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Step * of Lemma bl-all_wf

∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  ((∀x∈L.P[x])_b ∈ 𝔹)
BY
{ (InductionOnList
   THEN Unfold `bl-all` 0
   THEN Reduce 0
   THEN Try (Fold `bl-all` 0)
   THEN Auto
   THEN Try (BackThruSomeHyp)
   THEN DSetVars
   THEN MemTypeCD
   THEN Auto
   THEN RWO "cons_member" 0
   THEN Auto
   THEN TrivialOr) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:\{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  \mBbbB{}].    ((\mforall{}x\mmember{}L.P[x])\_b  \mmember{}  \mBbbB{})


By

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Latex:
(InductionOnList
  THEN  Unfold  `bl-all`  0
  THEN  Reduce  0
  THEN  Try  (Fold  `bl-all`  0)
  THEN  Auto
  THEN  Try  (BackThruSomeHyp)
  THEN  DSetVars
  THEN  MemTypeCD
  THEN  Auto
  THEN  RWO  "cons\_member"  0
  THEN  Auto
  THEN  TrivialOr)

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