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Step * of Lemma Memory-loc-class-invariant-sv

∀[Info,B,A:Type].
  ∀P:B ─→ ℙ. ∀f:Id ─→ A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
    (single-valued-classrel(es;X;A)
    ⇒ single-valued-bag(init loc(e);B)
    ⇒ (∀a:A. ∀e':E.  ((e' <loc e) ⇒ a ∈ X(e') ⇒ (∀s:B. (P[s] ⇒ P[f loc(e') a s]))))
    ⇒ (∀v:B. (v ↓∈ init loc(e) ⇒ P[v]))
    ⇒ v ∈ Memory-loc-class(f;init;X)(e)
    ⇒ P[v])
BY
{ ((UnivCD THENA Auto)
   THEN (RWO "Memory-classrel-loc" (-1) THENA Auto)
   THEN InstLemma `Memory-class-invariant-sv` [⌈Info⌉;⌈B⌉;⌈A⌉;⌈P⌉;⌈f loc(e)⌉;⌈init⌉;⌈X⌉;⌈es⌉;⌈e⌉;⌈v⌉]⋅
   THEN Auto
   THEN InstHyp [⌈a⌉;⌈e'⌉;⌈s⌉] (-9)⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,B,A:Type].
    \mforall{}P:B  {}\mrightarrow{}  \mBbbP{}.  \mforall{}f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B.  \mforall{}init:Id  {}\mrightarrow{}  bag(B).  \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.  \mforall{}v:B.
        (single-valued-classrel(es;X;A)
        {}\mRightarrow{}  single-valued-bag(init  loc(e);B)
        {}\mRightarrow{}  (\mforall{}a:A.  \mforall{}e':E.    ((e'  <loc  e)  {}\mRightarrow{}  a  \mmember{}  X(e')  {}\mRightarrow{}  (\mforall{}s:B.  (P[s]  {}\mRightarrow{}  P[f  loc(e')  a  s]))))
        {}\mRightarrow{}  (\mforall{}v:B.  (v  \mdownarrow{}\mmember{}  init  loc(e)  {}\mRightarrow{}  P[v]))
        {}\mRightarrow{}  v  \mmember{}  Memory-loc-class(f;init;X)(e)
        {}\mRightarrow{}  P[v])


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (RWO  "Memory-classrel-loc"  (-1)  THENA  Auto)
  THEN  InstLemma  `Memory-class-invariant-sv`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}f  loc(e)\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}v\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  InstHyp  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}e'\mkleeneclose{};\mkleeneopen{}s\mkleeneclose{}]  (-9)\mcdot{}
  THEN  Auto)

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