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Step * 2 1 1 of Lemma full-partition-non-dec

.....antecedent..... 
1. I : Interval
2. icompact(I)
3. p : partition(I)
4. sorted-by(λx,y. (x ≤ y);p @ [right-endpoint(I)])
5. z : ℝ
6. (z ∈ p)
⊢ z ∈ I
BY
{ ((InstLemma `partition-point-member` [⌜I⌝;⌜p⌝]⋅ THENM RWO "l_all_iff" (-1)) THEN Auto) }

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Latex:

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Latex:
.....antecedent..... 
1.  I  :  Interval
2.  icompact(I)
3.  p  :  partition(I)
4.  sorted-by(\mlambda{}x,y.  (x  \mleq{}  y);p  @  [right-endpoint(I)])
5.  z  :  \mBbbR{}
6.  (z  \mmember{}  p)
\mvdash{}  z  \mmember{}  I


By

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Latex:
((InstLemma  `partition-point-member`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{}]\mcdot{}  THENM  RWO  "l\_all\_iff"  (-1))  THEN  Auto)

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