module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 720,
"column": 37
} | {
"line": 720,
"column": 48
} | {
"line": 720,
"column": 49
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ (x : E), ... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ (x : E), (p x 0) ![] ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 720,
"column": 67
} | {
"line": 720,
"column": 78
} | {
"line": 720,
"column": 79
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ (m : ℕ), ... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ (m : ℕ), ↑m ≤ n → Con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 720,
"column": 37
} | {
"line": 720,
"column": 48
} | {
"line": 720,
"column": 49
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ x ∈ univ, (p x 0... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ (x : E), (p x 0) ![] = f x"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 720,
"column": 67
} | {
"line": 720,
"column": 78
} | {
"line": 720,
"column": 79
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ (m : ℕ), ↑m ≤ n ... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ (m : ℕ), ↑m ≤ n → Continuous... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 721,
"column": 4
} | {
"line": 721,
"column": 15
} | {
"line": 721,
"column": 16
} | [
{
"pp": "case mp\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ ... | [
"case mp\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpToOn n f p univ\n⊢ ∀ (m : ℕ), ↑m ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Pow | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 13
} | {
"line": 96,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedCommRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf : 𝕜 → 𝔸\nf' : 𝔸\nx : 𝕜\nh : HasStrictDerivAt f f' x\nn : ℕ\n⊢ HasStrictDerivAt (fun x ↦ f x ^ n) (↑n * f x ^ (n - 1) * f') x",
"ppTerm": "?m.40",
"assigned": false,
... | [
"𝕜 : Type u_1\n𝔸 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedCommRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf : 𝕜 → 𝔸\nf' : 𝔸\nx : 𝕜\nh : HasStrictDerivAt f f' x\nn : ℕ\n⊢ HasStrictDerivAt (fun x ↦ f x ^ n) (↑n * f x ^ (n - 1) * f') x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Pow | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 13
} | {
"line": 103,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedCommRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf : 𝕜 → 𝔸\nf' : 𝔸\nx : 𝕜\ns : Set 𝕜\nh : HasDerivWithinAt f f' s x\nn : ℕ\n⊢ HasDerivWithinAt (fun x ↦ f x ^ n) (↑n * f x ^ (n - 1) * f') s x",
"ppTerm": "?m.40",
"as... | [
"𝕜 : Type u_1\n𝔸 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedCommRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf : 𝕜 → 𝔸\nf' : 𝔸\nx : 𝕜\ns : Set 𝕜\nh : HasDerivWithinAt f f' s x\nn : ℕ\n⊢ HasDerivWithinAt (fun x ↦ f x ^ n) (↑n * f x ^ (n - 1) * f') s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 722,
"column": 4
} | {
"line": 722,
"column": 15
} | {
"line": 722,
"column": 16
} | [
{
"pp": "case mpr\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ (m : ℕ... | [
"case mpr\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nH : HasFTaylorSeriesUpTo n f p\n⊢ ∀ (m : ℕ), ↑m < n → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Pow | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 13
} | {
"line": 139,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nn : ℕ\nx : 𝕜\n⊢ HasDerivAt (fun x ↦ x ^ n) (↑n * x ^ (n - 1)) x",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nn : ℕ\nx : 𝕜\n⊢ HasDerivAt (fun x ↦ x ^ n) (↑n * x ^ (n - 1)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 13
} | {
"line": 46,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : 𝕜 → F\nf' g' : F\nL : Filter (𝕜 × 𝕜)\nhf : HasDerivAtFilter f f' L\nhg : HasDerivAtFilter g g' L\n⊢ HasDerivAtFilter (f + g) (f' + g') L",
"ppTerm": "?m.32",
"assigned... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : 𝕜 → F\nf' g' : F\nL : Filter (𝕜 × 𝕜)\nhf : HasDerivAtFilter f f' L\nhg : HasDerivAtFilter g g' L\n⊢ HasDerivAtFilter (f + g) (f' + g') L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 13
} | {
"line": 195,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nL : Filter (𝕜 × 𝕜)\nι : Type u_1\nu : Finset ι\nA : ι → 𝕜 → F\nA' : ι → F\nh : ∀ i ∈ u, HasDerivAtFilter (A i) (A' i) L\n⊢ HasDerivAtFilter (fun y ↦ ∑ i ∈ u, A i y) (∑ i ∈ u, A' i) ... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nL : Filter (𝕜 × 𝕜)\nι : Type u_1\nu : Finset ι\nA : ι → 𝕜 → F\nA' : ι → F\nh : ∀ i ∈ u, HasDerivAtFilter (A i) (A' i) L\n⊢ HasDerivAtFilter (fun y ↦ ∑ i ∈ u, A i y) (∑ i ∈ u, A' i) L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 256,
"column": 40
} | {
"line": 256,
"column": 51
} | {
"line": 256,
"column": 52
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nL : Filter (𝕜 × 𝕜)\nh : HasDerivAtFilter f f' L\n⊢ HasDerivAtFilter (-f) (-f') L",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"use... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nL : Filter (𝕜 × 𝕜)\nh : HasDerivAtFilter f f' L\n⊢ HasDerivAtFilter (-f) (-f') L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 348,
"column": 2
} | {
"line": 348,
"column": 35
} | {
"line": 348,
"column": 36
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : 𝕜 → F\nf' g' : F\nL : Filter (𝕜 × 𝕜)\nhf : HasDerivAtFilter f f' L\nhg : HasDerivAtFilter g g' L\n⊢ HasDerivAtFilter (f - g) (f' - g') L",
"ppTerm": "?m.32",
"assigned... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : 𝕜 → F\nf' g' : F\nL : Filter (𝕜 × 𝕜)\nhf : HasDerivAtFilter f f' L\nhg : HasDerivAtFilter g g' L\n⊢ HasDerivAtFilter (f + -g) (f' + -g') L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 458,
