module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Analytic.Constructions | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 35
} | {
"line": 171,
"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\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f pf x r\nh... | [
"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\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f pf x r\nhg : HasFPowe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 35
} | {
"line": 176,
"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\nhf : HasFPowerSeriesWithinAt f pf s x... | [
"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\nhf : HasFPowerSeriesWithinAt f pf s x\nhg : HasFP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 180,
"column": 2
} | {
"line": 180,
"column": 35
} | {
"line": 180,
"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\nx : E\nhf : HasFPowerSeriesAt f pf x\nhg : HasFPowerSer... | [
"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\nx : E\nhf : HasFPowerSeriesAt f pf x\nhg : HasFPowerSeriesAt g pg x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 35
} | {
"line": 184,
"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\ns : Set E\nx : E\nhf : AnalyticWithinAt 𝕜 f s x\nhg : AnalyticWithinAt 𝕜 g s x\n⊢ AnalyticWit... | [
"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\ns : Set E\nx : E\nhf : AnalyticWithinAt 𝕜 f s x\nhg : AnalyticWithinAt 𝕜 g s x\n⊢ AnalyticWithinAt 𝕜 (f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 35
} | {
"line": 189,
"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\nx : E\nhf : AnalyticAt 𝕜 f x\nhg : AnalyticAt 𝕜 g x\n⊢ AnalyticAt 𝕜 (f - g) x",
"ppTerm"... | [
"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\nx : E\nhf : AnalyticAt 𝕜 f x\nhg : AnalyticAt 𝕜 g x\n⊢ AnalyticAt 𝕜 (f + -g) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 479,
"column": 4
} | {
"line": 479,
"column": 18
} | {
"line": 480,
"column": 4
} | [
{
"pp": "case inr\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nr : ℝ≥0∞\np : (i : ι) → Form... | [
"case inr\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nr : ℝ≥0∞\np : (i : ι) → FormalMultilinea... | simp only [pi] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.Constructions | {
"line": 529,
"column": 2
} | {
"line": 529,
"column": 52
} | {
"line": 531,
"column": 0
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\ne : E\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nf : (i : ι) → E → Fm i\ns : Set... | [] | exact ⟨r, HasFPowerSeriesWithinOnBall.pi hr r_pos⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Analytic.Constructions | {
"line": 663,
"column": 4
} | {
"line": 663,
"column": 32
} | {
"line": 664,
"column": 2
} | [
{
"pp": "case zero\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nA : Type u_7\ninst✝¹ : NormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nf : E → A\nz : E\ns : Set E\nhf : AnalyticWithinAt 𝕜 f s z\n⊢ AnalyticWithinAt 𝕜 1 s z",
"ppTerm"... | [] | apply analyticWithinAt_const | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Analytic.Constructions | {
"line": 693,
"column": 2
} | {
"line": 693,
"column": 34
} | {
"line": 693,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\ns : Set E\nn : ℤ\nhf : AnalyticWithinAt 𝕜 f s z\nhn : 0 ≤ n\n⊢ AnalyticWithinAt 𝕜 ... | [
"𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\ns : Set E\nn : ℤ\nhf : AnalyticWithinAt 𝕜 f s z\nhn : 0 ≤ n\n⊢ AnalyticWithinAt 𝕜 (f ^ n) s z"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 700,
"column": 2
} | {
"line": 700,
"column": 34
} | {
"line": 700,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\nn : ℤ\nhf : AnalyticAt 𝕜 f z\nhn : 0 ≤ n\n⊢ AnalyticAt 𝕜 (f ^ n) z",
"ppTerm":... | [
"𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\nn : ℤ\nhf : AnalyticAt 𝕜 f z\nhn : 0 ≤ n\n⊢ AnalyticAt 𝕜 (f ^ n) z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 708,
"column": 2
} | {
"line": 708,
"column": 34
} | {
"line": 708,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\ns : Set E\nn : ℤ\nhf : AnalyticOn 𝕜 f s\nhn : 0 ≤ n\n⊢ AnalyticOn 𝕜 (f ^ n) s",
"ppTe... | [
"𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\ns : Set E\nn : ℤ\nhf : AnalyticOn 𝕜 f s\nhn : 0 ≤ n\n⊢ AnalyticOn 𝕜 (f ^ n) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 903,
"column": 2
} | {
"line": 903,
"column": 42
} | {
"line": 904,
"column": 4
} | [
{
"pp": "𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝¹ : NormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nn : ℕ\n⊢ ‖alternatingGeometricSeries 𝕜 A n‖ ≤ max 1 ‖1‖",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"one_pow",
"AddGroup.toSubtractionMonoid",
... | [
"𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝¹ : NormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nn : ℕ\n⊢ ‖ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n A‖ ≤ 1 ∨ ‖ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n A‖ ≤ ‖1‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 912,
"column": 2
} | {
"line": 914,
"column": 9
} | {
"line": 914,
"column": 10
} | [
{
"pp": "𝕜 : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝² : NormedRing A\ninst✝¹ : NormedAlgebra 𝕜 A\ninst✝ : Nontrivial A\n⊢ 1 ≤ (alternatingGeometricSeries 𝕜 A).radius",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSemino... | [
