Step * of Lemma Memory-loc-class-invariant-sv1

`∀[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)`
`    `` (∀v:B. (v ↓∈ init loc(e) `` P[v]))`
`    `` (∀a:A. ∀e':E. ∀s:B.`
`          ((e' <loc e) `` a ∈ X(e') `` s ∈ Memory-loc-class(f;init;X)(e') `` P[s] `` P[f loc(e') a s]))`
`    `` 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-sv1` [⌈Info⌉;⌈B⌉;⌈A⌉;⌈P⌉;⌈f loc(e)⌉;⌈init⌉;⌈X⌉;⌈es⌉;⌈e⌉;⌈v⌉]⋅`
`   THEN Auto`
`   THEN (InstHyp [⌈a⌉;⌈e'⌉;⌈s⌉] (-9)⋅ THEN Auto)`
`   THEN BLemma `Memory-classrel-loc``
`   THEN Auto) }`

Latex:

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{}v:B.  (v  \mdownarrow{}\mmember{}  init  loc(e)  {}\mRightarrow{}  P[v]))
{}\mRightarrow{}  (\mforall{}a:A.  \mforall{}e':E.  \mforall{}s:B.
((e'  <loc  e)
{}\mRightarrow{}  a  \mmember{}  X(e')
{}\mRightarrow{}  s  \mmember{}  Memory-loc-class(f;init;X)(e')
{}\mRightarrow{}  P[s]
{}\mRightarrow{}  P[f  loc(e')  a  s]))
{}\mRightarrow{}  v  \mmember{}  Memory-loc-class(f;init;X)(e)
{}\mRightarrow{}  P[v])

By

Latex:
((UnivCD  THENA  Auto)
THEN  (RWO  "Memory-classrel-loc"  (-1)  THENA  Auto)
THEN  InstLemma  `Memory-class-invariant-sv1`  [\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)
THEN  BLemma  `Memory-classrel-loc`
THEN  Auto)

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