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Step * 1 1 1 2 1 of Lemma rec-value-ext


1. a1 : co-value() × co-value()
2. (co-value-height(a1))↓@i
⊢ a1 ∈ atomic-values() ⋃ (rec-value() × rec-value()) ⋃ (rec-value() + rec-value())
BY
{ ((BUnionRight THEN Auto)
   THEN BUnionLeft
   THEN Auto
   THEN MemTypeCD
   THEN Auto
   THEN RecUnfold `co-value-height` (-1)
   THEN Reduce (-1)
   THEN HasValueD (-1)
   THEN Auto
   THEN Assert ⌜(co-value-height(a2) + co-value-height(a3))↓⌝⋅
   THEN Auto
   THEN HasValueD  (-1)
   THEN Auto) }

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Latex:

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Latex:

1.  a1  :  co-value()  \mtimes{}  co-value()
2.  (co-value-height(a1))\mdownarrow{}@i
\mvdash{}  a1  \mmember{}  atomic-values()  \mcup{}  (rec-value()  \mtimes{}  rec-value())  \mcup{}  (rec-value()  +  rec-value())


By

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Latex:
((BUnionRight  THEN  Auto)
  THEN  BUnionLeft
  THEN  Auto
  THEN  MemTypeCD
  THEN  Auto
  THEN  RecUnfold  `co-value-height`  (-1)
  THEN  Reduce  (-1)
  THEN  HasValueD  (-1)
  THEN  Auto
  THEN  Assert  \mkleeneopen{}(co-value-height(a2)  +  co-value-height(a3))\mdownarrow{}\mkleeneclose{}\mcdot{}
  THEN  Auto
  THEN  HasValueD    (-1)
  THEN  Auto)

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