite_cond_eq_true",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 520,
"column": 38
} | {
"line": 520,
"column": 63
} | [
{
"pp": "E : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : MeasurableSpace E\nμ : Measure E\nhμ : μ.HasTemperateGrowth\np : ℝ≥0\nhp : ↑p ≠ 0\nh_one_add : ∀ (x : E), 0 < 1 + ‖x‖\n⊢ 0 < ↑p",
"usedConstants": [
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.TemperateGrowth | {
"line": 523,
"column": 39
} | {
"line": 523,
"column": 71
} | [
{
"pp": "E : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : MeasurableSpace E\nμ : Measure E\nhμ : μ.HasTemperateGrowth\np : ℝ≥0\nhp : ↑p ≠ 0\nh_one_add : ∀ (x : E), 0 < 1 + ‖x‖\nhp_pos : 0 < ↑p\nl : ℕ\nhl : Integrable (fun x ↦ (1 + ‖x‖) ^ (-↑l)) μ\nk : ℕ := ⌈↑l / ↑p⌉₊\n⊢ ↑l ≤ ↑k * ↑p",
"usedConstants": [... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.SmoothApprox | {
"line": 48,
"column": 4
} | {
"line": 48,
"column": 37
} | [
{
"pp": "case inl\nE : Type u_3\nF : Type u_4\ninst✝⁷ : MeasurableSpace E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : BorelSpace E\ninst✝¹ : NormedSpace ℝ F\nμ : Measure E\ninst✝ : IsFiniteMeasureOnCompacts μ\nε : ℝ\nhε : 0 < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.SmoothApprox | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 61
} | [
{
"pp": "case h\nE : Type u_3\nF : Type u_4\ninst✝⁷ : MeasurableSpace E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : BorelSpace E\ninst✝¹ : NormedSpace ℝ F\nμ : Measure E\ninst✝ : IsFiniteMeasureOnCompacts μ\np : ℝ≥0∞\nε : ℝ\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ContinuousMapDense | {
"line": 201,
"column": 38
} | {
"line": 201,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : TopologicalSpace α\ninst✝⁷ : NormalSpace α\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : BorelSpace α\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\nμ : Measure α\ninst✝³ : NormedSpace ℝ E\ninst✝² : R1Space α\ninst✝¹ : WeaklyLocallyCompactSpace α\ninst✝ : μ.Regular\np : ℝ\nhp : 0 < p\nf :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.SmoothApprox | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 82
} | [
{
"pp": "E : Type u_3\nF : Type u_4\ninst✝⁷ : MeasurableSpace E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : BorelSpace E\ninst✝¹ : NormedSpace ℝ F\nμ : Measure E\ninst✝ : IsFiniteMeasureOnCompacts μ\np : ℝ≥0∞\nhp : p ≠ ∞\nhp₂ ... | refine (mem_closure_iff_nhds_basis Metric.nhds_basis_closedBall).2 fun ε hε ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.Function.ContinuousMapDense | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝⁸ : TopologicalSpace α\ninst✝⁷ : NormalSpace α\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : BorelSpace α\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\nμ : Measure α\ninst✝³ : NormedSpace ℝ E\ninst✝² : R1Space α\ninst✝¹ : WeaklyLocallyCompactSpace α\ninst✝ : μ.Regular\nf : α → E\nε : ℝ\nhε :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ContinuousMapDense | {
"line": 292,
"column": 38
} | {
"line": 292,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : NormalSpace α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : BorelSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\nμ : Measure α\ninst✝¹ : NormedSpace ℝ E\ninst✝ : μ.WeaklyRegular\np : ℝ\nhp : 0 < p\nf : α → E\nhf : MemLp f (ENNReal.ofReal p) μ\nε : ℝ\nhε... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ContinuousMapDense | {
"line": 316,
"column": 2
} | {
"line": 316,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : NormalSpace α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : BorelSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\nμ : Measure α\ninst✝¹ : NormedSpace ℝ E\ninst✝ : μ.WeaklyRegular\nf : α → E\nε : ℝ\nhε : 0 < ε\nhf : MemLp f (ENNReal.ofReal 1) μ\n⊢ ∃ g, ∫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.ContinuousMapDense | {
"line": 353,
"column": 2
} | {
"line": 354,
"column": 9
} | [
{
