module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 910,
"column": 2
} | {
"line": 910,
"column": 41
} | {
"line": 910,
"column": 42
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\nC : ℝ≥0\nhlip : LipschitzWith C f\n⊢ ‖deriv f x₀‖ ≤ ↑C",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\nC : ℝ≥0\nhlip : LipschitzWith C f\n⊢ ‖fderiv 𝕜 f x₀‖ ≤ ↑C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 340,
"column": 4
} | {
"line": 340,
"column": 15
} | {
"line": 340,
"column": 16
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module 𝕜 F\ninst✝⁴ : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ninst✝³ : ContinuousA... | [
"case refine_1\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module 𝕜 F\ninst✝⁴ : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ninst✝³ : ContinuousAdd E\ninst✝²... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FormalMultilinearSeries | {
"line": 290,
"column": 2
} | {
"line": 291,
"column": 9
} | {
"line": 291,
"column": 10
} | [
{
"pp": "𝕜 : Type u\nE : Type v\nF : Type w\ninst✝¹⁰ : Semiring 𝕜\ninst✝⁹ : AddCommMonoid E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousConstSMul 𝕜 E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousAdd F\nin... | [
"𝕜 : Type u\nE : Type v\nF : Type w\ninst✝¹⁰ : Semiring 𝕜\ninst✝⁹ : AddCommMonoid E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousConstSMul 𝕜 E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousAdd F\ninst✝ : Contin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 13
} | {
"line": 530,
"column": 14
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜 F\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nf₁... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜 F\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nf₁ f₂ f₃ : α →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 535,
"column": 2
} | {
"line": 535,
"column": 13
} | {
"line": 535,
"column": 14
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜 F\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nf₁... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜 F\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nf₁ f₂ f₃ : α →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 546,
"column": 14
} | {
"line": 546,
"column": 25
} | {
"line": 546,
"column": 26
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg E\nh : (-f)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 557,
"column": 14
} | {
"line": 557,
"column": 25
} | {
"line": 557,
"column": 26
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg E\nh : (-f)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 566,
"column": 2
} | {
"line": 566,
"column": 13
} | {
"line": 566,
"column": 14
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\ng : α → F\ninst✝ : ContinuousNeg E\nf₁ f₂ :... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\ng : α → F\ninst✝ : ContinuousNeg E\nf₁ f₂ : α → E\nh : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 579,
"column": 2
} | {
"line": 579,
"column": 13
} | {
"line": 579,
"column": 14
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\ng : α → F\ninst✝ : ContinuousNeg E\nf₁ f₂ :... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\ng : α → F\ninst✝ : ContinuousNeg E\nf₁ f₂ : α → E\nh : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 596,
"column": 16
} | {
"line": 596,
"column": 27
} | {
"line": 596,
"column": 28
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg F\nh : f =O... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 600,
"column": 14
} | {
"line": 600,
"column": 25
} | {
"line": 600,
"column": 26
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg F\nh : f =O... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 611,
"column": 14
} | {
"line": 611,
"column": 25
} | {
"line": 611,
"column": 26
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : AddCommGroup F\ninst✝² : TopologicalSpace F\ninst✝¹ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\ninst✝ : ContinuousNeg F\nh : f =o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 607,
"column": 2
} | {
"line": 607,
"column": 13
} | {
"line": 607,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\ninst✝¹ : ContinuousAdd ... | [
"𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\ninst✝¹ : ContinuousAdd F\ninst✝ : C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 652,
"column": 2
} | {
"line": 652,
"column": 55
} | {
"line": 653,
"column": 2
} | [
{
"pp": "case right\nα : Type u_1\n𝕜 : Type u_3\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : Module 𝕜 F\nl : Filter α\ng : α → F\nι : Type u_7\nE : ι → Type u_8\ninst✝³ : (i : ι) → AddCommGroup (E i)\ninst✝² : (i : ι) → Module 𝕜 (E i)\nins... | [
