File: Mathlib/Analysis/Calculus/FDeriv/Star.lean

full_name: HasStrictFDerivAt.star
code: @[fun_prop]
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
    HasStrictFDerivAt (fun x => star (f x)) (((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L f') x 
goal: HasStrictFDerivAt (fun x => star (f x)) ((↑(starL' 𝕜)).comp f') x

full_name: HasFDerivAtFilter.star
code: theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
    HasFDerivAtFilter (fun x => star (f x)) (((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L f') x L 
goal: HasFDerivAtFilter (fun x => star (f x)) ((↑(starL' 𝕜)).comp f') x L

full_name: HasFDerivWithinAt.star
code: @[fun_prop]
nonrec theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
    HasFDerivWithinAt (fun x => star (f x)) (((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L f') s x 
goal: HasFDerivWithinAt (fun x => star (f x)) ((↑(starL' 𝕜)).comp f') s x

full_name: HasFDerivAt.star
code: @[fun_prop]
nonrec theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
    HasFDerivAt (fun x => star (f x)) (((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L f') x 
goal: HasFDerivAt (fun x => star (f x)) ((↑(starL' 𝕜)).comp f') x

full_name: DifferentiableWithinAt.star
code: @[fun_prop]
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt 𝕜 f s x) :
    DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x 
goal: DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x

full_name: differentiableWithinAt_star_iff
code: @[simp]
theorem differentiableWithinAt_star_iff :
    DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x ↔ DifferentiableWithinAt 𝕜 f s x 
goal: DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x ↔ DifferentiableWithinAt 𝕜 f s x

full_name: DifferentiableAt.star
code: @[fun_prop]
theorem DifferentiableAt.star (h : DifferentiableAt 𝕜 f x) :
    DifferentiableAt 𝕜 (fun y => star (f y)) x 
goal: DifferentiableAt 𝕜 (fun y => star (f y)) x

full_name: differentiableAt_star_iff
code: @[simp]
theorem differentiableAt_star_iff :
    DifferentiableAt 𝕜 (fun y => star (f y)) x ↔ DifferentiableAt 𝕜 f x 
goal: DifferentiableAt 𝕜 (fun y => star (f y)) x ↔ DifferentiableAt 𝕜 f x

full_name: DifferentiableOn.star
code: @[fun_prop]
theorem DifferentiableOn.star (h : DifferentiableOn 𝕜 f s) :
    DifferentiableOn 𝕜 (fun y => star (f y)) s 
goal: DifferentiableOn 𝕜 (fun y => star (f y)) s

full_name: differentiableOn_star_iff
code: @[simp]
theorem differentiableOn_star_iff :
    DifferentiableOn 𝕜 (fun y => star (f y)) s ↔ DifferentiableOn 𝕜 f s 
goal: DifferentiableOn 𝕜 (fun y => star (f y)) s ↔ DifferentiableOn 𝕜 f s

full_name: Differentiable.star
code: @[fun_prop]
theorem Differentiable.star (h : Differentiable 𝕜 f) : Differentiable 𝕜 fun y => star (f y) 
goal: Differentiable 𝕜 fun y => star (f y)

full_name: differentiable_star_iff
code: @[simp]
theorem differentiable_star_iff : (Differentiable 𝕜 fun y => star (f y)) ↔ Differentiable 𝕜 f 
goal: (Differentiable 𝕜 fun y => star (f y)) ↔ Differentiable 𝕜 f

full_name: fderivWithin_star
code: theorem fderivWithin_star (hxs : UniqueDiffWithinAt 𝕜 s x) :
    fderivWithin 𝕜 (fun y => star (f y)) s x =
      ((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L fderivWithin 𝕜 f s x 
goal: fderivWithin 𝕜 (fun y => star (f y)) s x = (↑(starL' 𝕜)).comp (fderivWithin 𝕜 f s x)

full_name: fderiv_star
code: @[simp]
theorem fderiv_star :
    fderiv 𝕜 (fun y => star (f y)) x = ((starL' 𝕜 : F ≃L[𝕜] F) : F →L[𝕜] F) ∘L fderiv 𝕜 f x 
goal: fderiv 𝕜 (fun y => star (f y)) x = (↑(starL' 𝕜)).comp (fderiv 𝕜 f x)