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Step * 2 of Lemma derivative-is-zero


1. I : Interval
2. iproper(I)
3. f : I ⟶ℝ
4. ∃c:ℝ. ∀x:{x:ℝ| x ∈ I} . (f[x] = c)
⊢ d(f[x])/dx = λx.r0 on I
BY
{ (ExRepD
   THEN InstLemma `derivative_functionality` [⌜I⌝;⌜λ2x.c⌝;⌜λ2x.f[x]⌝;⌜λ2x.r0⌝;⌜λ2x.r0⌝]⋅
   THEN Auto
   THEN RepUR ``rfun-eq r-ap so_lambda`` 0
   THEN Auto
   THEN Symmetry
   THEN Auto) }

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Latex:

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Latex:

1.  I  :  Interval
2.  iproper(I)
3.  f  :  I  {}\mrightarrow{}\mBbbR{}
4.  \mexists{}c:\mBbbR{}.  \mforall{}x:\{x:\mBbbR{}|  x  \mmember{}  I\}  .  (f[x]  =  c)
\mvdash{}  d(f[x])/dx  =  \mlambda{}x.r0  on  I


By

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Latex:
(ExRepD
  THEN  InstLemma  `derivative\_functionality`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.c\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.f[x]\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.r0\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.r0\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  RepUR  ``rfun-eq  r-ap  so\_lambda``  0
  THEN  Auto
  THEN  Symmetry
  THEN  Auto)

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