"case right\nα : Type u_1\n𝕜 : Type u_3\nF : Type u_5\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : Module 𝕜 F\nl : Filter α\ng : α → F\nι : Type u_7\nE : ι → Type u_8\ninst✝³ : (i : ι) → AddCommGroup (E i)\ninst✝² : (i : ι) → Module 𝕜 (E i)\ninst✝¹ : (i : ι... | refine (hIf.eventually_all.mpr hV).mono fun x hx ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 971,
"column": 2
} | {
"line": 971,
"column": 13
} | {
"line": 971,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nV' : Type u_3\nW : Type u_4\nW' : Type u_5\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝⁹ : NormedAddCommGroup V\ninst✝⁸ : NormedSpace 𝕜 V\ninst✝⁷ : NormedAddCommGroup V'\ninst✝⁶ : NormedSpace 𝕜 V'\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : NormedSpace 𝕜 W... | [
"𝕜 : Type u_1\nV : Type u_2\nV' : Type u_3\nW : Type u_4\nW' : Type u_5\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝⁹ : NormedAddCommGroup V\ninst✝⁸ : NormedSpace 𝕜 V\ninst✝⁷ : NormedAddCommGroup V'\ninst✝⁶ : NormedSpace 𝕜 V'\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : NormedSpace 𝕜 W\ninst✝³ : N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 977,
"column": 2
} | {
"line": 977,
"column": 13
} | {
"line": 977,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nV' : Type u_3\nW : Type u_4\nW' : Type u_5\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝⁹ : NormedAddCommGroup V\ninst✝⁸ : NormedSpace 𝕜 V\ninst✝⁷ : NormedAddCommGroup V'\ninst✝⁶ : NormedSpace 𝕜 V'\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : NormedSpace 𝕜 W... | [
"𝕜 : Type u_1\nV : Type u_2\nV' : Type u_3\nW : Type u_4\nW' : Type u_5\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝⁹ : NormedAddCommGroup V\ninst✝⁸ : NormedSpace 𝕜 V\ninst✝⁷ : NormedAddCommGroup V'\ninst✝⁶ : NormedSpace 𝕜 V'\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : NormedSpace 𝕜 W\ninst✝³ : N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 30
} | {
"line": 190,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0\nh₀ : 0 < ↑r\na✝ : ℝ\nha✝ : a✝ ∈ Ioo (-1) 1\nhp✝ : (fun n ↦ ‖p n... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0\nh₀ : 0 < ↑r\na✝ : ℝ\nha✝ : a✝ ∈ Ioo (-1) 1\nhp✝ : (fun n ↦ ‖p n‖ * ↑r ^ n) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 729,
"column": 4
} | {
"line": 729,
"column": 32
} | {
"line": 729,
"column": 33
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto f l (𝓝 x)\n⊢ Tendsto (fun x_1 ↦ f x_1 - x) l (�... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto f l (𝓝 x)\n⊢ Tendsto (fun x_1 ↦ f x_1 + -x) l (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 737,
"column": 4
} | {
"line": 737,
"column": 15
} | {
"line": 737,
"column": 16
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ :... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ : U ∈ 𝓝 0\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 742,
"column": 6
} | {
"line": 742,
"column": 17
} | {
"line": 742,
"column": 18
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ :... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ : U ∈ 𝓝 0\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 748,
"column": 42
} | {
"line": 748,
"column": 53
} | {
"line": 748,
"column": 54
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ :... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝² : Module 𝕜 E\nl : Filter α\nf : α → E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\nx : E\nh : Tendsto (fun x_1 ↦ f x_1 - x) l (𝓝 0)\nU : Set E\nhU₀ : U ∈ 𝓝 0\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 341,
"column": 29
} | {
"line": 341,
"column": 40
} | {
"line": 341,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSeries 𝕜 F G\n... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSeries 𝕜 F G\nu : E →L[𝕜]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 343,
"column": 31
} | {
"line": 343,
"column": 42
} | {
"line": 343,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSeries 𝕜 F G\n... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSeries 𝕜 F G\nu : E →L[𝕜]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 361,
"column": 4
} | {
"line": 362,
"column": 11
} | {
"line": 362,
"column": 12
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSerie... | [
"case inr\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinearSeries 𝕜 F G\nu ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 372,
"column": 31
} | {
"line": 372,
"column": 61
} | {
"line": 372,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Nontrivial F\np : FormalMul... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Nontrivial F\np : FormalMultilinearSeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 48
