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Step * 2 of Lemma partition-point-member


1. I : Interval
2. icompact(I)
3. p : ℝ List
4. frs-non-dec(p)
5. i : ℕ||p||
6. (left-endpoint(I) ≤ p[0]) ∧ (last(p) ≤ right-endpoint(I))
⊢ p[i] ≤ right-endpoint(I)
BY
{ ((With ⌜i⌝ (D (-3))⋅ THENM InstHyp [⌜||p|| - 1⌝] (-1)⋅)
   THEN Auto
   THEN Fold `last` (-1)
   THEN Try ((RelRST THEN Auto))) }

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Latex:

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Latex:

1.  I  :  Interval
2.  icompact(I)
3.  p  :  \mBbbR{}  List
4.  frs-non-dec(p)
5.  i  :  \mBbbN{}||p||
6.  (left-endpoint(I)  \mleq{}  p[0])  \mwedge{}  (last(p)  \mleq{}  right-endpoint(I))
\mvdash{}  p[i]  \mleq{}  right-endpoint(I)


By

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Latex:
((With  \mkleeneopen{}i\mkleeneclose{}  (D  (-3))\mcdot{}  THENM  InstHyp  [\mkleeneopen{}||p||  -  1\mkleeneclose{}]  (-1)\mcdot{})
  THEN  Auto
  THEN  Fold  `last`  (-1)
  THEN  Try  ((RelRST  THEN  Auto)))

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