"column": 2
} | {
"line": 458,
"column": 56
} | {
"line": 460,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) a ↔ DifferentiableAt 𝕜 f (a - b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 458,
"column": 2
} | {
"line": 458,
"column": 56
} | {
"line": 460,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) a ↔ DifferentiableAt 𝕜 f (a - b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 458,
"column": 2
} | {
"line": 458,
"column": 56
} | {
"line": 460,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) a ↔ DifferentiableAt 𝕜 f (a - b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 470,
"column": 2
} | {
"line": 470,
"column": 56
} | {
"line": 472,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 f a ↔ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) (a + b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 470,
"column": 2
} | {
"line": 470,
"column": 56
} | {
"line": 472,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 f a ↔ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) (a + b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.Deriv.Add | {
"line": 470,
"column": 2
} | {
"line": 470,
"column": 56
} | {
"line": 472,
"column": 0
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na b : 𝕜\n⊢ DifferentiableAt 𝕜 f a ↔ DifferentiableAt 𝕜 (fun x ↦ f (x - b)) (a + b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"NormedCom... | [] | simp [sub_eq_add_neg, differentiableAt_comp_add_const] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.Deriv.Polynomial | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 65
} | {
"line": 63,
"column": 4
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R 𝕜\nq : R[X]\nx : 𝕜\n⊢ HasStrictDerivAt (fun x ↦ (aeval x) q) ((aeval x) (derivative q)) x",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Polynomial.derivative",
... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R 𝕜\nq : R[X]\nx : 𝕜\n⊢ HasStrictDerivAt (fun x ↦ eval x (map (algebraMap R 𝕜) q)) (eval x (map (algebraMap R 𝕜) (derivative q))) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Polynomial | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 65
} | {
"line": 122,
"column": 4
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R 𝕜\nq : R[X]\nhxs : UniqueDiffWithinAt 𝕜 s x\n⊢ derivWithin (fun x ↦ (aeval x) q) s x = (aeval x) (derivative q)",
"ppTerm": "?m.35",
"assigned": true,
"usedConsta... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R 𝕜\nq : R[X]\nhxs : UniqueDiffWithinAt 𝕜 s x\n⊢ derivWithin (fun x ↦ eval x (map (algebraMap R 𝕜) q)) s x = eval x (map (algebraMap R 𝕜) (derivative q))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 955,
"column": 2
} | {
"line": 955,
"column": 43
} | {
"line": 955,
"column": 44
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ (iteratedFDeriv 𝕜 n fun z ↦ f (a + z)) = fun x ↦ iteratedFDeriv 𝕜 n f (a + x)",
... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ iteratedFDerivWithin 𝕜 n (fun z ↦ f (a + z)) univ = fun x ↦ iteratedFDerivWithin 𝕜 n f univ (a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 965,
"column": 2
} | {
"line": 965,
"column": 26
} | {
"line": 965,
"column": 27
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ (iteratedFDeriv 𝕜 n fun z ↦ f (z + a)) = fun x ↦ iteratedFDeriv 𝕜 n f (x + a)",
... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ (iteratedFDeriv 𝕜 n fun z ↦ f (z + a)) = fun x ↦ iteratedFDeriv 𝕜 n f (x + a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 975,
"column": 2
} | {
"line": 975,
"column": 30
} | {
"line": 975,
"column": 31
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ (iteratedFDeriv 𝕜 n fun z ↦ f (z - a)) = fun x ↦ iteratedFDeriv 𝕜 n f (x - a)",
... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nn : ℕ\na : E\n⊢ (iteratedFDeriv 𝕜 n fun z ↦ f (z + -a)) = fun x ↦ iteratedFDeriv 𝕜 n f (x + -a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 710,
"column": 2
} | {
"line": 710,
"column": 13
} | {
"line": 710,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\ninst✝²... | [
"𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\ninst✝² : Decidable... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 720,
"column": 2
} | {
"line": 720,
"column": 13
} | {
"line": 720,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\ninst✝²... | [
"𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : (i : ι) → NormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\ninst✝² : Decidable... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Slope | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | {
"line": 155,
"column": 14
} | [
{
"pp": "k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\nhxy : x ≤ y\n⊢ slope f x y ≤ 0 ↔ f y ≤ f x",
"ppTe... | [
"k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\nhxy : x ≤ y\n⊢ slope f x y ≤ 0 ↔ f y ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Slope | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 13
} | {
"line": 159,
"column": 14
} | [
{
"pp": "k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\ns : Set k\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s... | [
"k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\ns : Set k\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\n⊢ slope f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Slope | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 13
} | {
"line": 171,
"column": 14
} | [
{
"pp": "k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\nhxy : x ≤ y\n⊢ slope f x y < 0 ↔ f y < f x",
"ppTe... | [