} | {
"line": 84,
"column": 49
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\ni : ... | [
"𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\ni : Fin (n + 1)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 41
} | {
"line": 88,
"column": 42
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nx : ... | [
"𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nx : Ei 0\nm : (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 93,
"column": 2
} | {
"line": 93,
"column": 45
} | {
"line": 93,
"column": 46
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : ... | [
"𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : (i : Fin n) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 61
} | {
"line": 189,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0\nhr : ↑r < p.radius\nk : ℕ\nr' : ℝ≥0\nh0 : 0 < r'\nhr' : ↑r + ↑r... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0\nhr : ↑r < p.radius\nk : ℕ\nr' : ℝ≥0\nh0 : 0 < r'\nhr' : ↑r + ↑r' < p.radius... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 452,
"column": 25
} | {
"line": 452,
"column": 36
} | {
"line": 452,
"column": 37
} | [
{
"pp": "𝕜 : Type u\nG : Type wG\nG' : Type wG'\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCommGroup G'\ninst✝ : NormedSpace 𝕜 G'\nf : G [×0]→L[𝕜] G'\n⊢ ‖f 0‖ ≤ ‖f‖",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
... | [
"𝕜 : Type u\nG : Type wG\nG' : Type wG'\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCommGroup G'\ninst✝ : NormedSpace 𝕜 G'\nf : G [×0]→L[𝕜] G'\n⊢ ‖f ![]‖ ≤ ‖f‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 34
} | {
"line": 456,
"column": 35
} | [
{
"pp": "𝕜 : Type u\nG : Type wG\nG' : Type wG'\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCommGroup G'\ninst✝ : NormedSpace 𝕜 G'\nf : G [×0]→L[𝕜] G'\nthis : ‖uncurry0 𝕜 G f.curry0‖ ≤ ‖f.curry0‖\n⊢ ‖f‖ ≤ ‖f 0‖",
"ppTerm": "?m.123",
... | [
"𝕜 : Type u\nG : Type wG\nG' : Type wG'\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCommGroup G'\ninst✝ : NormedSpace 𝕜 G'\nf : G [×0]→L[𝕜] G'\nthis : ‖uncurry0 𝕜 G f.curry0‖ ≤ ‖f.curry0‖\n⊢ ‖f‖ ≤ ‖f 0‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 553,
"column": 19
} | {
"line": 553,
"column": 65
} | {
"line": 553,
"column": 66
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nEi : Fin n.succ → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : Fintype ι'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁶ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁵ : (i : Fin n... | [
"𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nEi : Fin n.succ → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : Fintype ι'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁶ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁵ : (i : Fin n.succ) → Nor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 44
} | {
"line": 226,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0\n_h0 : 0 < r\nhr : ↑‖x‖₊ + ↑r < p.radius\nhr' : ↑‖x‖₊ < p... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0\n_h0 : 0 < r\nhr : ↑‖x‖₊ + ↑r < p.radius\nhr' : ↑‖x‖₊ < p.radius\nthi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 328,
"column": 8
} | {
"line": 328,
"column": 31
} | {
"line": 328,
"column": 32
} | [
{
"pp": "case h'y\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx y : E\nr : ℝ... | [
"case h'y\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx y : E\nr : ℝ≥0∞\nhf : Ha... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 359,
"column": 39
} | {
"line": 359,
"column": 50
} | {
"line": 359,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx y : E\nr : ℝ≥0∞\nhf : HasFPowerSe... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx y : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 25
} | {
"line": 70,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : Field 𝕜\ninst✝⁴ : Ring E\ninst✝³ : Algebra 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalRing E\ninst✝ : Nontrivial E\na₁✝ a₂✝ : ℕ → 𝕜\nh : ofScalars E a₁✝ = ofScalars E a₂✝\nn : ℕ\n⊢ a₁✝ n = a₂✝ n",
"ppTerm": "?m.24",
"assigned": false,
"u... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : Field 𝕜\ninst✝⁴ : Ring E\ninst✝³ : Algebra 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalRing E\ninst✝ : Nontrivial E\na₁✝ a₂✝ : ℕ → 𝕜\nh : ofScalars E a₁✝ = ofScalars E a₂✝\nn : ℕ\n⊢ a₁✝ n = a₂✝ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 212,
"column": 40
} | {
"line": 212,
"column": 72
} | {
"line": 212,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p s x r\ny... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 35