"pp": "α : Type u_1\ninst✝¹¹ : TopologicalSpace α\ninst✝¹⁰ : NormalSpace α\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : BorelSpace α\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\ninst✝⁶ : SecondCountableTopologyEither α E\n_i : Fact (1 ≤ p)\n𝕜 : Type u_3\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : Mo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Deriv | {
"line": 65,
"column": 6
} | {
"line": 66,
"column": 79
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF✝ : Type u_6\nV : Type u_7\nF : Type u_8\nF₁ : Type u_9\nF₂ : Type u_10\nF₃ : Type u_11\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedSpace ℝ E\ninst✝¹ : RCLike 𝕜\ninst✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Deriv | {
"line": 89,
"column": 6
} | {
"line": 90,
"column": 60
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF✝ : Type u_6\nV : Type u_7\nF : Type u_8\nF₁ : Type u_9\nF₂ : Type u_10\nF₃ : Type u_11\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedSpace ℝ E\ninst✝² : RCLike 𝕜\ninst✝¹... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 31
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nG : ι → Type u_4\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝ : DecidableEq ι\ni : ι\na : G i\nf : ↥(lp G 2)\n⊢ ⟪f, lp.single 2 i a⟫ = ⟪↑f i, a⟫",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 41
} | [
{
"pp": "T : ℝ\nm n : ℤ\nx : AddCircle T\n⊢ ↑((m + n) • x).toCircle = (fourier m) x * (fourier n) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"HMul.hMul",
"congrArg",
"ContinuousMap",
"AddCommMagma.to_isCommutat... | rw [← fourier_apply]; exact fourier_add | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 41
} | [
{
"pp": "T : ℝ\nm n : ℤ\nx : AddCircle T\n⊢ ↑((m + n) • x).toCircle = (fourier m) x * (fourier n) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"HMul.hMul",
"congrArg",
"ContinuousMap",
"AddCommMagma.to_isCommutat... | rw [← fourier_apply]; exact fourier_add | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 76
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝ : CompleteSpace E\nV : (i : ι) → G i →ₗᵢ[𝕜] E\nhV✝ hV : Ort... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 215,
"column": 2
} | {
"line": 221,
"column": 12
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁶ : RCLike 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝³ : (i : ι) → NormedAddCommGroup (G i)\ninst✝² : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝¹ : CompleteSpace E\nV : (i : ι) → G i →ₗᵢ[𝕜] E\nhV : Orthog... | rw [hV.linearIsometry_apply, ← tsum_ite_eq i (fun _ ↦ V i x)]
congr
ext j
rw [lp.single_apply]
split_ifs with h
· subst h; simp
· simp [h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 215,
"column": 2
} | {
"line": 221,
"column": 12
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁶ : RCLike 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝³ : (i : ι) → NormedAddCommGroup (G i)\ninst✝² : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝¹ : CompleteSpace E\nV : (i : ι) → G i →ₗᵢ[𝕜] E\nhV : Orthog... | rw [hV.linearIsometry_apply, ← tsum_ite_eq i (fun _ ↦ V i x)]
congr
ext j
rw [lp.single_apply]
split_ifs with h
· subst h; simp
· simp [h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 268,
"column": 2
} | {
"line": 268,
"column": 41
} | [
{
"pp": "case h.e'_2.h.e'_9.h\nT : ℝ\nhT : Fact (0 < T)\np : ℝ≥0∞\ninst✝ : Fact (1 ≤ p)\nhp : p ≠ ∞\ne_3✝ : Complex.instSemiring = NormedField.toNormedCommRing.toSemiring\ne_6✝ : Lp.instModule ≍ Lp.instModule\n⊢ span ℂ (⇑(toLp p haarAddCircle ℂ) '' range fourier) = span ℂ (⇑↑(toLp p haarAddCircle ℂ) '' range fo... | simp only [ContinuousLinearMap.coe_coe] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 274,
"column": 6
} | {
"line": 274,
"column": 76
} | [
{
"pp": "T : ℝ\nhT : Fact (0 < T)\ni j : ℤ\n⊢ inner ℂ (fourierLp 2 i) (fourierLp 2 j) = if i = j then 1 else 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.L2... | ContinuousMap.inner_toLp (@haarAddCircle T hT) (fourier i) (fourier j) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 242,
"column": 4
} | {
"line": 247,
"column": 80
} | [
{
