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Step * 1 of Lemma positive-lower-bound_wf


1. x : {x:ℝ| r0 < x} 
2. TERMOF{small-reciprocal-real-ext:o, 1:l} x ∈ ∃k:ℕ+. ((r1/r(k)) < x)
⊢ positive-lower-bound(x) ∈ {k:ℕ+| (r1/r(k)) < x} 
BY
{ (Assert positive-lower-bound(x) ~ fst((TERMOF{small-reciprocal-real-ext:o, 1:l} x)) BY
         (Unfold `positive-lower-bound` 0
          THEN RW (AddrC [2] (TagC (mk_tag_term 3))) 0
          THEN (CallByValueReduce 0 THENA Auto)
          THEN Reduce 0
          THEN Auto)) }

1
1. x : {x:ℝ| r0 < x} 
2. TERMOF{small-reciprocal-real-ext:o, 1:l} x ∈ ∃k:ℕ+. ((r1/r(k)) < x)
3. positive-lower-bound(x) ~ fst((TERMOF{small-reciprocal-real-ext:o, 1:l} x))
⊢ positive-lower-bound(x) ∈ {k:ℕ+| (r1/r(k)) < x} 

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Latex:

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Latex:

1.  x  :  \{x:\mBbbR{}|  r0  <  x\} 
2.  TERMOF\{small-reciprocal-real-ext:o,  1:l\}  x  \mmember{}  \mexists{}k:\mBbbN{}\msupplus{}.  ((r1/r(k))  <  x)
\mvdash{}  positive-lower-bound(x)  \mmember{}  \{k:\mBbbN{}\msupplus{}|  (r1/r(k))  <  x\} 


By

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Latex:
(Assert  positive-lower-bound(x)  \msim{}  fst((TERMOF\{small-reciprocal-real-ext:o,  1:l\}  x))  BY
              (Unfold  `positive-lower-bound`  0
                THEN  RW  (AddrC  [2]  (TagC  (mk\_tag\_term  3)))  0
                THEN  (CallByValueReduce  0  THENA  Auto)
                THEN  Reduce  0
                THEN  Auto))

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