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Step * 1 1 of Lemma rec-value-ext


1. x : co-value()@i
2. (co-value-height(x))↓@i
⊢ x ∈ atomic-values() ⋃ (rec-value() × rec-value()) ⋃ (rec-value() + rec-value())
BY
{ (SubsumeHyp ⌜atomic-values() ⋃ (co-value() × co-value()) ⋃ (co-value() + co-value())⌝ 1⋅
   THENA (InstLemma `co-value-ext` [] THEN Auto)
   ) }

1
1. x : atomic-values() ⋃ (co-value() × co-value()) ⋃ (co-value() + co-value())
2. (co-value-height(x))↓@i
⊢ x ∈ atomic-values() ⋃ (rec-value() × rec-value()) ⋃ (rec-value() + rec-value())

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Latex:

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Latex:

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


By

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Latex:
(SubsumeHyp  \mkleeneopen{}atomic-values()  \mcup{}  (co-value()  \mtimes{}  co-value())  \mcup{}  (co-value()  +  co-value())\mkleeneclose{}  1\mcdot{}
  THENA  (InstLemma  `co-value-ext`  []  THEN  Auto)
  )

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