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Step * 2 1 of Lemma adjacent-frs-points


1. p : ℝ List
2. ¬||p|| < 2
3. i : ℕ||p|| - 1
4. frs-non-dec(p)
⊢ (p[i + 1] - p[i]) ≤ rmaximum(0;||p|| - 2;i.p[i + 1] - p[i])
BY
{ (((InstLemma `rmaximum_ub` [⌜i⌝; ⌜0⌝; ⌜||p|| - 2⌝; ⌜λi.(p[i + 1] - p[i])⌝])⋅ THENA Auto)
   THEN (ReduceSOAps (-1))
   THEN Auto)⋅ }

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Latex:

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Latex:

1.  p  :  \mBbbR{}  List
2.  \mneg{}||p||  <  2
3.  i  :  \mBbbN{}||p||  -  1
4.  frs-non-dec(p)
\mvdash{}  (p[i  +  1]  -  p[i])  \mleq{}  rmaximum(0;||p||  -  2;i.p[i  +  1]  -  p[i])


By

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Latex:
(((InstLemma  `rmaximum\_ub`  [\mkleeneopen{}i\mkleeneclose{};  \mkleeneopen{}0\mkleeneclose{};  \mkleeneopen{}||p||  -  2\mkleeneclose{};  \mkleeneopen{}\mlambda{}i.(p[i  +  1]  -  p[i])\mkleeneclose{}])\mcdot{}  THENA  Auto)
  THEN  (ReduceSOAps  (-1))
  THEN  Auto)\mcdot{}

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