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Step * of Lemma derivative-rexp-function

∀I:Interval. ∀f,f':I ⟶ℝ.
  (iproper(I)
  ⇒ (∀x,y:{x:ℝ| x ∈ I} .  ((x = y) ⇒ (f'[x] = f'[y])))
  ⇒ d(f[x])/dx = λx.f'[x] on I
  ⇒ d(e^f[x])/dx = λx.e^f[x] * f'[x] on I)
BY
{ (InstLemma `simple-chain-rule` []
   THEN RepeatFor 3 (ParallelLast')
   THEN Auto
   THEN InstHyp [⌜λ2x.e^x⌝;⌜λ2x.e^x⌝] (-4)⋅
   THEN Auto) }

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Latex:

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


By

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Latex:
(InstLemma  `simple-chain-rule`  []
  THEN  RepeatFor  3  (ParallelLast')
  THEN  Auto
  THEN  InstHyp  [\mkleeneopen{}\mlambda{}\msubtwo{}x.e\^{}x\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.e\^{}x\mkleeneclose{}]  (-4)\mcdot{}
  THEN  Auto)

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