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Step * of Lemma select-map

∀[f:Top]. ∀[L:Top List]. ∀[i:ℕ||L||].  (map(f;L)[i] ~ f L[i])
BY
{ (((InductionOnList THENM All Reduce) THEN Auto)
   THEN (RWO "select-cons select-nil" 0 THENM Try (SplitOnConclITE))
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[f:Top].  \mforall{}[L:Top  List].  \mforall{}[i:\mBbbN{}||L||].    (map(f;L)[i]  \msim{}  f  L[i])


By

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Latex:
(((InductionOnList  THENM  All  Reduce)  THEN  Auto)
  THEN  (RWO  "select-cons  select-nil"  0  THENM  Try  (SplitOnConclITE))
  THEN  Auto)

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