"𝕜 : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝² : NormedRing A\ninst✝¹ : NormedAlgebra 𝕜 A\ninst✝ : Nontrivial A\n⊢ 1 ≤ (formalMultilinearSeries_geometric 𝕜 A).radius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 930,
"column": 4
} | {
"line": 930,
"column": 15
} | {
"line": 930,
"column": 16
} | [
{
"pp": "case convert_16\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝³ : NormedRing A\ninst✝² : NormedAlgebra 𝕜 A\ninst✝¹ : HasSummableGeomSeries A\ninst✝ : Nontrivial A\n⊢ HasFPowerSeriesOnBall (fun x ↦ (1 - x)⁻¹ʳ) (formalMultilinearSeries_geometric 𝕜 A) ((-ContinuousLinearMap.id ... | [
"case convert_16\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nA : Type u_7\ninst✝³ : NormedRing A\ninst✝² : NormedAlgebra 𝕜 A\ninst✝¹ : HasSummableGeomSeries A\ninst✝ : Nontrivial A\n⊢ HasFPowerSeriesOnBall (fun x ↦ (1 - x)⁻¹ʳ) (formalMultilinearSeries_geometric 𝕜 A) 0 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Bilinear | {
"line": 64,
"column": 8
} | {
"line": 64,
"column": 56
} | {
"line": 64,
"column": 57
} | [
{
"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\nb : E × F → G\nh : IsBoundedBilinear... | [
"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\nb : E × F → G\nh : IsBoundedBilinearMap 𝕜 b\np ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 104,
"column": 2
} | {
"line": 105,
"column": 9
} | {
"line": 105,
"column": 10
} | [
{
"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\niso : E ≃L[𝕜] F\nf : G → E\ns : Set... | [
"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\niso : E ≃L[𝕜] F\nf : G → E\ns : Set G\nx : G\nf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 39
} | {
"line": 168,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set 𝕜\nf : 𝕜 → F\nx : 𝕜\n⊢ fderivWithin 𝕜 (-f) s x = -fderivWithin 𝕜 f s x",
"ppTerm": "?m.56",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set 𝕜\nf : 𝕜 → F\nx : 𝕜\n⊢ fderivWithin 𝕜 (-f) s x = -fderivWithin 𝕜 f s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 324,
"column": 2
} | {
"line": 324,
"column": 29
} | {
"line": 324,
"column": 30
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ c + f x) f' L ↔ HasFDeri... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ c + f x) f' L ↔ HasFDerivAtFilter f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 29
} | {
"line": 331,
"column": 30
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nc : F\n⊢ HasStrictFDerivAt (fun x ↦ c + f x) f' x ↔ HasStrictFDerivAt f f... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nc : F\n⊢ HasStrictFDerivAt (fun x ↦ c + f x) f' x ↔ HasStrictFDerivAt f f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 386,
"column": 2
} | {
"line": 386,
"column": 29
} | {
"line": 386,
"column": 30
} | [
{
"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\nf : E → F\nx : E\ns : Set E\nc : F\n⊢ fderivWithin 𝕜 (fun y ↦ c + f y) s x = fderivWithin 𝕜 f s x",
"p... | [
"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\nf : E → F\nx : E\ns : Set E\nc : F\n⊢ fderivWithin 𝕜 (fun y ↦ c + f y) s x = fderivWithin 𝕜 f s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Alternating.Basic | {
"line": 641,
"column": 8
} | {
"line": 642,
"column": 15
} | {
"line": 642,
"column": 16
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\nι : Type u_4\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\ninst✝³ : TopologicalSpace N\ninst✝² : IsTopologicalAddGroup N\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι... | [
"R : Type u_1\nM : Type u_2\nN : Type u_3\nι : Type u_4\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\ninst✝³ : TopologicalSpace N\ninst✝² : IsTopologicalAddGroup N\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nf✝ f : Con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 536,
"column": 15
} | {
"line": 536,
"column": 41
} | {
"line": 536,
"column": 42
} | [
{
"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\nf : E → F\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (fun y ↦ -f y) s x\n⊢ DifferentiableWithinAt 𝕜 f... | [
"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\nf : E → F\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (fun y ↦ -f y) s x\n⊢ DifferentiableWithinAt 𝕜 f s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 541,
"column": 15
} | {
"line": 541,
"column": 41
} | {
"line": 541,
"column": 42
} | [
{
"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\nf : E → F\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (-f) s x\n⊢ DifferentiableWithinAt 𝕜 f s x",
... | [
"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\nf : E → F\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (-f) s x\n⊢ DifferentiableWithinAt 𝕜 f s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 550,
"column": 15
} | {
"line": 550,
"column": 41
} | {
"line": 550,
"column": 42
} | [
{
"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\nf : E → F\nx : E\nh : DifferentiableAt 𝕜 (fun y ↦ -f y) x\n⊢ DifferentiableAt 𝕜 f x",
"ppTerm": "?m.51... | [
"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\nf : E → F\nx : E\nh : DifferentiableAt 𝕜 (fun y ↦ -f y) x\n⊢ DifferentiableAt 𝕜 f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 554,
"column": 15
} | {
"line": 554,
"column": 41
} | {
"line": 554,
"column": 42
} | [
{
