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Step * of Lemma sq_stable__single-valued-iterated-classrel

∀[Info,A,S:Type].
  ∀init:Id ─→ bag(S). ∀f:A ─→ S ─→ S. ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:S.
    (single-valued-classrel(es;X;A)
    ⇒ single-valued-bag(init loc(e);S)
    ⇒ SqStable(iterated-classrel(es;S;A;f;init;X;e;v)))
BY
{ ((UnivCD THENA Auto)
   THEN Unfold `sq_stable` 0
   THEN Auto
   THEN (InstLemma `decidable__exists-iterated-classrel` [⌈Info⌉;⌈A⌉;⌈S⌉;⌈init⌉;⌈f⌉;⌈X⌉;⌈es⌉;⌈e⌉]⋅ THENA Auto)
   THEN D (-1)
   THEN Try (Complete ((Assert ⌈False⌉⋅ THEN Auto)))
   THEN ExRepD
   THEN (Assert ⌈v1 = v ∈ S⌉⋅ THENM Auto)
   THEN SquashExRepD
   THEN InstLemma `iterated-classrel-single-val` [⌈Info⌉;⌈A⌉;⌈S⌉;⌈init⌉;⌈f⌉;⌈X⌉;⌈es⌉;⌈e⌉;⌈v1⌉;⌈v⌉]⋅
   THEN Auto) }

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Latex:


\mforall{}[Info,A,S:Type].
    \mforall{}init:Id  {}\mrightarrow{}  bag(S).  \mforall{}f:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S.  \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.  \mforall{}v:S.
        (single-valued-classrel(es;X;A)
        {}\mRightarrow{}  single-valued-bag(init  loc(e);S)
        {}\mRightarrow{}  SqStable(iterated-classrel(es;S;A;f;init;X;e;v)))


By

((UnivCD  THENA  Auto)
  THEN  Unfold  `sq\_stable`  0
  THEN  Auto
  THEN  (InstLemma  `decidable\_\_exists-iterated-classrel`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  THEN  D  (-1)
  THEN  Try  (Complete  ((Assert  \mkleeneopen{}False\mkleeneclose{}\mcdot{}  THEN  Auto)))
  THEN  ExRepD
  THEN  (Assert  \mkleeneopen{}v1  =  v\mkleeneclose{}\mcdot{}  THENM  Auto)
  THEN  SquashExRepD
  THEN  InstLemma  `iterated-classrel-single-val`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}v1\mkleeneclose{};\mkleeneopen{}v\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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