---

Step * of Lemma no-member-sq-nil

∀[T:Type]. ∀[L:T List].  L ~ [] supposing ∀x:T. (¬(x ∈ L))
BY
{ (InductionOnList
   THEN Auto
   THEN AssertBY ⌜(u ∈ [u / v])⌝
      ((RWO "cons_member" 0 THENM OrLeft) THEN Auto)⋅
   THEN (InstHyp [⌜u⌝] 5)⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    L  \msim{}  []  supposing  \mforall{}x:T.  (\mneg{}(x  \mmember{}  L))


By

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Latex:
(InductionOnList
  THEN  Auto
  THEN  AssertBY  \mkleeneopen{}(u  \mmember{}  [u  /  v])\mkleeneclose{}
        ((RWO  "cons\_member"  0  THENM  OrLeft)  THEN  Auto)\mcdot{}
  THEN  (InstHyp  [\mkleeneopen{}u\mkleeneclose{}]  5)\mcdot{}
  THEN  Auto)

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