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Step * of Lemma member_upto

∀n,i:ℕ.  ((i ∈ upto(n)) ⇐⇒ i < n)
BY
{ (((Auto
     THEN (All (Unfold `l_member`))
     THEN ExRepD
     THEN Try (((InstConcl [⌜i⌝])⋅ THENA Auto))
     THEN (All (RWO "length_upto")))
    THENA Auto
    )
   THEN Try (((InstLemma `select_upto` [⌜n⌝; ⌜i⌝])⋅ THEN Complete (Auto)))
   THEN Try (((InstLemma `select_upto` [⌜n⌝; ⌜i@0⌝])⋅ THEN Complete (Auto)))) }

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Latex:

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Latex:
\mforall{}n,i:\mBbbN{}.    ((i  \mmember{}  upto(n))  \mLeftarrow{}{}\mRightarrow{}  i  <  n)


By

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Latex:
(((Auto
      THEN  (All  (Unfold  `l\_member`))
      THEN  ExRepD
      THEN  Try  (((InstConcl  [\mkleeneopen{}i\mkleeneclose{}])\mcdot{}  THENA  Auto))
      THEN  (All  (RWO  "length\_upto")))
    THENA  Auto
    )
  THEN  Try  (((InstLemma  `select\_upto`  [\mkleeneopen{}n\mkleeneclose{};  \mkleeneopen{}i\mkleeneclose{}])\mcdot{}  THEN  Complete  (Auto)))
  THEN  Try  (((InstLemma  `select\_upto`  [\mkleeneopen{}n\mkleeneclose{};  \mkleeneopen{}i@0\mkleeneclose{}])\mcdot{}  THEN  Complete  (Auto))))

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