"pp": "case refine_2\nι : Type u_1\n𝕜 : Type u_2\ninst✝⁶ : RCLike 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝³ : (i : ι) → NormedAddCommGroup (G i)\ninst✝² : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝¹ : CompleteSpace E\nV : (i : ι) → G i →ₗᵢ[𝕜]... | apply topologicalClosure_minimal
· refine iSup_le ?_
rintro i x ⟨x, rfl⟩
use lp.single 2 i x
exact hV.linearIsometry_apply_single x
exact hV.linearIsometry.isometry.isUniformInducing.isComplete_range.isClosed | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 242,
"column": 4
} | {
"line": 247,
"column": 80
} | [
{
"pp": "case refine_2\nι : Type u_1\n𝕜 : Type u_2\ninst✝⁶ : RCLike 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝³ : (i : ι) → NormedAddCommGroup (G i)\ninst✝² : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝¹ : CompleteSpace E\nV : (i : ι) → G i →ₗᵢ[𝕜]... | apply topologicalClosure_minimal
· refine iSup_le ?_
rintro i x ⟨x, rfl⟩
use lp.single 2 i x
exact hV.linearIsometry_apply_single x
exact hV.linearIsometry.isometry.isUniformInducing.isComplete_range.isClosed | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 44
} | [
{
"pp": "case h\nT : ℝ\nhT : Fact (0 < T)\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : AddCircle T → E\nhf : Integrable f haarAddCircle\nhg : Integrable g haarAddCircle\nx : ℤ\n⊢ fourierCoeff (f + g) x = (fourierCoeff f + fourierCoeff g) x",
"usedConstants": [
"Eq.mpr",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 287,
"column": 30
} | {
"line": 287,
"column": 80
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : RCLike 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : CompleteSpace E\nF : ι → Submodule 𝕜 E\ninst✝ : ∀ (i : ι), CompleteSpace ↥(F i)\nhFortho : OrthogonalFamily 𝕜 (fun i ↦ ↥(F i)) fun i ↦ (F i).subtypeₗᵢ\nhFtotal : ⊤ ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 332,
"column": 30
} | {
"line": 332,
"column": 41
} | [
{
"pp": "T : ℝ\nhT : Fact (0 < T)\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nι : Type u_2\nf : ι → AddCircle T → E\na : ι\ns : Finset ι\nha : a ∉ s\niha : (∀ i ∈ s, Integrable (f i) haarAddCircle) → fourierCoeff (∑ i ∈ s, f i) = ∑ i ∈ s, fourierCoeff (f i)\nhf : ∀ i ∈ insert a s, Int... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 327,
"column": 65
} | {
"line": 334,
"column": 68
} | [
{
"pp": "T : ℝ\nhT : Fact (0 < T)\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nι : Type u_2\ns : Finset ι\nf : ι → AddCircle T → E\nhf : ∀ i ∈ s, Integrable (f i) haarAddCircle\n⊢ fourierCoeff (∑ i ∈ s, f i) = ∑ i ∈ s, fourierCoeff (f i)",
"usedConstants": [
"Eq.mpr",
"... | by
classical
induction s using Finset.induction_on with
| empty => ext; simp [fourierCoeff]
| insert a s ha iha =>
obtain ⟨hf₁, hf₂⟩ := by simpa using hf
rw [s.sum_insert ha, s.sum_insert ha,
fourierCoeff.add hf₁ (integrable_finsetSum' s hf₂), iha hf₂] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 441,
"column": 47
} | {
"line": 441,
"column": 58
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝² : RCLike 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nb : HilbertBasis ι 𝕜 E\nx : E\n⊢ HasSum (fun i ↦ ↑(b.repr x) i • b i) x",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"NormedCommRing.toNormedRing",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 480,
"column": 6
} | {
"line": 480,
"column": 99
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝ : Fintype ι\nb : HilbertBasis ι 𝕜 E\nthis : IsClosed[Pseudo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 491,
"column": 2
} | {
"line": 491,
"column": 82
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\nU : Submodule 𝕜 E\ninst✝ : CompleteSpace ↥U\nb : HilbertBasis ι 𝕜 ↥U\nx : E\n⊢ HasSum (fun i ↦ ⟪↑(b i), x⟫ • b i) (U.orthogonalProjection x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 540,
"column": 4
} | {
"line": 540,
"column": 84
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁶ : RCLike 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\nG : ι → Type u_4\ninst✝³ : (i : ι) → NormedAddCommGroup (G i)\ninst✝² : (i : ι) → InnerProductSpace 𝕜 (G i)\ninst✝¹ : CompleteSpace E\nv : ι → E\nhv : Orthonormal 𝕜 v\ninst✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.l2Space | {
