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Step * of Lemma i-member-finite

∀[I:Interval]. ∀[r:ℝ]. left-endpoint(I)≤r≤right-endpoint(I) supposing r ∈ I supposing i-finite(I)
BY
{ (Auto
   THEN RepeatFor 2 (D 1)
   THEN (All (RepUR ``i-closed i-finite i-member``) THEN Auto)
   THEN RepeatFor 2 ((D 2 THEN All Reduce THEN Auto))
   THEN D 1
   THEN All Reduce
   THEN RepUR ``left-endpoint right-endpoint endpoints rbetween`` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[I:Interval].  \mforall{}[r:\mBbbR{}].  left-endpoint(I)\mleq{}r\mleq{}right-endpoint(I)  supposing  r  \mmember{}  I  supposing  i-finite(I)


By

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Latex:
(Auto
  THEN  RepeatFor  2  (D  1)
  THEN  (All  (RepUR  ``i-closed  i-finite  i-member``)  THEN  Auto)
  THEN  RepeatFor  2  ((D  2  THEN  All  Reduce  THEN  Auto))
  THEN  D  1
  THEN  All  Reduce
  THEN  RepUR  ``left-endpoint  right-endpoint  endpoints  rbetween``  0
  THEN  Auto)

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