"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\nf : E → F\nx : E\nh : DifferentiableAt 𝕜 (-f) x\n⊢ DifferentiableAt 𝕜 f x",
"ppTerm": "?m.50",
"as... | [
"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\nf : E → F\nx : E\nh : DifferentiableAt 𝕜 (-f) x\n⊢ DifferentiableAt 𝕜 f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 563,
"column": 15
} | {
"line": 563,
"column": 41
} | {
"line": 563,
"column": 42
} | [
{
"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\nf : E → F\ns : Set E\nh : DifferentiableOn 𝕜 (fun y ↦ -f y) s\n⊢ DifferentiableOn 𝕜 f s",
"ppTerm": "?... | [
"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\nf : E → F\ns : Set E\nh : DifferentiableOn 𝕜 (fun y ↦ -f y) s\n⊢ DifferentiableOn 𝕜 f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 567,
"column": 15
} | {
"line": 567,
"column": 41
} | {
"line": 567,
"column": 42
} | [
{
"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\nf : E → F\ns : Set E\nh : DifferentiableOn 𝕜 (-f) s\n⊢ DifferentiableOn 𝕜 f s",
"ppTerm": "?m.50",
... | [
"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\nf : E → F\ns : Set E\nh : DifferentiableOn 𝕜 (-f) s\n⊢ DifferentiableOn 𝕜 f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 575,
"column": 15
} | {
"line": 575,
"column": 41
} | {
"line": 575,
"column": 42
} | [
{
"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\nf : E → F\nh : Differentiable 𝕜 fun y ↦ -f y\n⊢ Differentiable 𝕜 f",
"ppTerm": "?m.51",
"assigned"... | [
"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\nf : E → F\nh : Differentiable 𝕜 fun y ↦ -f y\n⊢ Differentiable 𝕜 f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 579,
"column": 15
} | {
"line": 579,
"column": 41
} | {
"line": 579,
"column": 42
} | [
{
"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\nf : E → F\nh : Differentiable 𝕜 (-f)\n⊢ Differentiable 𝕜 f",
"ppTerm": "?m.50",
"assigned": false,... | [
"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\nf : E → F\nh : Differentiable 𝕜 (-f)\n⊢ Differentiable 𝕜 f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 614,
"column": 2
} | {
"line": 614,
"column": 35
} | {
"line": 614,
"column": 36
} | [
{
"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\nf g : E → F\nf' g' : E →L[𝕜] F\nL : Filter (E × E)\nhf : HasFDerivAtFilter f f' L\nhg : HasFDerivAtFilter g... | [
"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\nf g : E → F\nf' g' : E →L[𝕜] F\nL : Filter (E × E)\nhf : HasFDerivAtFilter f f' L\nhg : HasFDerivAtFilter g g' L\n⊢ Has... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 645,
"column": 2
} | {
"line": 645,
"column": 41
} | {
"line": 645,
"column": 42
} | [
{
"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\nf g : E → F\nx : E\nhg : DifferentiableAt 𝕜 g x\nh : DifferentiableAt 𝕜 (f + g) x\n⊢ DifferentiableAt 𝕜 f... | [
"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\nf g : E → F\nx : E\nhg : DifferentiableAt 𝕜 g x\nh : DifferentiableAt 𝕜 (f + g) x\n⊢ DifferentiableAt 𝕜 f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 670,
"column": 2
} | {
"line": 670,
"column": 41
} | {
"line": 670,
"column": 42
} | [
{
"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\nf g : E → F\ns : Set E\nhg : DifferentiableOn 𝕜 g s\nh : DifferentiableOn 𝕜 (f + g) s\n⊢ DifferentiableOn ... | [
"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\nf g : E → F\ns : Set E\nhg : DifferentiableOn 𝕜 g s\nh : DifferentiableOn 𝕜 (f + g) s\n⊢ DifferentiableOn 𝕜 f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 695,
"column": 2
} | {
"line": 695,
"column": 41
} | {
"line": 695,
"column": 42
} | [
{
"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\nf g : E → F\nhg : Differentiable 𝕜 g\nh : Differentiable 𝕜 (f + g)\n⊢ Differentiable 𝕜 f",
"ppTerm": ... | [
"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\nf g : E → F\nhg : Differentiable 𝕜 g\nh : Differentiable 𝕜 (f + g)\n⊢ Differentiable 𝕜 f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | {
"line": 735,
"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\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | [] | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | {
"line": 735,
"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\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | [] | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | {
"line": 735,
"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\nf : E → F\nf' : E →L[𝕜] F\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | [] | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 874,
"column": 2
} | {
"line": 874,
"column": 31
} | {
"line": 874,
"column": 32
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\na : E\n⊢ HasFDerivWithinAt (fun x ↦ f (x + a)) f' s x ↔ HasFDe... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\na : E\n⊢ HasFDerivWithinAt (fun x ↦ f (x + a)) f' s x ↔ HasFDerivWithinAt ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 53
} | {
"line": 166,
"column": 54
} | [
{
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set... | [
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set F\nx : E\nH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 899,
"column": 2
} | {
"line": 899,
"column": 26
} | {
"line": 899,
"column": 27
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx a : E\n⊢ HasFDerivAt (fun x ↦ f (a + x)) f' x ↔ HasFDerivAt f f' (a + x)",
... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx a : E\n⊢ HasFDerivAt (fun x ↦ f (x + a)) f' x ↔ HasFDerivAt f f' (x + a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 907,
"column": 2
} | {
"line": 907,
"column": 26
} | {
"line": 907,
"column": 27
} | [
{
"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\nf : E → F\nx a : E\n⊢ fderiv 𝕜 (fun x ↦ f (a + x)) x = fderiv 𝕜 f (a + x)",
"ppTerm": "?m.55",
"as... | [
"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\nf : E → F\nx a : E\n⊢ fderiv 𝕜 (fun x ↦ f (x + a)) x = fderiv 𝕜 f (x + a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 911,
"column": 2
} | {
"line": 911,
"column": 30
} | {
"line": 911,
"column": 31
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\na : E\n⊢ HasFDerivWithinAt (fun x ↦ f (x - a)) f' s x ↔ HasFDe... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\na : E\n⊢ HasFDerivWithinAt (fun x ↦ f (x + -a)) f' s x ↔ HasFDerivWithinAt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 920,
"column": 2
} | {
"line": 920,
"column": 30
} | {
"line": 920,
"column": 31
} | [
{
"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\nf : E → F\nx : E\ns : Set E\na : E\n⊢ fderivWithin 𝕜 (fun x ↦ f (x - a)) s x = fderivWithin 𝕜 f (-a +ᵥ s) ... | [
"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\nf : E → F\nx : E\ns : Set E\na : E\n⊢ fderivWithin 𝕜 (fun x ↦ f (x + -a)) s x = fderivWithin 𝕜 f (-a +ᵥ s) (x + -a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 51
} | {
"line": 179,
"column": 52
} | [
{
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set... | [
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set F\nH : Diff... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 51
} | {
"line": 198,
"column": 52
} | [
{
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set... | [
"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\niso : E ≃L[𝕜] F\nf : F → G\ns : Set F\nx : E\nf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 327,
"column": 25
} | {
"line": 327,
"column": 36
} | {
"line": 327,
"column": 37
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx✝ : E\ns : Set E\nh : HasFDerivWithinAt f f' s x✝\nC : ℝ≥0\nhC : AntilipschitzW... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx✝ : E\ns : Set E\nh : HasFDerivWithinAt f f' s x✝\nC : ℝ≥0\nhC : AntilipschitzWith C ⇑f'\nx... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 42
} | {
"line": 332,
"column": 43
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\nh : HasFDerivWithinAt f f' s x\nhf' : ∃ C, ∀ (z : E), ‖z‖ ≤ C ... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\nh : HasFDerivWithinAt f f' s x\nhf' : ∃ C, ∀ (z : E), ‖z‖ ≤ C * ‖f' z‖\nA ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 353,
"column": 2
} | {
"line": 353,
"column": 40
} | {
"line": 353,
"column": 41
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ Tendsto f (... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ Tendsto f (𝓝[univ \\ {... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 40
} | {
"line": 357,
"column": 41
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nc : F\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ ∀ᶠ (... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nc : F\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ ∀ᶠ (z : E) in 𝓝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 40
} | {
"line": 361,
"column": 41
} | [
{
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\nt : Set F\nht... | [
"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\nf : E → F\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\nt : Set F\nht : ¬AccPt (f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 409,
"column": 4
} | {
"line": 409,
"column": 15
} | {
"line": 409,
"column": 16
} | [
{
"pp": "case hd₀\n𝕜 : 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\nf : E → F\ns : Set E\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivWithinAt f f' s x\ny : E\nhy : y ∈ tang... | [
"case hd₀\n𝕜 : 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\nf : E → F\ns : Set E\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivWithinAt f f' s x\ny : E\nhy : y ∈ tangentConeAt 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 460,
"column": 14
} | {
"line": 460,
"column": 30
} | {
"line": 460,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ns : Set E\nx : E\nG : Type u_4\ninst✝³ : GroupWithZero G\ninst✝² : DistribMulAction G E\ninst✝¹ : ContinuousConstSMul G E\ninst✝ : SMulCommClass G 𝕜 E\nc : G\nhc : c ≠ 0\nh : Uni... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ns : Set E\nx : E\nG : Type u_4\ninst✝³ : GroupWithZero G\ninst✝² : DistribMulAction G E\ninst✝¹ : ContinuousConstSMul G E\ninst✝ : SMulCommClass G 𝕜 E\nc : G\nhc : c ≠ 0\nh : UniqueDiffWithi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 471,
"column": 92
} | {
"line": 479,
"column": 86
} | {
"line": 481,
"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\nf : E → F\ns : Set E\nf' : E →L[𝕜] F\nx : E\nc : 𝕜\n⊢ HasFDerivWithinAt (fun x ↦ f (c • x)) (c • f') s x ↔... | [] | by
rcases eq_or_ne c 0 with rfl | hc
· simp [hasFDerivWithinAt_const, HasFDerivWithinAt.of_subsingleton (subsingleton_zero_smul_set _)]
· lift c to 𝕜ˣ using IsUnit.mk0 c hc
have A : f'.comp ((ContinuousLinearEquiv.smulLeft c : E ≃L[𝕜] E) : E →L[𝕜] E) = c • f' := by
