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Step * of Lemma derivative-rexp-fun2

∀f,f':ℝ ⟶ ℝ.
  ((∀x,y:ℝ.  ((x = y) ⇒ (f'[x] = f'[y])))
  ⇒ d(f[x])/dx = λx.f'[x] on (-∞, ∞)
  ⇒ d(e^f[x])/dx = λx.e^f[x] * f'[x] on (-∞, ∞))
BY
{ (Auto THEN InstLemma `derivative-rexp-fun` [⌜(-∞, ∞)⌝;⌜f⌝;⌜f'⌝]⋅ THEN Auto) }

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Latex:

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Latex:
\mforall{}f,f':\mBbbR{}  {}\mrightarrow{}  \mBbbR{}.
    ((\mforall{}x,y:\mBbbR{}.    ((x  =  y)  {}\mRightarrow{}  (f'[x]  =  f'[y])))
    {}\mRightarrow{}  d(f[x])/dx  =  \mlambda{}x.f'[x]  on  (-\minfty{},  \minfty{})
    {}\mRightarrow{}  d(e\^{}f[x])/dx  =  \mlambda{}x.e\^{}f[x]  *  f'[x]  on  (-\minfty{},  \minfty{}))


By

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Latex:
(Auto  THEN  InstLemma  `derivative-rexp-fun`  [\mkleeneopen{}(-\minfty{},  \minfty{})\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}f'\mkleeneclose{}]\mcdot{}  THEN  Auto)

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