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Step * of Lemma fs-in-subtype_wf

∀[K:RngSig]. ∀[S,T:Type].  ∀[f:formal-sum(K;S)]. (fs-in-subtype(K;S;T;f) ∈ ℙ) supposing strong-subtype(T;S)
BY
{ (Intros
   THEN Unfold `fs-in-subtype` 0
   THEN MemCD
   THEN Try (Complete (Auto))
   THEN D -1
   THEN Reduce 0
   THEN (RWO "strong-subtype-iff-respects-equality" 4 THENA Auto)
   THEN InstLemma `equal-wf` [⌜S⌝;⌜S⌝;⌜T⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[K:RngSig].  \mforall{}[S,T:Type].
    \mforall{}[f:formal-sum(K;S)].  (fs-in-subtype(K;S;T;f)  \mmember{}  \mBbbP{})  supposing  strong-subtype(T;S)


By

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Latex:
(Intros
  THEN  Unfold  `fs-in-subtype`  0
  THEN  MemCD
  THEN  Try  (Complete  (Auto))
  THEN  D  -1
  THEN  Reduce  0
  THEN  (RWO  "strong-subtype-iff-respects-equality"  4  THENA  Auto)
  THEN  InstLemma  `equal-wf`  [\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}T\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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