ext; simp
rw [← Units.smul_def ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Normed.Module.Alternating.Basic | {
"line": 468,
"column": 88
} | {
"line": 482,
"column": 25
} | {
"line": 484,
"column": 0
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : ... | [] | by
intro dg v a b heq hne
trans ∑ i, f fun j ↦ Function.update (fun _ ↦ g) i dg j (v j)
· simp
· rw [← Finset.sum_add_sum_compl {a, b}, Finset.sum_pair hne, Finset.sum_eq_zero, add_zero]
· convert! f.map_add_swap _ hne with i
rcases eq_or_ne i a with rfl | hia
· simp [heq, hne, hne... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Normed.Module.Alternating.Basic | {
"line": 527,
"column": 39
} | {
"line": 527,
"column": 50
} | {
"line": 527,
"column": 51
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : ... | [
"𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : Fintype ι\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Alternating.Basic | {
"line": 527,
"column": 6
} | {
"line": 527,
"column": 61
} | {
"line": 527,
"column": 62
} | [
{
"pp": "case h1\n𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\n... | [
"case h1\n𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Alternating.Basic | {
"line": 583,
"column": 29
} | {
"line": 583,
"column": 40
} | {
"line": 583,
"column": 41
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : ... | [
"𝕜 : Type u\nn : ℕ\nE : Type wE\nF : Type wF\nG : Type wG\nι : Type v\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : Fintype ι\nι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Completion | {
"line": 130,
"column": 12
} | {
"line": 130,
"column": 85
} | {
"line": 130,
"column": 86
} | [
{
"pp": "α : Type u\ninst✝ : PseudoMetricSpace α\ns : Set (Completion α × Completion α)\nε : ℝ\nεpos : ε > 0\nhε : ∀ {a b : Completion α}, dist a b < ε → (a, b) ∈ s\nr : Set (ℝ × ℝ) := {p | dist p.1 p.2 < ε}\nthis✝ : r ∈ 𝓤 ℝ\nt1 : Set (Completion α × Completion α)\nht1 : t1 ∈ 𝓤 (Completion α)\nt2 : Set (Compl... | [
"α : Type u\ninst✝ : PseudoMetricSpace α\ns : Set (Completion α × Completion α)\nε : ℝ\nεpos : ε > 0\nhε : ∀ {a b : Completion α}, dist a b < ε → (a, b) ∈ s\nr : Set (ℝ × ℝ) := {p | dist p.1 p.2 < ε}\nthis✝ : r ∈ 𝓤 ℝ\nt1 : Set (Completion α × Completion α)\nht1 : t1 ∈ 𝓤 (Completion α)\nt2 : Set (Completion α × Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Completion | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 28
} | {
"line": 144,
"column": 29
} | [
{
"pp": "α : Type u\ninst✝ : PseudoMetricSpace α\n⊢ 𝓤 (Completion α) = ⨅ ε, ⨅ (_ : ε > 0), 𝓟 {p | dist p.1 p.2 < ε}",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"iInf",
"Real.instZero",
"Iff.of_eq",
"congrArg",
"Filter.instIn... | [
"α : Type u\ninst✝ : PseudoMetricSpace α\n⊢ 𝓤 (Completion α) = ⨅ ε, ⨅ (_ : 0 < ε), 𝓟 {p | dist p.1 p.2 < ε}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Completion | {
"line": 187,
"column": 6
} | {
"line": 187,
"column": 78
} | {
"line": 187,
"column": 79
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : MetricSpace β\ninst✝ : CompleteSpace β\nf : α → β\nK : ℝ≥0\nh : LipschitzWith K f\nx y : Completion α\n⊢ ∀ (a b : α), dist (Completion.extension f ↑a) (Completion.extension f ↑b) ≤ ↑K * dist ↑a ↑b",
"ppTerm": "?m.41",
"assigned": tr... | [
"α : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : MetricSpace β\ninst✝ : CompleteSpace β\nf : α → β\nK : ℝ≥0\nh : LipschitzWith K f\nx y : Completion α\n⊢ ∀ (a b : α), dist (f a) (f b) ≤ ↑K * dist a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Completion | {
"line": 81,
"column": 16
} | {
"line": 81,
"column": 54
} | {
"line": 81,
"column": 55
} | [
{
"pp": "case ih\n𝕜 : Type u_1\nE : Type u_2\nA : Type u_3\ninst✝ : SeminormedRing A\nx y : A\n⊢ ‖↑x * ↑y‖ ≤ ‖↑x‖ * ‖↑y‖",
"ppTerm": "?ih",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"UniformSpace.Completion.coe'",
"Real.instLE",
"Semigroup.toMul",
... | [
"case ih\n𝕜 : Type u_1\nE : Type u_2\nA : Type u_3\ninst✝ : SeminormedRing A\nx y : A\n⊢ ‖x * y‖ ≤ ‖x‖ * ‖y‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 212,
"column": 2
} | {
"line": 212,
"column": 13
} | {
"line": 212,
"column": 14
} | [
{
"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\ns : Set E\nf : E → F\nN : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nhN : ∞ ≤ N\n⊢ HasFTaylorSeriesUpToOn N f ... | [
"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\ns : Set E\nf : E → F\nN : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nhN : ∞ ≤ N\n⊢ HasFTaylorSeriesUpToOn N f p s ↔ ∀ (n :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 96,
"column": 2
} | {
"line": 98,
"column": 9
} | {
"line": 98,
"column": 10
} | [
{
"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\nh : HasFPowerSeriesAt f p x\n⊢ HasStrictFDerivAt f ((conti... | [
"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\nh : HasFPowerSeriesAt f p x\n⊢ (fun p_1 ↦ f p_1.1 - f p_1.2 - ((contin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 77
} | {
"line": 149,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\n⊢ HasStrictDerivAt f (deriv f x) x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedComm... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\n⊢ HasStrictFDerivAt f (fderiv 𝕜 f x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 191,