"k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\nhxy : x ≤ y\n⊢ slope f x y < 0 ↔ f y < f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Slope | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 13
} | {
"line": 175,
"column": 14
} | [
{
"pp": "k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\ns : Set k\nhf : StrictAntiOn f s\nhx : x ∈ s\nhy : y ∈... | [
"k : Type u_1\nE : Type u_2\ninst✝⁷ : Field k\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module k E\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : PartialOrder E\ninst✝¹ : IsOrderedAddMonoid E\ninst✝ : PosSMulMono k E\nf : k → E\nx y : k\ns : Set k\nhf : StrictAntiOn f s\nhx : x ∈ s\nhy : y ∈ s\nhxy : x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 755,
"column": 4
} | {
"line": 755,
"column": 11
} | {
"line": 756,
"column": 4
} | [
{
"pp": "case fderiv\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝² : (i : ι) → NormedAddCommGroup (E i)\ninst✝¹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap 𝕜... | [
"case fderiv\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝² : (i : ι) → NormedAddCommGroup (E i)\ninst✝¹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\nn : ℕ\... | ext v m | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 769,
"column": 10
} | {
"line": 769,
"column": 21
} | {
"line": 769,
"column": 22
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝² : (i : ι) → NormedAddCommGroup (E i)\ninst✝¹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\nn : ℕ\n... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝² : (i : ι) → NormedAddCommGroup (E i)\ninst✝¹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\nn : ℕ\nx v : (i : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Slope | {
"line": 62,
"column": 6
} | {
"line": 62,
"column": 55
} | {
"line": 62,
"column": 55
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nL : Filter 𝕜\n⊢ Tendsto (fun y ↦ slope f x y - f') (L ⊓ 𝓟 {x}ᶜ) (𝓝 0) ↔ Tendsto (slope f x) (L ⊓ 𝓟 {x}ᶜ) (𝓝 f')",
"ppTerm": "?m.213",
"assigned... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nL : Filter 𝕜\n⊢ Tendsto (fun y ↦ slope f x y - f') (L ⊓ 𝓟 {x}ᶜ) (𝓝 0) ↔ Tendsto ((fun x ↦ x - f') ∘ slope f x) (L ⊓ 𝓟 {x}ᶜ) (𝓝 0)"
] | rw [← nhds_translation_sub f', tendsto_comap_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.Deriv.Slope | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 62
} | {
"line": 104,
"column": 63
} | [
{
"pp": "case neg\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns t : Set 𝕜\nh : s ⊆ closure[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (s ∩ t)\nx : 𝕜\nH : ¬UniqueDiffWithinAt 𝕜 s x\n⊢ derivWithin f s x ∈ closure[... | [
"case neg\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns t : Set 𝕜\nh : s ⊆ closure[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (s ∩ t)\nx : 𝕜\nH : ¬UniqueDiffWithinAt 𝕜 s x\n⊢ 0 ∈ closure[PseudoMetricSpace.toUniformS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Uniqueness | {
"line": 115,
"column": 57
} | {
"line": 115,
"column": 84
} | {
"line": 115,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np₁ p₂ : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nh₁ : HasFPowerSeriesAt f p₁ x\nh₂ : HasFPowerSeriesAt f p₂ x\n⊢ HasFPowerSeriesAt 0 (p₁ - p₂) x",
"ppTerm": "?m.56"... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np₁ p₂ : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nh₁ : HasFPowerSeriesAt f p₁ x\nh₂ : HasFPowerSeriesAt f p₂ x\n⊢ HasFPowerSeriesAt 0 (p₁ - p₂) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Uniqueness | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 15
} | {
"line": 171,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nU : Set E\nhf : AnalyticOnNhd 𝕜 f U\nhU : IsPreconnected U\nz₀ : E\nh₀... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nU : Set E\nhf : AnalyticOnNhd 𝕜 f U\nhU : IsPreconnected U\nz₀ : E\nh₀ : z₀ ∈ U\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 836,
"column": 2
} | {
"line": 836,
"column": 13
} | {
"line": 836,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nf : E → F\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesOnBall f p x r\nx✝ : Fin 0 → ... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nf : E → F\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesOnBall f p x r\nx✝ : Fin 0 → E\n⊢ f x = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DSlope | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 52
} | {
"line": 89,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : ContinuousWithinAt (dslope f a) s b\nthis : ContinuousWithinAt (fun x ↦ (x - a) • dslope f a x + f a) s b\n⊢ ContinuousWithinAt f s b",
"p... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : ContinuousWithinAt (dslope f a) s b\nthis : ContinuousWithinAt (fun x ↦ (x - a) • dslope f a x + f a) s b\n⊢ ContinuousWithinAt f s b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DSlope | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 53
} | {
"line": 100,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : b ≠ a\n⊢ ContinuousWithinAt (dslope f a) s b ↔ ContinuousWithinAt f s b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : b ≠ a\nhc : ContinuousWithinAt f s b\n⊢ ContinuousWithinAt (dslope f a) s b"
] | refine ⟨ContinuousWithinAt.of_dslope, fun hc => ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Calculus.DSlope | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 60
} | {
