---

Step * of Lemma deq-member-append

∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[L1,L2:A List]. ∀[x:A].  (x ∈b L1 @ L2 ~ x ∈b L1 ∨bx ∈b L2)
BY
{ (Auto
   THEN BLemma `iff_imp_equal_bool`
   THEN Auto
   THEN All (RW assert_pushdownC)
   THEN Auto
   THEN All (RWO "member_append")
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[L1,L2:A  List].  \mforall{}[x:A].    (x  \mmember{}\msubb{}  L1  @  L2  \msim{}  x  \mmember{}\msubb{}  L1  \mvee{}\msubb{}x  \mmember{}\msubb{}  L2)


By

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Latex:
(Auto
  THEN  BLemma  `iff\_imp\_equal\_bool`
  THEN  Auto
  THEN  All  (RW  assert\_pushdownC)
  THEN  Auto
  THEN  All  (RWO  "member\_append")
  THEN  Auto)

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