} | {
"line": 213,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p s x r\ny... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 213,
"column": 50
} | {
"line": 213,
"column": 83
} | {
"line": 213,
"column": 84
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p s x r\ny... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 217,
"column": 40
} | {
"line": 217,
"column": 72
} | {
"line": 217,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\ny : E\nh... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\ny : E\nhy : y ∈ Metr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 35
} | {
"line": 218,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\ny : E\nh... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\ny : E\nhy : y ∈ Metr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 249,
"column": 4
} | {
"line": 249,
"column": 15
} | {
"line": 249,
"column": 16
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWi... | [
"case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 252,
"column": 4
} | {
"line": 252,
"column": 36
} | {
"line": 252,
"column": 37
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWi... | [
"case inr\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 262,
"column": 19
} | {
"line": 262,
"column": 51
} | {
"line": 262,
"column": 52
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f p s x r\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 284,
"column": 6
} | {
"line": 284,
"column": 38
} | {
"line": 284,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\nhg : E... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f p x r\nhg : EqOn f g (Met... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 401,
"column": 39
} | {
"line": 401,
"column": 69
} | {
"line": 401,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f p (insert x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 283,
"column": 6
} | {
"line": 285,
"column": 11
} | {
"line": 286,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nhc✝ : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop atTop\nr : ℝ≥0\nhr : ↑r < (ofScalars E c).radius\nthis : 0 < r\nn : ℕ\nhc : 2 * ↑r⁻¹ ≤ ‖c n.succ‖ / ... | [] | convert! hc
rw [pow_succ, div_mul_cancel_left₀, NNReal.coe_inv]
aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Basic | {
"line": 401,
"column": 39
} | {
"line": 401,
"column": 69
} | {
"line": 401,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f p s x r\ny ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 283,
"column": 6
} | {
"line": 285,
"column": 11
} | {
"line": 286,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nhc✝ : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop atTop\nr : ℝ≥0\nhr : ↑r < (ofScalars E c).radius\nthis : 0 < r\nn : ℕ\nhc : 2 * ↑r⁻¹ ≤ ‖c n.succ‖ / ... | [] | convert! hc
rw [pow_succ, div_mul_cancel_left₀, NNReal.coe_inv]
aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Basic | {
"line": 421,
"column": 2
} | {
"line": 421,
"column": 20
} | {
"line": 421,
"column": 21
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\npf : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\npf : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f pf s x r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 552,
"column": 4
} | {
"line": 553,
"column": 86
} | {
"line": 554,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\np : FormalMultilinearSeri... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 614,
"column": 28
} | {
"line": 614,
"column": 39
} | {
"line": 614,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 618,
"column": 4
} | {
"line": 618,
"column": 15
} | {
"line": 618,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 619,
"column": 30
} | {
"line": 619,
"column": 56
} | {
"line": 619,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 631,
"column": 69
} | {
"line": 631,
"column": 80
} | {
"line": 631,
"column": 81
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 632,
"column": 45
} | {
"line": 632,
"column": 71
} | {
"line": 632,
"column": 72
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 313,
"column": 10
} | {
"line": 313,
"column": 39
} | {
"line": 313,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nn : ℕ\np : FormalMultilinearSeries �... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nn : ℕ\np : FormalMultilinearSeries 𝕜 E F\nc : C... | ← c.blocksFinEquiv.prod_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 426,
"column": 34
} | {
"line": 426,
"column": 80
} | {
"line": 426,
"column": 81
