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

full_name: HasStrictFDerivAt.restrictScalars
code: @[fun_prop]
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
    HasStrictFDerivAt f (f'.restrictScalars 𝕜) x 
goal: HasStrictFDerivAt f (ContinuousLinearMap.restrictScalars 𝕜 f') x

full_name: HasFDerivAtFilter.restrictScalars
code: theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
    HasFDerivAtFilter f (f'.restrictScalars 𝕜) x L 
goal: HasFDerivAtFilter f (ContinuousLinearMap.restrictScalars 𝕜 f') x L

full_name: HasFDerivAt.restrictScalars
code: @[fun_prop]
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
    HasFDerivAt f (f'.restrictScalars 𝕜) x 
goal: HasFDerivAt f (ContinuousLinearMap.restrictScalars 𝕜 f') x

full_name: HasFDerivWithinAt.restrictScalars
code: @[fun_prop]
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
    HasFDerivWithinAt f (f'.restrictScalars 𝕜) s x 
goal: HasFDerivWithinAt f (ContinuousLinearMap.restrictScalars 𝕜 f') s x

full_name: DifferentiableAt.restrictScalars
code: @[fun_prop]
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt 𝕜' f x) : DifferentiableAt 𝕜 f x 
goal: DifferentiableAt 𝕜 f x

full_name: DifferentiableWithinAt.restrictScalars
code: @[fun_prop]
theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt 𝕜' f s x) :
    DifferentiableWithinAt 𝕜 f s x 
goal: DifferentiableWithinAt 𝕜 f s x

full_name: DifferentiableOn.restrictScalars
code: @[fun_prop]
theorem DifferentiableOn.restrictScalars (h : DifferentiableOn 𝕜' f s) : DifferentiableOn 𝕜 f s 
goal: DifferentiableOn 𝕜 f s

full_name: Differentiable.restrictScalars
code: @[fun_prop]
theorem Differentiable.restrictScalars (h : Differentiable 𝕜' f) : Differentiable 𝕜 f 
goal: Differentiable 𝕜 f

full_name: HasFDerivWithinAt.of_restrictScalars
code: @[fun_prop]
theorem HasFDerivWithinAt.of_restrictScalars {g' : E →L[𝕜] F} (h : HasFDerivWithinAt f g' s x)
    (H : f'.restrictScalars 𝕜 = g') : HasFDerivWithinAt f f' s x 
goal: HasFDerivWithinAt f f' s x

full_name: hasFDerivAt_of_restrictScalars
code: @[fun_prop]
theorem hasFDerivAt_of_restrictScalars {g' : E →L[𝕜] F} (h : HasFDerivAt f g' x)
    (H : f'.restrictScalars 𝕜 = g') : HasFDerivAt f f' x 
goal: HasFDerivAt f f' x

full_name: DifferentiableAt.fderiv_restrictScalars
code: theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt 𝕜' f x) :
    fderiv 𝕜 f x = (fderiv 𝕜' f x).restrictScalars 𝕜 
goal: fderiv 𝕜 f x = ContinuousLinearMap.restrictScalars 𝕜 (fderiv 𝕜' f x)

full_name: differentiableWithinAt_iff_restrictScalars
code: theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt 𝕜 f s x)
    (hs : UniqueDiffWithinAt 𝕜 s x) : DifferentiableWithinAt 𝕜' f s x ↔
      ∃ g' : E →L[𝕜'] F, g'.restrictScalars 𝕜 = fderivWithin 𝕜 f s x 
goal: DifferentiableWithinAt 𝕜' f s x ↔ ∃ g', ContinuousLinearMap.restrictScalars 𝕜 g' = fderivWithin 𝕜 f s x

full_name: differentiableAt_iff_restrictScalars
code: theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt 𝕜 f x) :
    DifferentiableAt 𝕜' f x ↔ ∃ g' : E →L[𝕜'] F, g'.restrictScalars 𝕜 = fderiv 𝕜 f x 
goal: DifferentiableAt 𝕜' f x ↔ ∃ g', ContinuousLinearMap.restrictScalars 𝕜 g' = fderiv 𝕜 f x