"line": 119,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : DifferentiableWithinAt 𝕜 (dslope f a) s b\n⊢ DifferentiableWithinAt 𝕜 f s b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstan... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : DifferentiableWithinAt 𝕜 (dslope f a) s b\n⊢ DifferentiableWithinAt 𝕜 f s b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Slope | {
"line": 199,
"column": 53
} | {
"line": 199,
"column": 64
} | {
"line": 199,
"column": 65
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx✝ : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\ng' : 𝕜\nhx✝ : AccPt x✝ (𝓟 s)\nhd : HasDerivWithinAt g g' s x✝\nhg : AntitoneOn g s\nx : 𝕜\nhx : x ∈ s\ny : 𝕜\nhy : y ∈ s\nhxy : x ≤... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx✝ : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\ng' : 𝕜\nhx✝ : AccPt x✝ (𝓟 s)\nhd : HasDerivWithinAt g g' s x✝\nhg : AntitoneOn g s\nx : 𝕜\nhx : x ∈ s\ny : 𝕜\nhy : y ∈ s\nhxy : x ≤ y\n⊢ g y ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Slope | {
"line": 200,
"column": 2
} | {
"line": 200,
"column": 13
} | {
"line": 200,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\ng' : 𝕜\nhx : AccPt x (𝓟 s)\nhd : HasDerivWithinAt g g' s x\nhg : AntitoneOn g s\nthis : MonotoneOn (-g) s\n⊢ g' ≤ 0",
"ppTerm": "?... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\ng' : 𝕜\nhx : AccPt x (𝓟 s)\nhd : HasDerivWithinAt g g' s x\nhg : AntitoneOn g s\nthis : MonotoneOn (-g) s\n⊢ g' ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Slope | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 35
} | {
"line": 205,
"column": 36
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\nhg : AntitoneOn g s\n⊢ derivWithin g s x ≤ 0",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : OrderTopology 𝕜\ng : 𝕜 → 𝕜\nhg : AntitoneOn g s\n⊢ derivWithin g s x ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.CircleMap | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 37
} | {
"line": 53,
"column": 38
} | [
{
"pp": "c : ℂ\nR : ℝ\nhR : 0 ≤ R\nθ : ℝ\n⊢ circleMap c R θ ∈ sphere c R",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"c : ℂ\nR : ℝ\nhR : 0 ≤ R\nθ : ℝ\n⊢ circleMap c R θ ∈ sphere c R"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Comp | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 13
} | {
"line": 76,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nL : Filter (𝕜 × 𝕜)\n𝕜' : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜'\ninst✝² : NormedAlgebra 𝕜 𝕜'\ninst✝¹ : NormedSpace 𝕜' F\ninst✝ : IsScalarTower 𝕜 𝕜' F\nh : 𝕜 → 𝕜'\nh'... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nL : Filter (𝕜 × 𝕜)\n𝕜' : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜'\ninst✝² : NormedAlgebra 𝕜 𝕜'\ninst✝¹ : NormedSpace 𝕜' F\ninst✝ : IsScalarTower 𝕜 𝕜' F\nh : 𝕜 → 𝕜'\nh' : 𝕜'\ng₁ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 62,
"column": 34
} | {
"line": 62,
"column": 58
} | {
"line": 62,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : z = 0\n⊢ HasSum (fun m ↦ z ^ m • a m) 0",
"ppTerm": "?m.123",
"... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : z = 0\n⊢ HasSum (fun m ↦ 0 ^ m • a m) 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 63,
"column": 46
} | {
"line": 63,
"column": 61
} | {
"line": 63,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : z = 0\nthis : s = 0\n⊢ HasSum (fun m ↦ z ^ m • a (m + n)) (a n)",
"... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : z = 0\nthis : s = 0\n⊢ HasSum (fun m ↦ 0 ^ m • a (m + n)) (a n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 29,
"column": 2
} | {
"line": 29,
"column": 33
} | {
"line": 29,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\na x : 𝕜\nhf : HasDerivAt f f' (a + x)\n⊢ HasDerivAt (fun x ↦ f (a + x)) f' x",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"used... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\na x : 𝕜\nhf : HasDerivAt f f' (a + x)\n⊢ HasDerivAt (fun x ↦ f (a + x)) f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 33
} | {
"line": 34,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx a : 𝕜\nhf : HasDerivAt f f' (x + a)\n⊢ HasDerivAt (fun x ↦ f (x + a)) f' x",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"used... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx a : 𝕜\nhf : HasDerivAt f f' (x + a)\n⊢ HasDerivAt (fun x ↦ f (x + a)) f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 33
} | {
"line": 39,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\na x : 𝕜\nhf : HasDerivAt f f' (a - x)\n⊢ HasDerivAt (fun x ↦ f (a - x)) (-f') x",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"u... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\na x : 𝕜\nhf : HasDerivAt f f' (a - x)\n⊢ HasDerivAt (fun x ↦ f (a - x)) (-f') x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 33
} | {
"line": 44,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx a : 𝕜\nhf : HasDerivAt f f' (x - a)\n⊢ HasDerivAt (fun x ↦ f (x - a)) f' x",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"used... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx a : 𝕜\nhf : HasDerivAt f f' (x - a)\n⊢ HasDerivAt (fun x ↦ f (x - a)) f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Comp | {
"line": 330,
"column": 17
} | {
"line": 330,
"column": 33
} | {
"line": 330,
"column": 34
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nf' : 𝕜\nhf : HasDerivAt 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.37",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"NormedCo... | [
"𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nf' : 𝕜\nhf : HasDerivAt 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.Deriv.Shift | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 13
} | {