"column": 6
} | {
"line": 191,
"column": 17
} | {
"line": 191,
"column": 18
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : CompleteSpace F\nh... | [
"case inr\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : CompleteSpace F\nh : HasFPower... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 13
} | {
"line": 57,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\ns : Set 𝕜\nB : E →L[𝕜] F →L[𝕜] ... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\ns : Set 𝕜\nB : E →L[𝕜] F →L[𝕜] G\nu : 𝕜 → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 65,
"column": 6
} | {
"line": 65,
"column": 17
} | {
"line": 65,
"column": 18
} | [
{
"pp": "case pos\n𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\nB : E →L[𝕜] F →L[𝕜] G\... | [
"case pos\n𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\nB : E →L[𝕜] F →L[𝕜] G\nu : 𝕜 → E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 227,
"column": 41
} | {
"line": 227,
"column": 52
} | {
"line": 227,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ x ∈ Metric.eball 0 p... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ ‖x‖ₑ < p.radius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 235,
"column": 29
} | {
"line": 235,
"column": 40
} | {
"line": 235,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ x ∈ Metric.eball 0 p... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ ‖x‖ₑ < p.radius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 13
} | {
"line": 80,
"column": 4
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\nB : E →L[𝕜] F →L[𝕜] G\nu : 𝕜 → ... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : 𝕜\nB : E →L[𝕜] F →L[𝕜] G\nu : 𝕜 → E\nv : 𝕜 → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 13
} | {
"line": 108,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\ns : Set 𝕜\n𝕜' : Type u_2\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : NormedAlgebra 𝕜 𝕜'\ninst✝² : Module 𝕜' F\ninst✝¹ : IsBoundedSMul 𝕜' F\ninst✝ : IsScalarTo... | [
"𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\ns : Set 𝕜\n𝕜' : Type u_2\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : NormedAlgebra 𝕜 𝕜'\ninst✝² : Module 𝕜' F\ninst✝¹ : IsBoundedSMul 𝕜' F\ninst✝ : IsScalarTower 𝕜 𝕜' F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 13
} | {
"line": 119,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\n𝕜' : Type u_2\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : NormedAlgebra 𝕜 𝕜'\ninst✝² : Module 𝕜' F\ninst✝¹ : IsBoundedSMul 𝕜' F\ninst✝ : IsScalarTower 𝕜 𝕜' F... | [
"𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\n𝕜' : Type u_2\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : NormedAlgebra 𝕜 𝕜'\ninst✝² : Module 𝕜' F\ninst✝¹ : IsBoundedSMul 𝕜' F\ninst✝ : IsScalarTower 𝕜 𝕜' F\nc : 𝕜 → �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 13
} | {
"line": 181,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nR : Type u_2\ninst✝³ : Monoid R\ninst✝² : DistribMulAction R F\ninst✝¹ : SMulCommClass 𝕜 R F\ninst✝ : ContinuousConstSMul R F\nc : R\nhf : HasStrictDerivA... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nR : Type u_2\ninst✝³ : Monoid R\ninst✝² : DistribMulAction R F\ninst✝¹ : SMulCommClass 𝕜 R F\ninst✝ : ContinuousConstSMul R F\nc : R\nhf : HasStrictDerivAt f f' x\n⊢ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 186,
"column": 2
} | {
"line": 186,
"column": 13
} | {
"line": 186,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nL : Filter (𝕜 × 𝕜)\nR : Type u_2\ninst✝³ : Monoid R\ninst✝² : DistribMulAction R F\ninst✝¹ : SMulCommClass 𝕜 R F\ninst✝ : ContinuousConstSMul R F\nc : R\nhf : H... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nL : Filter (𝕜 × 𝕜)\nR : Type u_2\ninst✝³ : Monoid R\ninst✝² : DistribMulAction R F\ninst✝¹ : SMulCommClass 𝕜 R F\ninst✝ : ContinuousConstSMul R F\nc : R\nhf : HasDerivAtFil... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 24
} | {
"line": 265,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\n𝔸 : Type u_3\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nc d : 𝕜 → 𝔸\nc' d' : 𝔸\nhc : HasDerivWithinAt c c' s x\nhd : HasDerivWithinAt d d' s x\n⊢ HasDerivWithinAt (c * d) (c' * d x + c x * d') s x",
"ppTerm": "?m.4... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\n𝔸 : Type u_3\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nc d : 𝕜 → 𝔸\nc' d' : 𝔸\nhc : HasDerivWithinAt c c' s x\nhd : HasDerivWithinAt d d' s x\n⊢ HasDerivWithinAt (c * d) (c' * d x + c x * d') s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 24
} | {
"line": 276,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝔸 : Type u_3\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nc d : 𝕜 → 𝔸\nc' d' : 𝔸\nhc : HasStrictDerivAt c c' x\nhd : HasStrictDerivAt d d' x\n⊢ HasStrictDerivAt (c * d) (c' * d x + c x * d') x",
"ppTerm": "?m.48",
"assigned"... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝔸 : Type u_3\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nc d : 𝕜 → 𝔸\nc' d' : 𝔸\nhc : HasStrictDerivAt c c' x\nhd : HasStrictDerivAt d d' x\n⊢ HasStrictDerivAt (c * d) (c' * d x + c x * d') x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 28
} | {
"line": 311,
"column": 29
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx c : 𝕜\n⊢ HasDerivAt (fun x ↦ x * c) c x",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx c : 𝕜\n⊢ HasDerivAt (fun x ↦ x * c) c x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 346,
