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Step * of Lemma fset-all-filter

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[P:T ⟶ 𝔹]. ∀[s:fset(T)].  fset-all({x ∈ s | P[x]};x.P[x])
BY
{ (Auto
   THEN (InstLemma `fset-all-iff` [⌜T⌝;⌜eq⌝]⋅ THENA Auto)
   THEN (RWO "-1" 0 THENA Auto)
   THEN Thin (-1)
   THEN Auto
   THEN RWO "member-fset-filter" (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[s:fset(T)].    fset-all(\{x  \mmember{}  s  |  P[x]\};x.P[x])


By

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Latex:
(Auto
  THEN  (InstLemma  `fset-all-iff`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}eq\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (RWO  "-1"  0  THENA  Auto)
  THEN  Thin  (-1)
  THEN  Auto
  THEN  RWO  "member-fset-filter"  (-1)
  THEN  Auto)

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