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nv0 : Fin 0 → E\nn : ℕ\nn_pos : n > 0\nb : Composition n\na✝ : b ∈ Finset... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nv0 : Fin 0 → E\nn : ℕ\nn_pos : n > 0\nb : Composition n\na✝ : b ∈ Finset.univ\nhb : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 647,
"column": 27
} | {
"line": 647,
"column": 53
} | {
"line": 647,
"column": 54
} | [
{
"pp": "case hab\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSe... | [
"case hab\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ny : E\nhf : HasFPowerSeriesWithinOn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 707,
"column": 2
} | {
"line": 712,
"column": 62
} | {
"line": 714,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWit... | [] | calc
‖(p n) fun _ : Fin n => y‖
_ ≤ ‖p n‖ * ∏ _i : Fin n, ‖y‖ := ContinuousMultilinearMap.le_opNorm _ _
_ = ‖p n‖ * (r' : ℝ) ^ n * (‖y‖ / r') ^ n := by simp [field, div_pow]
_ ≤ C * a ^ n * (‖y‖ / r') ^ n := by gcongr ?_ * _; apply hp
_ ≤ C * (a * (‖y‖ / r')) ^ n := by rw [mul_pow, mul_assoc] | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.Analysis.Analytic.Basic | {
"line": 724,
"column": 2
} | {
"line": 724,
"column": 13
} | {
"line": 724,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f p univ x r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 750,
"column": 2
} | {
"line": 750,
"column": 13
} | {
"line": 750,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f p univ x r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 765,
"column": 2
} | {
"line": 766,
"column": 9
} | {
"line": 766,
"column": 10
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 642,
"column": 4
} | {
"line": 642,
"column": 38
} | {
"line": 642,
"column": 39
} | [
{
"pp": "case i_surj\nα : Type u_6\ninst✝ : AddCommMonoid α\nm M N : ℕ\nf : (n : ℕ) × (Fin n → ℕ) → α\ng : (n : ℕ) × Composition n → α\nh : ∀ (e : (n : ℕ) × (Fin n → ℕ)) (he : e ∈ compPartialSumSource m M N), f e = g (compChangeOfVariables m M N e he)\ni : (n : ℕ) × Composition n\nhi : i ∈ compPartialSumTarget ... | [
"case i_surj\nα : Type u_6\ninst✝ : AddCommMonoid α\nm M N : ℕ\nf : (n : ℕ) × (Fin n → ℕ) → α\ng : (n : ℕ) × Composition n → α\nh : ∀ (e : (n : ℕ) × (Fin n → ℕ)) (he : e ∈ compPartialSumSource m M N), f e = g (compChangeOfVariables m M N e he)\ni : (n : ℕ) × Composition n\nhi : i ∈ compPartialSumTarget m M N\n⊢ i ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 766,
"column": 26
} | {
"line": 766,
"column": 37
} | {
"line": 766,
"column": 38
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 773,
"column": 2
} | {
"line": 773,
"column": 13
} | {
"line": 773,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\nn : ℕ\n⊢ (fun... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\nn : ℕ\n⊢ (fun y ↦ f (x + ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 684,
"column": 4
} | {
"line": 684,
"column": 98
} | {
"line": 684,
"column": 99
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nq : FormalMultilinearSeries 𝕜 F G\n... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nq : FormalMultilinearSeries 𝕜 F G\np : FormalMu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 35
} | {
"line": 83,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nn m : ℕ\nhf : HasFiniteFPowerSeriesOnB... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nn m : ℕ\nhf : HasFiniteFPowerSeriesOnBall f pf x n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 35
} | {
"line": 88,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nn m : ℕ\nhf : HasFiniteFPowerSeriesAt f pf x n\n... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nn m : ℕ\nhf : HasFiniteFPowerSeriesAt f pf x n\nhg : HasFini... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 35
} | {
"line": 92,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\nx : E\nhf : CPolynomialAt 𝕜 f x\nhg : CPolynomialAt 𝕜 g x\n⊢ CPolynomialAt 𝕜 (f - g) x",
... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\nx : E\nhf : CPolynomialAt 𝕜 f x\nhg : CPolynomialAt 𝕜 g x\n⊢ CPolynomialAt 𝕜 (f + -g) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 800,
"column": 64
} | {
"line": 801,
"column": 50
} | {
"line": 802,
"column": 8
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : FormalMult... | [] | by
apply ContinuousMultilinearMap.le_opNorm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Basic | {
"line": 850,
"column": 2
} | {
"line": 850,
"column": 13
} | {
"line": 850,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x r\nhr : r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 873,
"column": 2
} | {
"line": 873,
"column": 59
} | {
"line": 873,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x r\nhr : r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 895,
