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Step * 2 2 of Lemma rec-value-ext

.....set predicate..... 
1. x : atomic-values() ⋃ (rec-value() × rec-value()) ⋃ (rec-value() + rec-value())@i
⊢ (co-value-height(x))↓
BY
{ (Repeat (D_b_union (-1))
   THEN D -1
   THEN RecUnfold `co-value-height` 0
   THEN Reduce 0
   THEN Fold `rec-value-height` 0
   THEN Auto) }

1
1. a1 : Value()@i
2. ↑is-atomic(a1)@i
⊢ (if a1 is a pair then let a,b = a1 
                        in 1 + rec-value-height(a) + rec-value-height(b) otherwise if a1 is inl then 1
                                                                                   + rec-value-height(outl(a1))
                                                                                   else if a1 is inr then 1
                                                                                        + rec-value-height(outr(a1))
                                                                                        else 0)↓

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Latex:

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Latex:
.....set  predicate..... 
1.  x  :  atomic-values()  \mcup{}  (rec-value()  \mtimes{}  rec-value())  \mcup{}  (rec-value()  +  rec-value())@i
\mvdash{}  (co-value-height(x))\mdownarrow{}


By

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Latex:
(Repeat  (D\_b\_union  (-1))
  THEN  D  -1
  THEN  RecUnfold  `co-value-height`  0
  THEN  Reduce  0
  THEN  Fold  `rec-value-height`  0
  THEN  Auto)

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