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Step * of Lemma reduce-fast-mapfilter1

∀[L,z,k,d,f,p:Top].
  (reduce(λx,a. case d[x;a] of inl() => z | inr() => a;k;fast-mapfilter(p;f;L)) ~ reduce(λx,a. if p x
                                                                                          then case d[f x;a]
                                                                                                of inl() =>
                                                                                                z
                                                                                                | inr() =>
                                                                                                a
                                                                                          else a
                                                                                          fi ;k;L))
BY
{ (RepUR ``fast-mapfilter so_apply`` 0
   THEN ListIndSq `L'
   THEN (RWO  "reduce-ifthenelse" 0 THENA Auto)
   THEN Reduce 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[L,z,k,d,f,p:Top].
    (reduce(\mlambda{}x,a.  case  d[x;a]  of  inl()  =>  z  |  inr()  =>  a;k;fast-mapfilter(p;f;L)) 
    \msim{}  reduce(\mlambda{}x,a.  if  p  x  then  case  d[f  x;a]  of  inl()  =>  z  |  inr()  =>  a  else  a  fi  ;k;L))


By

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Latex:
(RepUR  ``fast-mapfilter  so\_apply``  0
  THEN  ListIndSq  `L'
  THEN  (RWO    "reduce-ifthenelse"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  Auto)

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