---

Step * of Lemma member_append

∀[T:Type]. ∀x:T. ∀l1,l2:T List.  ((x ∈ l1 @ l2) ⇐⇒ (x ∈ l1) ∨ (x ∈ l2))
BY
{ (InductionOnList
   THEN Reduce 0
   THEN (RWW "nil_member cons_member -1" 0 THENA Auto)
   THEN Auto
   THEN SplitOrHyps
   THEN TrivialOr
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}x:T.  \mforall{}l1,l2:T  List.    ((x  \mmember{}  l1  @  l2)  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  l1)  \mvee{}  (x  \mmember{}  l2))


By

---

Latex:
(InductionOnList
  THEN  Reduce  0
  THEN  (RWW  "nil\_member  cons\_member  -1"  0  THENA  Auto)
  THEN  Auto
  THEN  SplitOrHyps
  THEN  TrivialOr
  THEN  Auto)

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