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Step * of Lemma map-simple-reduce

∀[f,d,c,as:Top].
  (map(f;reduce(λx,a. case d[x] of inl(u) => a | inr(v) => [c[x] / a];[];as)) ~ reduce(λx,a. case d[x]
                                                                                         of inl(u) =>
                                                                                         a
                                                                                         | inr(v) =>
                                                                                         [f c[x] / a];[];as))
BY
{ (ListIndSq `as' THEN Fold `ifthenelse` 0 THEN (RWO "map-ifthenelse" 0 THENA Auto) THEN Reduce 0 THEN Auto) }

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Latex:

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Latex:
\mforall{}[f,d,c,as:Top].
    (map(f;reduce(\mlambda{}x,a.  case  d[x]  of  inl(u)  =>  a  |  inr(v)  =>  [c[x]  /  a];[];as)) 
    \msim{}  reduce(\mlambda{}x,a.  case  d[x]  of  inl(u)  =>  a  |  inr(v)  =>  [f  c[x]  /  a];[];as))


By

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Latex:
(ListIndSq  `as'
  THEN  Fold  `ifthenelse`  0
  THEN  (RWO  "map-ifthenelse"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  Auto)

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