"line": 50,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\n⊢ derivWithin (fun x ↦ f (-x)) s x = -derivWithin f (-s) (-x)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVar... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\n⊢ derivWithin (fun x ↦ f (-x)) s x = -derivWithin f (-s) (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | {
"line": 54,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\n⊢ deriv (fun x ↦ f (-x)) x = -deriv f (-x)",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\n⊢ deriv (fun x ↦ f (-x)) x = -deriv f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Comp | {
"line": 359,
"column": 2
} | {
"line": 359,
"column": 13
} | {
"line": 359,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → F\nf' : F\nx : 𝕜\ns : Set 𝕜\nl : F → E\nl' : F →L[𝕜] E\nt : Set F\nhl : HasFDerivWithinAt l l' t (f x)... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → F\nf' : F\nx : 𝕜\ns : Set 𝕜\nl : F → E\nl' : F →L[𝕜] E\nt : Set F\nhl : HasFDerivWithinAt l l' t (f x)\nhf : HasDe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Shift | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 24
} | {
"line": 72,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na x : 𝕜\n⊢ deriv (fun x ↦ f (x + a)) x = deriv f (x + a)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\na x : 𝕜\n⊢ deriv (fun x ↦ f (a + x)) x = deriv f (a + x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Comp | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 13
} | {
"line": 371,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → F\nf' : F\nx : 𝕜\nl : F → E\nl' : F →L[𝕜] E\nt : Set F\nhl : HasFDerivWithinAt l l' t (f x)\nhf : HasDe... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → F\nf' : F\nx : 𝕜\nl : F → E\nl' : F →L[𝕜] E\nt : Set F\nhl : HasFDerivWithinAt l l' t (f x)\nhf : HasDerivAt f f' x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 68,
"column": 6
} | {
"line": 68,
"column": 22
} | {
"line": 68,
"column": 23
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : ¬z = 0\nh1 : ∑ i ∈ Finset.range n, z ^ i • a i = 0\n⊢ HasSum (fun m ↦ z... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\nn : ℕ\nz : 𝕜\na : ℕ → E\nhs : HasSum (fun m ↦ z ^ m • a m) s\nha : ∀ k < n, a k = 0\nhn : n > 0\nh : ¬z = 0\nh1 : ∑ i ∈ Finset.range n, z ^ i • a i = 0\n⊢ HasSum (fun m ↦ z ^ (m + n) •... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 470,
"column": 27
} | {
"line": 470,
"column": 38
} | {
"line": 470,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nι : Type u_5\n𝔸' : Type u_7\ninst✝³ : NormedCommRing 𝔸'\ninst✝² : NormedAlgebra 𝕜 𝔸'\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nu : Multiset ι\nx : ι → 𝔸'\nthis : Fintype ι\nl : List ι\n⊢ HasStrictFDerivAt (fun x ↦ (Multiset.map x ⟦l⟧).prod)\n ... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nι : Type u_5\n𝔸' : Type u_7\ninst✝³ : NormedCommRing 𝔸'\ninst✝² : NormedAlgebra 𝕜 𝔸'\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nu : Multiset ι\nx : ι → 𝔸'\nthis : Fintype ι\nl : List ι\n⊢ HasStrictFDerivAt (fun x ↦ (List.map x l).prod)\n (List.map (fun x_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 88,
"column": 6
} | {
"line": 88,
"column": 52
} | {
"line": 88,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhpd : deriv f z₀ = p.coeff 1\nhp0 : p.coeff 0 = f z₀\nhp : ∀ᶠ (z : 𝕜) in 𝓝 0, HasSum (fun n ↦ z ^ n • p.coeff n) (f (z₀ ... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhpd : deriv f z₀ = p.coeff 1\nhp0 : p.coeff 0 = f z₀\nhp : ∀ᶠ (z : 𝕜) in 𝓝 0, HasSum (fun n ↦ z ^ n • p.coeff n) (f (z₀ + z))\nx : �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 21
} | {
"line": 89,
"column": 22
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhpd : deriv f z₀ = p.coeff 1\nhp0 : p.coeff 0 = f z₀\nhp : ∀ᶠ (z : 𝕜) in 𝓝 0, HasSum (fun n ↦ z ^ n • p.coeff ... | [
"case neg\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhpd : deriv f z₀ = p.coeff 1\nhp0 : p.coeff 0 = f z₀\nhp : ∀ᶠ (z : 𝕜) in 𝓝 0, HasSum (fun n ↦ z ^ n • p.coeff n) (f (z₀ + ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 95,
"column": 17
} | {
"line": 95,
"column": 28
} | {
"line": 95,
"column": 29
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nz₀ : 𝕜\nn : ℕ\nih :\n ∀ {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E},\n HasFPowerSeriesAt f p z₀ → HasFPowerSeriesAt ((swap dslope z₀)^[n] f) (fslope^[n] p) z... | [
"case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nz₀ : 𝕜\nn : ℕ\nih :\n ∀ {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E},\n HasFPowerSeriesAt f p z₀ → HasFPowerSeriesAt ((swap dslope z₀)^[n] f) (fslope^[n] p) z₀\np : Forma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 29
} | {
"line": 100,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhp : HasFPowerSeriesAt f p z₀\nh : p ≠ 0\n⊢ (fslope^[p.order] p 0) 1 ≠ 0",
"ppTerm": "?m.98",
"assigned": true,
... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhp : HasFPowerSeriesAt f p z₀\nh : p ≠ 0\n⊢ ¬p p.order = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 58
} | {
"line": 113,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhp : HasFPowerSeriesAt f p z₀\nh : p ≠ 0\nh2 : ContinuousAt ((swap dslope z₀)^[p.order] f) z₀\nh3 : ∀ᶠ (z : 𝕜) in 𝓝 z₀, ... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhp : HasFPowerSeriesAt f p z₀\nh : p ≠ 0\nh2 : ContinuousAt ((swap dslope z₀)^[p.order] f) z₀\nh3 : ∀ᶠ (z : 𝕜) in 𝓝 z₀, (swap dslope... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 127,
"column": 2
} | {
"line": 130,
"column": 39
} | {