"line": 556,
"column": 8
} | {
"line": 557,
"column": 73
} | [
{
"pp": "𝕜 : Type u_2\ninst✝³ : RCLike 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : CompleteSpace E\ns : Set E\nhs : Orthonormal 𝕜 Subtype.val\nw : Set E\nhws : w ⊇ s\nhw_ortho : Orthonormal 𝕜 Subtype.val\nhw_max : ∀ u ⊇ w, Orthonormal 𝕜 Subtype.val → u = w\n⊢ (s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 547,
"column": 2
} | {
"line": 547,
"column": 13
} | [
{
"pp": "T : ℝ\nn : ℤ\nx : ℝ\n⊢ HasDerivAt (fun y ↦ (fourier (-n)) ↑y) (-2 * ↑π * I * ↑n / ↑T * (fourier (-n)) ↑x) x",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Int.cast",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 555,
"column": 16
} | {
"line": 555,
"column": 34
} | [
{
"pp": "case h.e'_8.h\nT : ℝ\nhT : Fact (0 < T)\nn : ℤ\nhn : n ≠ 0\nx y : ℝ\n⊢ ↑T / (-2 * ↑π * I * ↑n) * (fourier (-n)) ↑y = (fourier (-n)) ↑y / (-2 * ↑π * I * ↑n / ↑T)",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHDiv",
... | div_div_eq_mul_div | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Fourier.AddCircle | {
"line": 578,
"column": 4
} | {
"line": 578,
"column": 15
} | [
{
"pp": "a b : ℝ\nhab : a < b\nf f' : ℝ → ℂ\nn : ℤ\nhn : n ≠ 0\nhf : ContinuousOn f [[a, b]]\nhff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x\nhf' : IntervalIntegrable f' volume a b\nhT : Fact (0 < b - a)\nthis : ∀ (u v w : ℂ), u * (↑(b - a) / v * w) = ↑(b - a) / v * (u * w)\n⊢ ↑b = ↑a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 514,
"column": 2
} | {
"line": 515,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulCommClass ℝ 𝕜 F\nn : ℕ∞\nK : Compacts E\nf g : 𝓓^{n}_{K}(E, F)\nhfg ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 664,
"column": 24
} | {
"line": 664,
"column": 35
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulCommClass ℝ 𝕜 F\nn : ℕ∞\nK : Compacts E\ni : ℕ\nhin : n < ↑i\n⊢ ¬↑i ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 766,
"column": 4
} | {
"line": 766,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type u_4\ninst✝¹¹ : NontriviallyNormedField 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace 𝕜 F\ninst✝⁵ : SMulCommClass ℝ 𝕜 F\ninst✝⁴ : NormedAddCommGroup F'\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 805,
"column": 4
} | {
"line": 805,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type u_4\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : NormedSpace 𝕜 F\ninst✝⁴ : SMulCommClass ℝ 𝕜 F\ninst✝³ : NormedAddCommGroup F'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 828,
"column": 4
} | {
"line": 828,
"column": 48
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulCommClass ℝ 𝕜 F\nn k : ℕ∞\nK : Compacts E\ni : ℕ\nf : 𝓓^{n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 847,
"column": 4
} | {
"line": 847,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type u_4\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : NormedSpace 𝕜 F\ninst✝⁴ : SMulCommClass ℝ 𝕜 F\ninst✝³ : NormedAddCommGroup F'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {
"line": 976,
"column": 4
} | {
"line": 976,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type u_4\ninst✝²¹ : NontriviallyNormedField 𝕜\ninst✝²⁰ : NormedAddCommGroup E\ninst✝¹⁹ : NormedSpace ℝ E\ninst✝¹⁸ : NormedAddCommGroup F\ninst✝¹⁷ : NormedSpace ℝ F\ninst✝¹⁶ : NormedSpace 𝕜 F\ninst✝¹⁵ : SMulCommClass ℝ 𝕜 F\ninst✝¹⁴ : NormedAddCommGroup ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 52
} | [
{
"pp": "case h\nα : Type u_1\nE : Type u_2\nι : Type u_3\nhm : MeasurableSpace α\nμ : Measure α\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\ns t : Set α\nφ : ι → α → ℝ\na : E\nhs : MeasurableSet s\nh'st : t ∈ 𝓝[s]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 164,
"column": 8
} | {
"line": 164,
"column": 56
} | [
{
