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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
{ xxx(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)xxx }

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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:
xxx(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)xxx

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