"line": 132,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ (∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0) ∨ ∀ᶠ (z : 𝕜) in 𝓝[≠] z₀, f z ≠ 0",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants... | [] | rcases hf with ⟨p, hp⟩
by_cases h : p = 0
· exact Or.inl (HasFPowerSeriesAt.eventually_eq_zero (by rwa [h] at hp))
· exact Or.inr (hp.locally_ne_zero h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 127,
"column": 2
} | {
"line": 130,
"column": 39
} | {
"line": 132,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ (∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0) ∨ ∀ᶠ (z : 𝕜) in 𝓝[≠] z₀, f z ≠ 0",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants... | [] | rcases hf with ⟨p, hp⟩
by_cases h : p = 0
· exact Or.inl (HasFPowerSeriesAt.eventually_eq_zero (by rwa [h] at hp))
· exact Or.inr (hp.locally_ne_zero h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 27
} | {
"line": 134,
"column": 28
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nhg : AnalyticAt 𝕜 g z₀\n⊢ (∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = g z) ∨ ∀ᶠ (z : 𝕜) in 𝓝[≠] z₀, f z ≠ g z",
"ppTerm": "?m.54",
"assi... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nhg : AnalyticAt 𝕜 g z₀\n⊢ (∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = g z) ∨ ∀ᶠ (z : 𝕜) in 𝓝[≠] z₀, ¬f z = g z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 27
} | {
"line": 143,
"column": 28
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nhg : AnalyticAt 𝕜 g z₀\n⊢ (∃ᶠ (z : 𝕜) in 𝓝[≠] z₀, f z = g z) ↔ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = g z",
"ppTerm": "?m.54",
"assi... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nhg : AnalyticAt 𝕜 g z₀\n⊢ (∃ᶠ (z : 𝕜) in 𝓝[≠] z₀, f z = g z) ↔ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = g z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.ZPow | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 30
} | {
"line": 167,
"column": 31
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nk : ℕ\nc d : 𝕜\n⊢ (deriv^[k] fun x ↦ (c * x - d)⁻¹) = fun x ↦ (-1) ^ k * ↑k ! * c ^ k * (c * x - d) ^ (-1 - ↑k)",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSem... | [
"𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nk : ℕ\nc d : 𝕜\n⊢ (deriv^[k] fun x ↦ (c * x + -d)⁻¹) = fun x ↦ (-1) ^ k * ↑k ! * c ^ k * (c * x + -d) ^ (-1 + -↑k)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 604,
"column": 2
} | {
"line": 604,
"column": 38
} | {
"line": 604,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx : E\nhg : ... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx : E\nhg : ∀ i ∈ u, Has... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 614,
"column": 2
} | {
"line": 614,
"column": 38
} | {
"line": 614,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx : E\nhg : ... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx : E\nhg : ∀ i ∈ u, Has... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 623,
"column": 2
} | {
"line": 623,
"column": 38
} | {
"line": 623,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ns : Set E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ns : Set E\nι : Type u_5\n𝔸' : Type u_7\ninst✝² : NormedCommRing 𝔸'\ninst✝¹ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\ng : ι → E → 𝔸'\ng' : ι → E →L[𝕜] 𝔸'\ninst✝ : DecidableEq ι\nx : E\nhg : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 729,
"column": 2
} | {
"line": 729,
"column": 13
} | {
"line": 729,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_5\ninst✝¹ : NormedDivisionRing R\ninst✝ : NormedAlgebra 𝕜 R\nx : R\nhx : x ≠ 0\n⊢ HasStrictFDerivAt Inv.inv (-((mulLeftRight 𝕜 R) x⁻¹) x⁻¹) x",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_5\ninst✝¹ : NormedDivisionRing R\ninst✝ : NormedAlgebra 𝕜 R\nx : R\nhx : x ≠ 0\n⊢ HasStrictFDerivAt Inv.inv (-((mulLeftRight 𝕜 R) x⁻¹) x⁻¹) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Mul | {
"line": 737,
"column": 2
} | {
"line": 737,
"column": 13
} | {
"line": 737,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_5\ninst✝¹ : NormedDivisionRing R\ninst✝ : NormedAlgebra 𝕜 R\nx : R\nhx : x ≠ 0\n⊢ HasFDerivAt Inv.inv (-((mulLeftRight 𝕜 R) x⁻¹) x⁻¹) x",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nR : Type u_5\ninst✝¹ : NormedDivisionRing R\ninst✝ : NormedAlgebra 𝕜 R\nx : R\nhx : x ≠ 0\n⊢ HasFDerivAt Inv.inv (-((mulLeftRight 𝕜 R) x⁻¹) x⁻¹) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.AffineMap | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 13
} | {
"line": 66,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\na b : E\nx : 𝕜\n⊢ HasStrictDerivAt (⇑(lineMap a b)) (b - a) x",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\na b : E\nx : 𝕜\n⊢ HasStrictDerivAt (⇑(lineMap a b)) (b - a) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 192,
"column": 22
} | {
"line": 192,
"column": 89
} | {
"line": 192,
"column": 89
} | [
{
"pp": "case mp\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\ng : 𝕜 → E\nhg_an : AnalyticAt 𝕜 g z₀\nhg_eq : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g z\nhg_ne : ∀ᶠ (z : 𝕜) in... | [
"case mp\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\ng : 𝕜 → E\nhg_an : AnalyticAt 𝕜 g z₀\nhg_eq : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g z\nhg_ne : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z ... | ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 189,
"column": 4
} | {
"line": 196,
"column": 44
} | {
"line": 197,
"column": 2
} | [
{
"pp": "case mp\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ (∃ n g, AnalyticAt 𝕜 g z₀ ∧ g z₀ ≠ 0 ∧ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g z) → ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0",
... | [] | rintro ⟨n, g, hg_an, hg_ne, hg_eq⟩