"column": 2
} | {
"line": 895,
"column": 13
} | {
"line": 895,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\n⊢ (fun y ↦ f ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\n⊢ (fun y ↦ f y.1 - f y.2 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 226,
"column": 2
} | {
"line": 227,
"column": 72
} | {
"line": 229,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nhn : 0 < n\np : FormalMultilinearSeries 𝕜 E F\nq : FormalMultilinearSeries 𝕜 F E\nv : Fin n → F\nA ... | [] | simp [FormalMultilinearSeries.comp, A, Finset.sum_union B, C, -Set.toFinset_setOf,
-add_right_inj, -Composition.single_length, -Finset.union_singleton] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.Basic | {
"line": 922,
"column": 2
} | {
"line": 922,
"column": 13
} | {
"line": 922,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f p univ x r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 939,
"column": 4
} | {
"line": 939,
"column": 34
} | {
"line": 939,
"column": 35
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeri... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 13
} | {
"line": 948,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x r\n⊢ Tendsto... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 969,
"column": 2
} | {
"line": 969,
"column": 13
} | {
"line": 969,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f p univ x r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 992,
"column": 2
} | {
"line": 992,
"column": 13
} | {
"line": 992,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x r\n⊢ Tendsto... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1007,
"column": 2
} | {
"line": 1007,
"column": 13
} | {
"line": 1007,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x r\n⊢ Continu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1110,
"column": 66
} | {
"line": 1110,
"column": 77
} | {
"line": 1110,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nx✝¹ : HasFPowerSeriesAt f p z₀\nr : ℝ≥0∞\nr_le✝ : r ≤ p.radius\nr_pos : 0 < r\nh : ∀ {y : 𝕜}, y ∈ Metric.eball 0 r → HasS... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nx✝¹ : HasFPowerSeriesAt f p z₀\nr : ℝ≥0∞\nr_le✝ : r ≤ p.radius\nr_pos : 0 < r\nh : ∀ {y : 𝕜}, y ∈ Metric.eball 0 r → HasSum (fun n ↦ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1127,
"column": 4
} | {
"line": 1127,
"column": 63
} | {
"line": 1127,
"column": 64
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nr : ℝ\nr_pos : r > 0\nh : ∀ ⦃y : 𝕜⦄, ‖y‖ < r → HasSum (fun n ↦ y ^ n • p.coeff n) (f (z₀ + y))\ny : 𝕜\nx✝... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nr : ℝ\nr_pos : r > 0\nh : ∀ ⦃y : 𝕜⦄, ‖y‖ < r → HasSum (fun n ↦ y ^ n • p.coeff n) (f (z₀ + y))\ny : 𝕜\nx✝ : edist y 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 1055,
"column": 4
} | {
"line": 1055,
"column": 68
} | {
"line": 1055,
"column": 69
} | [
{
"pp": "n : ℕ\na : Composition n\nb : (i : Fin a.length) → Composition (a.blocksFun i)\na' : Composition n\nb' : (i : Fin a'.length) → Composition (a'.blocksFun i)\nH : (ofFn fun i ↦ (b i).blocks) = ofFn fun i ↦ (b' i).blocks\nthis : (ofFn fun i ↦ (b i).blocks.sum) = ofFn fun i ↦ (b' i).blocks.sum\n⊢ a.blocks ... | [
"n : ℕ\na : Composition n\nb : (i : Fin a.length) → Composition (a.blocksFun i)\na' : Composition n\nb' : (i : Fin a'.length) → Composition (a'.blocksFun i)\nH : (ofFn fun i ↦ (b i).blocks) = ofFn fun i ↦ (b' i).blocks\nthis : (ofFn fun i ↦ (b i).blocks.sum) = ofFn fun i ↦ (b' i).blocks.sum\n⊢ a.blocks = a'.blocks"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 397,
"column": 6
} | {
"line": 398,
"column": 62
} | {
"line": 399,
"column": 6
} | [
{
"pp": "case h\nn : ℕ\np : ℕ → ℝ\nhp : ∀ (k : ℕ), 0 ≤ p k\nr a : ℝ\nhr : 0 ≤ r\nha : 0 ≤ a\nk : ℕ\nc : Composition k\nhd : (2 ≤ k ∧ k < n + 1) ∧ 1 < c.length\nj : Fin c.length\n⊢ c.blocksFun j < n",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"False",
"Preorder.toLT",
"Na... | [
"case h\nn : ℕ\np : ℕ → ℝ\nhp : ∀ (k : ℕ), 0 ≤ p k\nr a : ℝ\nhr : 0 ≤ r\nha : 0 ≤ a\nk : ℕ\nc : Composition k\nhd : (2 ≤ k ∧ k < n + 1) ∧ 1 < c.length\nj : Fin c.length\nthis : c ≠ Composition.single k ⋯\n⊢ c.blocksFun j < n"
] | have : c ≠ Composition.single k (zero_lt_two.trans_le hd.1.1) := by
simp [Composition.eq_single_iff_length, ne_of_gt hd.2] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Analytic.Basic | {
"line": 1131,
"column": 6
} | {
"line": 1131,
"column": 31
} | {
"line": 1131,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ HasFPowerSeriesAt f p z₀ ↔ ∀ᶠ (z : 𝕜) in 𝓝 z₀, HasSum (fun n ↦ (z - z₀) ^ n • p.coeff n) (f z)",