"pp": "case refine_3.hbc\nα : Type u_1\nE : Type u_2\nι : Type u_3\nhm : MeasurableSpace α\nμ : Measure α\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\ns t : Set α\nφ : ι → α → ℝ\nhs : MeasurableSet s\nht : Measura... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 173,
"column": 22
} | {
"line": 173,
"column": 44
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nι : Type u_3\nhm : MeasurableSpace α\nμ : Measure α\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\ns t : Set α\nφ : ι → α → ℝ\nhs : MeasurableSet s\nht : MeasurableSet t\nhts : t ⊆... | ← diff_union_inter s u | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 233,
"column": 8
} | {
"line": 233,
"column": 42
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nι : Type u_3\nhm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : BorelSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\nφ : ι → α → ℝ\na : E\ninst✝ : CompleteSpace E\nt : Set α\nht : MeasurableSet t\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 166,
"column": 2
} | {
"line": 166,
"column": 38
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : 𝓢(E, F)\ninst✝ : ProperSpace E\nk : ℤ\n⊢ ⇑f =O[cocompact E] fun x ↦ ‖x‖ ^ k",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 273,
"column": 19
} | {
"line": 273,
"column": 59
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : NormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 279,
"column": 19
} | {
"line": 279,
"column": 59
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : NormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Fourier.FourierTransformDeriv | {
"line": 104,
"column": 2
} | {
"line": 104,
"column": 67
} | [
{
"pp": "x : ℝ\nh1 : ∀ (y : ℝ), ↑(𝐞 y) = (fourier 1) ↑y\n⊢ HasDerivAt (fun x ↦ ↑(𝐞 x)) (2 * ↑π * I * ↑(𝐞 x)) x",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Real.pi"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 556,
"column": 18
} | {
"line": 556,
"column": 29
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : 𝓢(E, F)\nn : ℕ\nC : ℝ\nCpos : 0 < C\nhC : ∀ (x : E), ‖x‖ ^ 0 * ‖iteratedFDeriv ℝ n (⇑f) x‖ ≤ C\n⊢ ∀ (x : E), ‖iteratedFDeriv ℝ n (⇑f) x‖ ≤ C * (1 + ‖x‖) ^ 0"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 662,
"column": 93
} | {
"line": 664,
"column": 78
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst... | by
gcongr
exact norm_iteratedFDeriv_clm_apply_const (f.smooth _).contDiffAt le_rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Fourier.FourierTransformDeriv | {
"line": 235,
"column": 33
} | {
"line": 235,
"column": 63
} | [
{
"pp": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℂ E\nV : Type u_2\nW : Type u_3\ninst✝⁶ : NormedAddCommGroup V\ninst✝⁵ : NormedSpace ℝ V\ninst✝⁴ : NormedAddCommGroup W\ninst✝³ : NormedSpace ℝ W\nL : V →L[ℝ] W →L[ℝ] ℝ\nf : V → E\ninst✝² : MeasurableSpace V\ninst✝¹ : BorelSpace V\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Integral | {
"line": 67,
"column": 4
} | {
"line": 68,
"column": 27
} | [
{
"pp": "case refine_1\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : C(ℝ, E)\nhf : Summable fun n ↦ ‖ContinuousMap.restrict (Icc 0 1) (f.comp (ContinuousMap.addRight ↑n))‖\nn : ℤ\nx : ↑(Icc (↑n) (↑n + 1))\nthis :\n ‖(ContinuousMap.restrict (Icc 0 1) (f.comp (ContinuousMap.addRight ↑n))) ⟨↑x - ↑n, ⋯⟩‖ ≤\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Integral | {
"line": 93,
"column": 75
} | {
"line": 95,
"column": 21
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nc : ℝ\nf : ℝ → E\n⊢ ∫ (x : ℝ) in Ioi c, f (-x) = ∫ (x : ℝ) in Iic (-c), f x",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",... | by
rw [← neg_neg c, ← integral_comp_neg_Iic]
simp only [neg_neg] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 299,
"column": 4
} | {
"line": 318,
"column": 21
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nhm : MeasurableSpace α\nμ : Measure α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : BorelSpace α\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ng : α → E\nx₀ : α\ns : Set α\ninst✝² : CompleteSpace E\ninst✝¹ : MetrizableSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nhs : IsCo... | have M : ∀ n, ∀ x ∈ s \ u, φ n x ≤ (μ.real (v ∩ s))⁻¹ * (t / t') ^ n := by