contrapose hg_ne
apply EventuallyEq.eq_of_nhds
rw [EventuallyEq, ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const]
refine (eventually_nhdsWithin_iff.mpr ?_).frequently
filter_upwards [hg_eq, hg_ne] with z hf_eq hf0 hz
rwa [hf0, eq_comm, smul_... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 189,
"column": 4
} | {
"line": 196,
"column": 44
} | {
"line": 197,
"column": 2
} | [
{
"pp": "case mp\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ (∃ n g, AnalyticAt 𝕜 g z₀ ∧ g z₀ ≠ 0 ∧ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g z) → ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0",
... | [] | rintro ⟨n, g, hg_an, hg_ne, hg_eq⟩
contrapose hg_ne
apply EventuallyEq.eq_of_nhds
rw [EventuallyEq, ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const]
refine (eventually_nhdsWithin_iff.mpr ?_).frequently
filter_upwards [hg_eq, hg_ne] with z hf_eq hf0 hz
rwa [hf0, eq_comm, smul_... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.IsolatedZeros | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 22
} | {
"line": 286,
"column": 23
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nA : Type u_3\ninst✝⁶ : NormedRing A\ninst✝⁵ : IsDomain A\ninst✝⁴ : NormedAlgebra 𝕜 A\nB : Type u_4\ninst✝³ : NormedAddCommGroup B\ninst✝² : NormedSpace 𝕜 B\ninst✝¹ : Module A B\ninst✝ : IsTorsionFree A B\nf : 𝕜 → A\ng : 𝕜 → B... | [
"case pos\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nA : Type u_3\ninst✝⁶ : NormedRing A\ninst✝⁵ : IsDomain A\ninst✝⁴ : NormedAlgebra 𝕜 A\nB : Type u_4\ninst✝³ : NormedAddCommGroup B\ninst✝² : NormedSpace 𝕜 B\ninst✝¹ : Module A B\ninst✝ : IsTorsionFree A B\nf : 𝕜 → A\ng : 𝕜 → B\nhf : Analy... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LogDeriv | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 43
} | {
"line": 83,
"column": 44
} | [
{
"pp": "case cons.hg\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_3\nf : ι → 𝕜 → 𝕜'\nx : 𝕜\na : ι\ns : Finset ι\nha : a ∉ s\nih :\n (∀ i ∈ s, f i x ≠ 0) →\n (∀ i ∈ s, DifferentiableAt 𝕜 (f i) x) → log... | [
"case cons.hg\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_3\nf : ι → 𝕜 → 𝕜'\nx : 𝕜\na : ι\ns : Finset ι\nha : a ∉ s\nih :\n (∀ i ∈ s, f i x ≠ 0) →\n (∀ i ∈ s, DifferentiableAt 𝕜 (f i) x) → logDeriv (fun x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LogDeriv | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 13
} | {
"line": 109,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\n⊢ logDeriv (fun x ↦ x⁻¹) x = -1 / x",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\n⊢ logDeriv (fun x ↦ x⁻¹) x = -1 / x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LogDeriv | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 15
} | {
"line": 121,
"column": 16
} | [
{
"pp": "case inl\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NontriviallyNormedField 𝕜'\ninst✝¹ : NormedAlgebra 𝕜 𝕜'\ninst✝ : IsRCLikeNormedField 𝕜\nf g : 𝕜 → 𝕜'\nhf : DifferentiableOn 𝕜 f ∅\nhg : DifferentiableOn 𝕜 g ∅\nhs2 : IsOpen[PseudoMetricSpace.toUniformSpace.to... | [
"case inl\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NontriviallyNormedField 𝕜'\ninst✝¹ : NormedAlgebra 𝕜 𝕜'\ninst✝ : IsRCLikeNormedField 𝕜\nf g : 𝕜 → 𝕜'\nhf : DifferentiableOn 𝕜 f ∅\nhg : DifferentiableOn 𝕜 g ∅\nhs2 : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 38
} | {
"line": 350,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf f' : ℝ → E\nC : ℝ\nhf : ∀ x ∈ Icc 0 1, HasDerivWithinAt f (f' x) (Icc 0 1) x\nbound : ∀ x ∈ Ico 0 1, ‖f' x‖ ≤ C\n⊢ ‖f 1 - f 0‖ ≤ C",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf f' : ℝ → E\nC : ℝ\nhf : ∀ x ∈ Icc 0 1, HasDerivWithinAt f (f' x) (Icc 0 1) x\nbound : ∀ x ∈ Ico 0 1, ‖f' x‖ ≤ C\n⊢ ‖f 1 - f 0‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 38
} | {
"line": 358,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nC : ℝ\nhf : DifferentiableOn ℝ f (Icc 0 1)\nbound : ∀ x ∈ Ico 0 1, ‖derivWithin f (Icc 0 1) x‖ ≤ C\n⊢ ‖f 1 - f 0‖ ≤ C",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nC : ℝ\nhf : DifferentiableOn ℝ f (Icc 0 1)\nbound : ∀ x ∈ Ico 0 1, ‖derivWithin f (Icc 0 1) x‖ ≤ C\n⊢ ‖f 1 - f 0‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 364,
"column": 2
} | {
"line": 364,
"column": 60
} | {
"line": 364,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhcont : ContinuousOn f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, HasDerivWithinAt f 0 (Ici x) x\nthis : ∀ x ∈ Icc a b, ‖f x - f a‖ ≤ 0 * (x - a)\n⊢ ∀ x ∈ Icc a b, f x = f a",
"ppTerm": "?m.78",
"assigned": false,... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhcont : ContinuousOn f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, HasDerivWithinAt f 0 (Ici x) x\nthis : ∀ x ∈ Icc a b, ‖f x - f a‖ ≤ 0 * (x - a)\n⊢ ∀ x ∈ Icc a b, f x = f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 39
} | {
"line": 369,
"column": 40
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhdiff : DifferentiableOn ℝ f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, derivWithin f (Icc a b) x = 0\n⊢ ∀ x ∈ Ico a b, ‖derivWithin f (Icc a b) x‖ ≤ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhdiff : DifferentiableOn ℝ f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, derivWithin f (Icc a b) x = 0\n⊢ ∀ x ∈ Ico a b, derivWithin f (Icc a b) x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 370,
"column": 2
} | {
"line": 370,
"column": 60
} | {
"line": 370,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhdiff : DifferentiableOn ℝ f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, derivWithin f (Icc a b) x = 0\nH : ∀ x ∈ Ico a b, ‖derivWithin f (Icc a b) x‖ ≤ 0\n⊢ ∀ x ∈ Icc a b, f x = f a",
