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Step * of Lemma partition-endpoints

∀[I:Interval]
  ∀[p:partition(I)]. ∀[x:ℝ].  full-partition(I;p)[0]≤x≤full-partition(I;p)[||full-partition(I;p)|| - 1] supposing x ∈ I 
  supposing icompact(I)
BY
{ (BasicUniformUnivCD Auto
   THEN RepUR ``full-partition`` 0
   THEN (RWO "length-append" 0 THENA Auto)
   THEN Reduce 0
   THEN (RWO "select_cons_tl" 0 THENA Auto')
   THEN (RWO "select_append_back" 0 THENA Auto')
   THEN RW IntNormC 0
   THEN Auto
   THEN (Reduce 0
         THEN Auto
         THEN Unfold `rbetween` 0
         THEN (Unhide THEN Auto THEN OnMaybeHyp 5 (\h. (FLemma `i-member-compact` [h]⋅ THEN Complete (Auto))))⋅)⋅) }

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Latex:

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Latex:
\mforall{}[I:Interval]
    \mforall{}[p:partition(I)].  \mforall{}[x:\mBbbR{}].
        full-partition(I;p)[0]\mleq{}x\mleq{}full-partition(I;p)[||full-partition(I;p)||  -  1]  supposing  x  \mmember{}  I 
    supposing  icompact(I)


By

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Latex:
(BasicUniformUnivCD  Auto
  THEN  RepUR  ``full-partition``  0
  THEN  (RWO  "length-append"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  (RWO  "select\_cons\_tl"  0  THENA  Auto')
  THEN  (RWO  "select\_append\_back"  0  THENA  Auto')
  THEN  RW  IntNormC  0
  THEN  Auto
  THEN  (Reduce  0
              THEN  Auto
              THEN  Unfold  `rbetween`  0
              THEN  (Unhide
                          THEN  Auto
                          THEN  OnMaybeHyp  5  (\mbackslash{}h.  (FLemma  `i-member-compact`  [h]\mcdot{}  THEN  Complete  (Auto))))\mcdot{})\mcdot{})

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