intro n x hx
have B : t' ^ n * μ.real (v ∩ s) ≤ ∫ y in s, c y ^ n ∂μ :=
calc
t' ^ n * μ.real (v ∩ s) = ∫ _ in v ∩ s, t' ^ n ∂μ := by simp [mul_comm]
_ ≤ ∫ y in v ∩ s, c y ^ n ∂μ := by
apply set... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 828,
"column": 4
} | {
"line": 828,
"column": 38
} | [
{
"pp": "case pos\n𝕜 : Type u_2\nE : Type u_5\nF : Type u_6\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAlgebra ℝ 𝕜\ninst✝ : NormedSpace 𝕜 F\ng : E → 𝕜\nf : 𝓢(E, F)\nhg : Function.HasT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 42
} | [
{
"pp": "c : ℝ\n⊢ ∫ (x : ℝ) in Ioi c, rexp (-x) = rexp (-c)",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"Set.Ioi",
"Real.instRCLike",
"congrArg",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"Real.measureSpace",
"MeasureT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 39
} | [
{
"pp": "⊢ ∫ (x : ℝ) in Ioi 0, rexp (-x) = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 69,
"column": 4
} | {
"line": 69,
"column": 34
} | [
{
"pp": "case refine_2\na : ℂ\nha : a.re < 0\nc : ℝ\n⊢ Integrable (fun a_1 ↦ ‖Complex.exp (a * ↑a_1)‖) (volume.restrict (Ioi c))",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Set.Ioi",
"MeasureTheory.Measure",
"Complex.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 13
} | [
{
"pp": "a : ℂ\nha : 0 < a.re\nc : ℝ\n⊢ IntegrableOn (fun x ↦ Complex.exp (a * ↑x)) (Iic c) volume",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 80,
"column": 75
} | {
"line": 80,
"column": 86
} | [
{
"pp": "a : ℝ\nha : a < 0\nc : ℝ\n⊢ (↑a).re < 0",
"usedConstants": [
"Real",
"Real.instZero",
"Real.instLT",
"id",
"Complex.ofReal",
"Complex.re",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 32
} | [
{
"pp": "a : ℝ\nha : a < 0\nc : ℝ\nthis : Integrable (fun a_1 ↦ ‖Complex.exp (↑a * ↑a_1)‖) (volume.restrict (Ioi c))\n⊢ IntegrableOn (fun x ↦ rexp (a * x)) (Ioi c) volume",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 85,
"column": 75
} | {
"line": 85,
"column": 86
} | [
{
"pp": "a : ℝ\nha : 0 < a\nc : ℝ\n⊢ 0 < (↑a).re",
"usedConstants": [
"Real",
"Real.instZero",
"Real.instLT",
"id",
"Complex.ofReal",
"Complex.re",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 869,
"column": 28
} | {
"line": 869,
"column": 39
} | [
{
"pp": "case h\nι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Norme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 32
} | [
{
"pp": "a : ℝ\nha : 0 < a\nc : ℝ\nthis : Integrable (fun a_1 ↦ ‖Complex.exp (↑a * ↑a_1)‖) (volume.restrict (Iic c))\n⊢ IntegrableOn (fun x ↦ rexp (a * x)) (Iic c) volume",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 94,
"column": 4
} | {
"line": 94,
"column": 15
} | [
{
"pp": "a : ℂ\nha : a.re < 0\nc : ℝ\nthis : Tendsto (fun x ↦ Complex.exp (a * ↑x)) atTop (𝓝 0)\n⊢ Tendsto (fun i ↦ (Complex.exp (a * ↑i) - Complex.exp (a * ↑c)) / a) atTop (𝓝 (-Complex.exp (a * ↑c) / a))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 49
} | [
{
"pp": "a : ℂ\nha : a.re < 0\nc : ℝ\n⊢ Tendsto (fun x ↦ Complex.exp (a * ↑x)) atTop (𝓝 0)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Complex.mul_re",
"HMul.hMul",
"congrArg",
"sub_zero",
"Complex.im",
"Real.instSub",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 99,
"column": 2
} | {
"line": 101,
"column": 9
} | [
{
"pp": "a : ℂ\nha : 0 < a.re\nc : ℝ\n⊢ ∫ (x : ℝ) in Iic c, Complex.exp (a * ↑x) = Complex.exp (a * ↑c) / a",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 106,
"column": 52
} | {
"line": 106,
"column": 63
} | [
{
"pp": "a : ℝ\nha : a < 0\nc : ℝ\n⊢ (↑a).re < 0",
"usedConstants": [
"Real",
"Real.instZero",
"Real.instLT",
"id",
"Complex.ofReal",
"Complex.re",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 56
} | [
{
"pp": "a : ℝ\nha : a < 0\nc : ℝ\n⊢ (↑a).re < 0",
"usedConstants": [
"Real",
"Real.instZero",
"Real.instLT",
"id",
"Complex.ofReal",
"Complex.re",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 112,
"column": 2
} | {
"line": 113,
"column": 9
} | [
{