"ppTerm": "?m.62",
"assigned"... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nhdiff : DifferentiableOn ℝ f (Icc a b)\nhderiv : ∀ x ∈ Ico a b, derivWithin f (Icc a b) x = 0\nH : ∀ x ∈ Ico a b, ‖derivWithin f (Icc a b) x‖ ≤ 0\n⊢ ∀ x ∈ Icc a b, f x = f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 436,
"column": 4
} | {
"line": 436,
"column": 15
} | {
"line": 436,
"column": 16
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nC : ℝ\ns : Set E\nx y : E\nf' : E → E ... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nC : ℝ\ns : Set E\nx y : E\nf' : E → E →L[𝕜] G\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 440,
"column": 2
} | {
"line": 440,
"column": 17
} | {
"line": 440,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nC : ℝ\ns : Set E\nx y : E\nf' : E → E ... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nC : ℝ\ns : Set E\nx y : E\nf' : E → E →L[𝕜] G\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 562,
"column": 2
} | {
"line": 562,
"column": 77
} | {
"line": 563,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\ns : Set E\nx y : E\nhs : Convex ℝ s\nh... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\ns : Set E\nx y : E\nhs : Convex ℝ s\nhf : Differen... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 613,
"column": 49
} | {
"line": 613,
"column": 74
} | {
"line": 613,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\ns : Set E\nhs : IsOpen[PseudoMetricSpa... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniform... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 640,
"column": 2
} | {
"line": 640,
"column": 13
} | {
"line": 640,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → G\ns : Set E\nx : E\nhs : IsOpen[Pseudo... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\n𝕜 : Type u_3\nG : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → G\ns : Set E\nx : E\nhs : IsOpen[PseudoMetricSpace.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 650,
"column": 37
} | {
"line": 650,
"column": 48
} | {
"line": 650,
"column": 49
} | [
{
"pp": "𝕜 : Type u_3\nG : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nE : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : E → G\nhf : Differentiable 𝕜 f\nhg : Differentiable 𝕜 g\nhf' : ∀ (x... | [
"𝕜 : Type u_3\nG : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nE : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : E → G\nhf : Differentiable 𝕜 f\nhg : Differentiable 𝕜 g\nhf' : ∀ (x : E), fderi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.MeanValue | {
"line": 681,
"column": 4
} | {
"line": 681,
"column": 15
} | {
"line": 681,
"column": 16
} | [
{
"pp": "case refine_2\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf f' : ℝ → E\nx₀ : ℝ\nn : ℕ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nhff' : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\nhf' : f' =o[𝓝[s] x₀] fun x ↦ (x - x₀) ^ n\nh : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in 𝓝[s] x₀, ‖f x - f... | [
"case refine_2\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf f' : ℝ → E\nx₀ : ℝ\nn : ℕ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nhff' : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\nhf' : f' =o[𝓝[s] x₀] fun x ↦ (x - x₀) ^ n\nh : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in 𝓝[s] x₀, ‖f x - f x₀‖ ≤ c * ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 333,
"column": 4
} | {
"line": 333,
"column": 76
} | {
"line": 334,
"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\ns : Set E\nf : E → F\nx : E\nn : ℕ∞ω... | [
"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\ns : Set E\nf : E → F\nx : E\nn : ℕ∞ω\ne : F ≃L[�... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Comp | {
"line": 107,
"column": 8
} | {
"line": 107,
"column": 19
} | {
"line": 107,
"column": 20
} | [
{
"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∞ω\ns : Set E\nt : Set F\ng : F... | [
"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∞ω\ns : Set E\nt : Set F\ng : F → G\nf : E ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 491,
"column": 4
} | {
"line": 491,
"column": 52
} | {
"line": 491,
"column": 53
} | [
{
"pp": "case mp\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\ns : Set E\nf : E → F\nx : E... | [
"case mp\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\ns : Set E\nf : E → F\nx : E\nn : ℕ∞ω\ne... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 507,
"column": 15
} | {
"line": 507,
"column": 46
} | {
"line": 507,
"column": 47
} | [
{
"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\ns : Set E\nf : E → F\nn : ℕ∞ω\ne : G... | [
"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\ns : Set E\nf : E → F\nn : ℕ∞ω\ne : G ≃L[𝕜] E\nH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 602,
"column": 4
} | {
"line": 602,
"column": 67
} | {
"line": 603,
"column": 2
} | [
{
"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\ns t : Set E\nf : E → F\nn : ℕ∞ω\nhf : ContDiffOn 𝕜 n f s\nhf' : ContDiffOn 𝕜 n f t\nhs : IsOpen[... | [] | exact (hf x hx).contDiffAt (hs.mem_nhds hx) |>.contDiffWithinAt | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 602,
"column": 4
} | {
"line": 602,
"column": 67
} | {
"line": 603,
"column": 2
} | [
{
"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\ns t : Set E\nf : E → F\nn : ℕ∞ω\nhf : ContDiffOn 𝕜 n f s\nhf' : ContDiffOn 𝕜 n f t\nhs : IsOpen[... | [] | exact (hf x hx).contDiffAt (hs.mem_nhds hx) |>.contDiffWithinAt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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