"column": 6
} | {
"line": 346,
"column": 49
} | {
"line": 346,
"column": 50
} | [
{
"pp": "case neg.inr\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nu : 𝕜 → 𝕜'\nv : 𝕜'\nhu : ¬DifferentiableAt 𝕜 u x\nhd : v ≠ 0\nH : DifferentiableAt 𝕜 (fun y ↦ u y * v) x\n⊢ DifferentiableAt 𝕜 u x",
"ppTerm":... | [
"case neg.inr\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nu : 𝕜 → 𝕜'\nv : 𝕜'\nhu : ¬DifferentiableAt 𝕜 u x\nhd : v ≠ 0\nH : DifferentiableAt 𝕜 (fun y ↦ u y * v) x\n⊢ DifferentiableAt 𝕜 u x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 28
} | {
"line": 363,
"column": 29
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx c : 𝕜\n⊢ HasDerivAt (fun y ↦ c * y) c x",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nx c : 𝕜\n⊢ HasDerivAt (fun y ↦ c * y) c x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 39
} | {
"line": 389,
"column": 40
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nv : 𝕜 → 𝕜'\nu : 𝕜'\n⊢ deriv (fun y ↦ u * v y) x = u * deriv v x",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.h... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nv : 𝕜 → 𝕜'\nu : 𝕜'\n⊢ derivWithin (fun y ↦ u * v y) univ x = u * derivWithin v univ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 13
} | {
"line": 413,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasDerivAt (f i) (f' i) x\n⊢ HasDerivAt (fun x ↦ ∏ i ∈ u, f i x) (∑ i ∈ ... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasDerivAt (f i) (f' i) x\n⊢ HasDerivAt (fun x ↦ ∏ i ∈ u, f i x) (∑ x_1 ∈ u, (∏ j ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 425,
"column": 2
} | {
"line": 425,
"column": 13
} | {
"line": 425,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasDerivWithinAt (f i) (f' i) s x\n⊢ HasDerivWithinAt (fun x... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasDerivWithinAt (f i) (f' i) s x\n⊢ HasDerivWithinAt (fun x ↦ ∏ i ∈ u, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 439,
"column": 2
} | {
"line": 439,
"column": 13
} | {
"line": 439,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasStrictDerivAt (f i) (f' i) x\n⊢ HasStrictDerivAt (fun x ↦ ∏ i ∈ u, f ... | [
"𝕜 : Type u\ninst✝³ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_2\ninst✝² : DecidableEq ι\n𝔸' : Type u_3\ninst✝¹ : NormedCommRing 𝔸'\ninst✝ : NormedAlgebra 𝕜 𝔸'\nu : Finset ι\nf : ι → 𝕜 → 𝔸'\nf' : ι → 𝔸'\nhf : ∀ i ∈ u, HasStrictDerivAt (f i) (f' i) x\n⊢ HasStrictDerivAt (fun x ↦ ∏ i ∈ u, f i x) (∑ x_1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 560,
"column": 2
} | {
"line": 560,
"column": 35
} | {
"line": 560,
"column": 36
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasDerivAt c c' x\nd : 𝕜'\n⊢ HasDerivAt (fun x ↦ c x / d) (c' / d) x",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants":... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasDerivAt c c' x\nd : 𝕜'\n⊢ HasDerivAt (fun x ↦ c x * d⁻¹) (c' * d⁻¹) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 564,
"column": 2
} | {
"line": 564,
"column": 35
} | {
"line": 564,
"column": 36
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasDerivWithinAt c c' s x\nd : 𝕜'\n⊢ HasDerivWithinAt (fun x ↦ c x / d) (c' / d) s x",
"ppTerm": "?m.32",
"assigned"... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\ns : Set 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasDerivWithinAt c c' s x\nd : 𝕜'\n⊢ HasDerivWithinAt (fun x ↦ c x * d⁻¹) (c' * d⁻¹) s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 568,
"column": 2
} | {
"line": 568,
"column": 35
} | {
"line": 568,
"column": 36
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasStrictDerivAt c c' x\nd : 𝕜'\n⊢ HasStrictDerivAt (fun x ↦ c x / d) (c' / d) x",
"ppTerm": "?m.32",
"assigned": true,
"use... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_2\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nc : 𝕜 → 𝕜'\nc' : 𝕜'\nhc : HasStrictDerivAt c c' x\nd : 𝕜'\n⊢ HasStrictDerivAt (fun x ↦ c x * d⁻¹) (c' * d⁻¹) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 610,
"column": 2
} | {
"line": 610,
"column": 24
} | {
"line": 610,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜]... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nd : 𝕜 →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 615,
"column": 2
} | {
"line": 615,
"column": 24
} | {
"line": 615,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nx : 𝕜\ns : Set 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nx : 𝕜\ns : Set 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 432,
"column": 2
} | {
"line": 432,
"column": 46
} | {
"line": 434,
"column": 0
} | [
{
"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\nf : OpenPartialHomeomorph E F\na : F\ni : E ≃L[𝕜] F\nh0 : a ∈ f.target\nh : AnalyticAt 𝕜 (↑f) (↑f.symm a)\nh' ... | [] | exact f.analyticAt_symm' (by simp [h0]) h h' | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 468,
"column": 17
} | {
"line": 468,
"column": 79
} | {
"line": 468,
"column": 80
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\ninst✝ : CompleteSpace F\nh : AnalyticOnNhd 𝕜 f s\nn : ℕ\nIH : AnalyticOnNhd 𝕜 (deriv^[n] f) s\n⊢ AnalyticOnNhd 𝕜 (deriv^[n + 1] f) s",
"ppT... | [