"pp": "a : ℝ\nha : 0 < a\nc : ℝ\n⊢ ∫ (x : ℝ) in Iic c, rexp (a * x) = rexp (a * c) / a",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 13
} | [
{
"pp": "a c : ℝ\nha : a < -1\nhc : 0 < c\n⊢ IntegrableOn (fun t ↦ t ^ a) (Ioi c) volume",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 365,
"column": 32
} | {
"line": 365,
"column": 53
} | [
{
"pp": "case h.h₂\nα : Type u_1\nE : Type u_2\nhm : MeasurableSpace α\nμ : Measure α\ninst✝⁷ : TopologicalSpace α\ninst✝⁶ : BorelSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ng : α → E\nx₀ : α\ns : Set α\ninst✝³ : CompleteSpace E\ninst✝² : MetrizableSpace α\ninst✝¹ : IsLocallyFiniteMeasure ... | apply interior_subset | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 905,
"column": 17
} | {
"line": 908,
"column": 14
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAlgebra... | by
simp only [Finset.sup_insert, schwartzSeminormFamily_apply, Finset.sup_singleton,
Seminorm.coe_sup, Pi.sup_apply]
ring | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 30
} | [
{
"pp": "case hf\na : ℝ\nha : a < -1\nc : ℝ\nhc : 0 < c\nhd : ∀ x ∈ Ici c, HasDerivAt (fun t ↦ t ^ (a + 1) / (a + 1)) (x ^ a) x\n⊢ Tendsto (fun a_1 ↦ a_1 ^ (a + 1)) atTop (𝓝 0)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 175,
"column": 2
} | {
"line": 183,
"column": 41
} | [
{
"pp": "a : ℝ\nha : a < -1\nc : ℝ\nhc : 0 < c\n⊢ ∫ (t : ℝ) in Ioi c, t ^ a = -c ^ (a + 1) / (a + 1)",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",... | have hd : ∀ x ∈ Ici c, HasDerivAt (fun t => t ^ (a + 1) / (a + 1)) (x ^ a) x := by
intro x hx
convert! (hasDerivAt_rpow_const (p := a + 1) (Or.inl (hc.trans_le hx).ne')).div_const _ using 1
simp [show a + 1 ≠ 0 from ne_of_lt (by linarith), mul_comm]
have ht : Tendsto (fun t => t ^ (a + 1) / (a + 1)) atTop... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.ImproperIntegrals | {
"line": 175,
"column": 2
} | {
"line": 183,
"column": 41
} | [
{
"pp": "a : ℝ\nha : a < -1\nc : ℝ\nhc : 0 < c\n⊢ ∫ (t : ℝ) in Ioi c, t ^ a = -c ^ (a + 1) / (a + 1)",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",... | have hd : ∀ x ∈ Ici c, HasDerivAt (fun t => t ^ (a + 1) / (a + 1)) (x ^ a) x := by
intro x hx
convert! (hasDerivAt_rpow_const (p := a + 1) (Or.inl (hc.trans_le hx).ne')).div_const _ using 1
simp [show a + 1 ≠ 0 from ne_of_lt (by linarith), mul_comm]
have ht : Tendsto (fun t => t ^ (a + 1) / (a + 1)) atTop... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Integral.PeakFunction | {
"line": 414,
"column": 6
} | {
"line": 414,
"column": 17
} | [
{
"pp": "E : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : FiniteDimensional ℝ F\ninst✝² : MeasurableSpace F\ninst✝¹ : BorelSpace F\nμ : Measure F\ninst✝ : μ.IsAddHaarMeasure\nφ : F → ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Asymptotics | {
"line": 181,
"column": 21
} | {
"line": 181,
"column": 49
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\nf : α → E\ng : α → F\ninst✝¹⁰ : TopologicalSpace α\ninst✝⁹ : SecondCountableTopology α\ninst✝⁸ : MeasurableSpace α\nμ : Measure α\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : AddCommGroup α\ninst✝⁵ : LinearOrder α\ninst✝⁴ : IsOrdered... | ← Measure.map_neg_eq_self μ, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.MeasureTheory.Integral.ExpDecay | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 21
} | [
{
"pp": "a b : ℝ\nh : 0 < b\nthis : Tendsto (fun x ↦ -rexp (-b * x) / b) atTop (𝓝 (-0 / b))\nx : ℝ\nx✝ : x ∈ Ici a\n⊢ HasDerivAt (fun x ↦ -rexp (-b * x) / b) (rexp (-b * x)) x",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1155,
"column": 4
} | {
"line": 1155,
"column": 15
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : NormedAddCommGroup D\ninst✝⁶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1156,
"column": 27
} | {
"line": 1156,
"column": 38
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : NormedAddCommGroup D\ninst✝⁶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1206,
"column": 6
} | {
"line": 1206,
"column": 72
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1249,
"column": 30
