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Step * of Lemma l_disjoint_cons

∀[T:Type]. ∀[a,b:T List]. ∀[x:T].  uiff(l_disjoint(T;a;[x / b]);(¬(x ∈ a)) ∧ l_disjoint(T;a;b))
BY
{ ((UnivCD THENA Auto)
   THEN (Subst ⌜[x / b] ~ [x] @ b⌝ 0⋅ THENA (Reduce 0 THEN Auto))
   THEN (RWO "l_disjoint_append" 0 THENA Auto)
   THEN (RWO "l_disjoint_singleton" 0 THENA Auto)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[a,b:T  List].  \mforall{}[x:T].    uiff(l\_disjoint(T;a;[x  /  b]);(\mneg{}(x  \mmember{}  a))  \mwedge{}  l\_disjoint(T;a;b))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (Subst  \mkleeneopen{}[x  /  b]  \msim{}  [x]  @  b\mkleeneclose{}  0\mcdot{}  THENA  (Reduce  0  THEN  Auto))
  THEN  (RWO  "l\_disjoint\_append"  0  THENA  Auto)
  THEN  (RWO  "l\_disjoint\_singleton"  0  THENA  Auto)
  THEN  Auto)

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