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Step * of Lemma fs-in-subtype-basic

∀[K:RngSig]. ∀[S,T:Type].
  ∀[f:formal-sum(K;S)]. ↓∃b:basic-formal-sum(K;T). (f = b ∈ formal-sum(K;S)) supposing fs-in-subtype(K;S;T;f) 
  supposing strong-subtype(T;S)
BY
{ ((Intros THEN Unhide)
   THEN RepUR ``fs-in-subtype fs-predicate`` -1
   THEN SqExRepD
   THEN RepUR ``bfs-predicate`` -1
   THEN (Assert b ∈ basic-formal-sum(K;T) BY
               (All (Unfold `basic-formal-sum`)
                THEN (InstLemma `bag-in-subtype` [⌜|K| × T⌝;⌜|K| × S⌝]⋅ THENA Auto)
                THEN BHyp -1
                THEN Auto))
   THEN D 0
   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)].  \mdownarrow{}\mexists{}b:basic-formal-sum(K;T).  (f  =  b)  supposing  fs-in-subtype(K;S;T;f) 
    supposing  strong-subtype(T;S)


By

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Latex:
((Intros  THEN  Unhide)
  THEN  RepUR  ``fs-in-subtype  fs-predicate``  -1
  THEN  SqExRepD
  THEN  RepUR  ``bfs-predicate``  -1
  THEN  (Assert  b  \mmember{}  basic-formal-sum(K;T)  BY
                          (All  (Unfold  `basic-formal-sum`)
                            THEN  (InstLemma  `bag-in-subtype`  [\mkleeneopen{}|K|  \mtimes{}  T\mkleeneclose{};\mkleeneopen{}|K|  \mtimes{}  S\mkleeneclose{}]\mcdot{}  THENA  Auto)
                            THEN  BHyp  -1
                            THEN  Auto))
  THEN  D  0
  THEN  Auto)

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