} | {
"line": 1250,
"column": 65
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\n𝕜' : Type u_3\nD : Type u_4\nE : Type u_5\nF : Type u_6\nG : Type u_7\nH : Type u_8\nV : Type u_9\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : ProperSpace E\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Basic | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 52
} | [
{
"pp": "s : ℂ\n⊢ ((starRingEnd ℂ) s).GammaIntegral = (starRingEnd ℂ) s.GammaIntegral",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Set.Ioi",
"RCLike.toNormedAlge... | rw [GammaIntegral, GammaIntegral, ← integral_conj] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1294,
"column": 4
} | {
"line": 1294,
"column": 59
} | [
{
"pp": "case bc\n𝕜 : Type u_2\nE : Type u_5\nF : Type u_6\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : MeasurableSpace E\ninst✝³ : OpensMeasurableSpace E\ninst✝² : NormedField 𝕜\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulCommClass ℝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Basic | {
"line": 134,
"column": 2
} | {
"line": 135,
"column": 18
} | [
{
"pp": "⊢ GammaIntegral 1 = 1",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instPow",
"Real",
"Set.Ioi",
"HMul.hMul",
"sub_self",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"Real.instSub",
"AddMonoid.toAd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1313,
"column": 2
} | {
"line": 1313,
"column": 13
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst✝ : SecondCountableTopologyEither E F\nf : 𝓢(E, F)\nμ : Measure E\nC : ℝ\nleft✝ : 0 < C\nhC : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1334,
"column": 17
} | {
"line": 1334,
"column": 89
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst✝ : SecondCountableTopologyEither E F\nf : 𝓢(E, F)\np : ℝ≥0∞\nμ : Measure E\nhp₁ : p ≠ 0\nhp₂ :... | MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm hp₁ hp₂ (f.memLp p μ), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1339,
"column": 2
} | {
"line": 1339,
"column": 13
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst✝ : SecondCountableTopologyEither E F\nf : 𝓢(E, F)\nμ : Measure E\nhμ : μ.HasTemperateGrowth\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1349,
"column": 15
} | {
"line": 1349,
"column": 33
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : MeasurableSpace E\ninst✝² : OpensMeasurableSpace E\ninst✝¹ : SecondCountableTopologyEither E F\np : ℝ≥0∞\nμ : Measure E\nhμ : μ.HasTemperateGrowth\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1361,
"column": 2
} | {
"line": 1361,
"column": 13
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_5\nF : Type u_6\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : MeasurableSpace E\ninst✝⁴ : OpensMeasurableSpace E\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : SMulCommClass ℝ 𝕜 F\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.SchwartzSpace.Basic | {
"line": 1383,
"column": 2
} | {
"line": 1383,
"column": 82
} | [
{
"pp": "E : Type u_5\nF : Type u_6\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : MeasurableSpace E\ninst✝⁴ : OpensMeasurableSpace E\ninst✝³ : SecondCountableTopologyEither E F\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : BorelSpace E\np... | refine (mem_closure_iff_nhds_basis Metric.nhds_basis_closedBall).2 fun ε hε ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Basic | {
"line": 195,
"column": 6
} | {
"line": 195,
"column": 17
} | [
{
"pp": "s : ℂ\nhs : 0 < s.re\nX : ℝ\nhX : 0 ≤ X\nx : ℝ\nhx : x ∈ Ioo 0 X\n⊢ HasDerivAt (fun y ↦ rexp (-y)) (-rexp (-x)) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Basic | {
"line": 198,
"column": 8
} | {
"line": 198,
"column": 34
} | [
{
"pp": "case refine_2\ns : ℂ\nhs : 0 < s.re\nX : ℝ\nhX : 0 ≤ X\nx : ℝ\nhx : x ∈ Ioo 0 X\nd1 : HasDerivAt (fun y ↦ rexp (-y)) (-rexp (-x)) x\nt : HasDerivAt (fun x ↦ id x ^ s) (s * id ↑x ^ (s - 1) * 1) ↑x\n⊢ HasDerivAt (fun y ↦ ↑y ^ s) (s * ↑x ^ (s - 1)) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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