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Step * 1 of Lemma l-all-property

.....assertion..... 
∀[T:Type]. ∀[P:T ⟶ ℙ'].  ∀L:T List. (∀x∈L.P[x] ⇐⇒ (∀x∈L.P[x]))
BY
{ ((InductionOnList THENA Auto)⋅
   THEN Unfold `l-all` 0
   THEN Reduce 0
   THEN Try (Fold `l-all` 0)
   THEN RWW "l_all_cons" 0⋅
   THEN Auto) }

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Latex:

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Latex:
.....assertion..... 
\mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}'].    \mforall{}L:T  List.  (\mforall{}x\mmember{}L.P[x]  \mLeftarrow{}{}\mRightarrow{}  (\mforall{}x\mmember{}L.P[x]))


By

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Latex:
((InductionOnList  THENA  Auto)\mcdot{}
  THEN  Unfold  `l-all`  0
  THEN  Reduce  0
  THEN  Try  (Fold  `l-all`  0)
  THEN  RWW  "l\_all\_cons"  0\mcdot{}
  THEN  Auto)

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