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Step * of Lemma fpf-dom_functionality

∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq1,eq2:EqDecider(A)]. ∀[f:a:A fp-> B[a]]. ∀[x:A].  x ∈ dom(f) = x ∈ dom(f)
BY
{ (Auto
   THEN Unfold `fpf-dom` 0
   THEN (D (-2))
   THEN Reduce 0
   THEN AutoBoolCase ⌜x ∈b d⌝⋅
   THEN AutoBoolCase ⌜x ∈b d⌝⋅
   THEN (All (RWO "assert-deq-member"))
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[eq1,eq2:EqDecider(A)].  \mforall{}[f:a:A  fp->  B[a]].  \mforall{}[x:A].
    x  \mmember{}  dom(f)  =  x  \mmember{}  dom(f)


By

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Latex:
(Auto
  THEN  Unfold  `fpf-dom`  0
  THEN  (D  (-2))
  THEN  Reduce  0
  THEN  AutoBoolCase  \mkleeneopen{}x  \mmember{}\msubb{}  d\mkleeneclose{}\mcdot{}
  THEN  AutoBoolCase  \mkleeneopen{}x  \mmember{}\msubb{}  d\mkleeneclose{}\mcdot{}
  THEN  (All  (RWO  "assert-deq-member"))
  THEN  Auto)

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