"ppTerm": "?m.53"... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ HasFPowerSeriesAt f p z₀ ↔ ∀ᶠ (z : 𝕜) in map (fun x ↦ z₀ + x) (𝓝 0), HasSum (fun n ↦ (z - z₀) ^ n • p.coeff n) (f z)"
] | ← map_add_left_nhds_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.Within | {
"line": 57,
"column": 35
} | {
"line": 57,
"column": 46
} | {
"line": 57,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\ns : Set E\nx : E\nh : {x} ∈ 𝓝[s] x\nt : Set E\not : IsOpen[PseudoMetricSpace.toUniformSpace.toTo... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\ns : Set E\nx : E\nh : {x} ∈ 𝓝[s] x\nt : Set E\not : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 143,
"column": 6
} | {
"line": 143,
"column": 85
} | {
"line": 143,
"column": 86
} | [
{
"pp": "case mpr.a\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ... | [
"case mpr.a\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\ng : E →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 187,
"column": 6
} | {
"line": 187,
"column": 32
} | {
"line": 187,
"column": 33
} | [
{
"pp": "case refine_1.refine_1\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[inser... | [
"case refine_1.refine_1\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[insert x s] x] g\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 191,
"column": 8
} | {
"line": 191,
"column": 35
} | {
"line": 191,
"column": 36
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[insert x s] x] g\nh... | [
"case pos\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[insert x s] x] g\nhg : Analytic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 589,
"column": 64
} | {
"line": 590,
"column": 50
} | {
"line": 591,
"column": 8
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | [] | by
apply ContinuousMultilinearMap.le_opNorm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 18
} | {
"line": 239,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝 x ×ˢ pure x) (𝓝 x ×ˢ pure x)",
"ppTerm": "?m.77",
"assigned":... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f ∘ fun a ↦ (a, x)) (𝓝 x) (map (fun a ↦ (a, x)) (𝓝 x))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 18
} | {
"line": 246,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\ns : Set E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivWithinAt f f' s x\nhx : f x = x\nhs : MapsTo f s s\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝[s] x ×ˢ pure x) (𝓝[s] x ×ˢ pure... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\ns : Set E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivWithinAt f f' s x\nhx : f x = x\nhs : MapsTo f s s\nn : ℕ\n⊢ Tendsto (Prod.map f f ∘ fun a ↦ (a, x)) (𝓝[s] x) (map (fun a ↦ (a, x))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 32
} | {
"line": 253,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasStrictFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝 (x, x)) (𝓝 (x, x))",
"ppTerm": "?m.77",
"assigned": fal... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasStrictFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝 (x, x)) (𝓝 (x, x))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 599,
"column": 4
} | {
"line": 599,
"column": 46
} | {
"line": 599,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeries 𝕜 F G\np... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 604,
"column": 34
} | {
"line": 604,
"column": 63
} | {
"line": 604,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeries 𝕜 F G\np... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 624,
"column": 6
} | {
"line": 624,
"column": 17
} | {
"line": 624,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMult... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMultilinearSerie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 635,
"column": 6
} | {
"line": 635,
"column": 17
} | {
"line": 635,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMult... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMultilinearSerie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 155,
"column": 14
} | {
"line": 155,
"column": 25
} | {
"line": 155,
"column": 26
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nhf : AnalyticAt 𝕜 (-f) x\n⊢ AnalyticAt 𝕜 f x",
"ppTerm": "?m.63",
"assigned": fa... | [
"𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nhf : AnalyticAt 𝕜 (-f) x\n⊢ AnalyticAt 𝕜 f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 35
} | {
"line": 167,
"column": 36
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinO... | [
"𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f pf s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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