"case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\ninst✝ : CompleteSpace F\nh : AnalyticOnNhd 𝕜 f s\nn : ℕ\nIH : AnalyticOnNhd 𝕜 (deriv^[n] f) s\n⊢ AnalyticOnNhd 𝕜 (deriv (deriv^[n] f)) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 479,
"column": 17
} | {
"line": 479,
"column": 79
} | {
"line": 479,
"column": 80
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\ninst✝ : CompleteSpace F\nh : AnalyticAt 𝕜 f x\nn : ℕ\nIH : AnalyticAt 𝕜 (deriv^[n] f) x\n⊢ AnalyticAt 𝕜 (deriv^[n + 1] f) x",
"ppTerm": "?succ"... | [
"case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx : 𝕜\ninst✝ : CompleteSpace F\nh : AnalyticAt 𝕜 f x\nn : ℕ\nIH : AnalyticAt 𝕜 (deriv^[n] f) x\n⊢ AnalyticAt 𝕜 (deriv (deriv^[n] f)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 636,
"column": 2
} | {
"line": 636,
"column": 24
} | {
"line": 636,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasStrictDerivAt c c' x\nhu : HasStrictDe... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasStrictDerivAt c c' x\nhu : HasStrictDerivAt u u' x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 641,
"column": 2
} | {
"line": 641,
"column": 24
} | {
"line": 641,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\ns : Set 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasDerivWithinAt c c' s x\nhu... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\ns : Set 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasDerivWithinAt c c' s x\nhu : HasDerivW... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Mul | {
"line": 645,
"column": 2
} | {
"line": 645,
"column": 24
} | {
"line": 645,
"column": 25
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasDerivAt c c' x\nhu : HasDerivAt u u' x... | [
"𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nx : 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nc : 𝕜 → F →L[𝕜] G\nc' : F →L[𝕜] G\nu : 𝕜 → F\nu' : F\nhc : HasDerivAt c c' x\nhu : HasDerivAt u u' x\n⊢ HasDeriv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pow | {
"line": 40,
"column": 85
} | {
"line": 46,
"column": 30
} | {
"line": 48,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\nn : ℕ\n⊢ f x •> ∑ i ∈ Finset.range (n + 1), f x ^ ((n + 1).pred - i) •> f'... | [] | by
rw [Finset.sum_range_succ _ (n + 1), Finset.smul_sum]
simp only [Nat.pred_eq_sub_one, add_tsub_cancel_right, tsub_self, pow_zero, one_smul]
simp_rw [smul_comm (_ : 𝔸) (_ : 𝔸ᵐᵒᵖ), smul_smul, ← pow_succ']
congr! 5 with x hx
simp only [Finset.mem_range, Nat.lt_succ_iff] at hx
rw [tsub_add_eq_add_tsub hx] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.FDeriv.Pow | {
"line": 54,
"column": 12
} | {
"line": 54,
"column": 23
} | {
"line": 54,
"column": 24
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\nh : HasStrictFDerivAt f f' x\nn : ℕ\n⊢ HasStrictFDerivAt (f ^ 1) (∑ i ∈ Fi... | [
"𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\nh : HasStrictFDerivAt f f' x\nn : ℕ\n⊢ HasStrictFDerivAt f f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pow | {
"line": 71,
"column": 12
} | {
"line": 71,
"column": 23
} | {
"line": 71,
"column": 24
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\ns : Set E\nh : HasFDerivWithinAt f f' s x\nn : ℕ\n⊢ HasFDerivWithinAt (f ^... | [
"𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\ns : Set E\nh : HasFDerivWithinAt f f' s x\nn : ℕ\n⊢ HasFDerivWithinAt f f' s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pow | {
"line": 87,
"column": 12
} | {
"line": 87,
"column": 23
} | {
"line": 87,
"column": 24
} | [
{
"pp": "𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\nh : HasFDerivAt f f' x\nn : ℕ\n⊢ HasFDerivAt (f ^ 1) (∑ i ∈ Finset.range 1... | [
"𝕜 : Type u_1\n𝔸 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAlgebra 𝕜 𝔸\ninst✝ : NormedSpace 𝕜 E\nf : E → 𝔸\nf' : E →L[𝕜] 𝔸\nx : E\nh : HasFDerivAt f f' x\nn : ℕ\n⊢ HasFDerivAt f f' x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 578,
"column": 17
} | {
"line": 578,
"column": 79
} | {
"line": 578,
"column": 80
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nh : CPolynomialOn 𝕜 f s\nn : ℕ\nIH : CPolynomialOn 𝕜 (deriv^[n] f) s\n⊢ CPolynomialOn 𝕜 (deriv^[n + 1] f) s",
"ppTerm": "?succ",
"assign... | [
"case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nh : CPolynomialOn 𝕜 f s\nn : ℕ\nIH : CPolynomialOn 𝕜 (deriv^[n] f) s\n⊢ CPolynomialOn 𝕜 (deriv (deriv^[n] f)) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 675,
"column": 2
} | {
"line": 675,
"column": 26
} | {
"line": 675,
"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\ns : Set E\nf : E → F\nn : ℕ\na : E\n⊢ iteratedFDerivWithin 𝕜 n (fun z ↦ f (z + a)) s = fun x ↦ iteratedFDerivWi... | [
"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\ns : Set E\nf : E → F\nn : ℕ\na : E\n⊢ iteratedFDerivWithin 𝕜 n (fun z ↦ f (z + a)) s = fun x ↦ iteratedFDerivWithin 𝕜 n f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 687,
"column": 2
} | {
"line": 687,
"column": 30
} | {
"line": 687,
"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\ns : Set E\nf : E → F\nn : ℕ\na : E\n⊢ iteratedFDerivWithin 𝕜 n (fun z ↦ f (z - a)) s = fun x ↦ iteratedFDerivWi... | [
"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\ns : Set E\nf : E → F\nn : ℕ\na : E\n⊢ iteratedFDerivWithin 𝕜 n (fun z ↦ f (z + -a)) s = fun x ↦ iteratedFDerivWithin 𝕜 n f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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