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Step * of Lemma Memory-loc-class-trans-refl

∀[Info,B,A:Type].
  ∀R:B ─→ B ─→ ℙ. ∀f:Id ─→ A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e1,e2:E. ∀v1,v2:B.
    (Refl(B;x,y.R[x;y])
    ⇒ Trans(B;x,y.R[x;y])
    ⇒ (∀s1,s2:B.  SqStable(R[s1;s2]))
    ⇒ (∀a:A. ∀e:E.
          (e1 ≤loc e  ⇒ (e <loc e2) ⇒ a ∈ X(e) ⇒ (∀s:B. (s ∈ Memory-loc-class(f;init;X)(e) ⇒ R[s;f loc(e) a s]))))
    ⇒ single-valued-classrel(es;X;A)
    ⇒ single-valued-bag(init loc(e1);B)
    ⇒ v1 ∈ Memory-loc-class(f;init;X)(e1)
    ⇒ v2 ∈ Memory-loc-class(f;init;X)(e2)
    ⇒ e1 ≤loc e2 
    ⇒ R[v1;v2])
BY
{ ((UnivCD THENA Auto)
   THEN All (\h. RWO "Memory-classrel-loc" h THENA Auto)
   THEN InstLemma `Memory-class-trans-refl` [⌈Info⌉;⌈B⌉;⌈A⌉;⌈R⌉;⌈f loc(e2)⌉;⌈init⌉;⌈X⌉;⌈es⌉;⌈e1⌉;⌈e2⌉;⌈v1⌉;⌈v2⌉]⋅
   THEN Auto
   THEN InstHyp [⌈a⌉;⌈e⌉;⌈s⌉] (-13)⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,B,A:Type].
    \mforall{}R:B  {}\mrightarrow{}  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{}e1,e2:E.
    \mforall{}v1,v2:B.
        (Refl(B;x,y.R[x;y])
        {}\mRightarrow{}  Trans(B;x,y.R[x;y])
        {}\mRightarrow{}  (\mforall{}s1,s2:B.    SqStable(R[s1;s2]))
        {}\mRightarrow{}  (\mforall{}a:A.  \mforall{}e:E.
                    (e1  \mleq{}loc  e 
                    {}\mRightarrow{}  (e  <loc  e2)
                    {}\mRightarrow{}  a  \mmember{}  X(e)
                    {}\mRightarrow{}  (\mforall{}s:B.  (s  \mmember{}  Memory-loc-class(f;init;X)(e)  {}\mRightarrow{}  R[s;f  loc(e)  a  s]))))
        {}\mRightarrow{}  single-valued-classrel(es;X;A)
        {}\mRightarrow{}  single-valued-bag(init  loc(e1);B)
        {}\mRightarrow{}  v1  \mmember{}  Memory-loc-class(f;init;X)(e1)
        {}\mRightarrow{}  v2  \mmember{}  Memory-loc-class(f;init;X)(e2)
        {}\mRightarrow{}  e1  \mleq{}loc  e2 
        {}\mRightarrow{}  R[v1;v2])


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  All  (\mbackslash{}h.  RWO  "Memory-classrel-loc"  h  THENA  Auto)
  THEN  InstLemma  `Memory-class-trans-refl`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}R\mkleeneclose{};\mkleeneopen{}f  loc(e2)\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e1\mkleeneclose{};\mkleeneopen{}e2\mkleeneclose{};
  \mkleeneopen{}v1\mkleeneclose{};\mkleeneopen{}v2\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  InstHyp  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}s\mkleeneclose{}]  (-13)\mcdot{}
  THEN  Auto)

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