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Step * of Lemma Memory-loc-class-total

∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:Id ⟶ A ⟶ S ⟶ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
  es-total-class(es;Memory-loc-class(f;init;X)) supposing ∀l:Id. (1 ≤ #(init l))
BY
{ ((UnivCD THENA MaAuto)
   THEN Unfold `es-total-class` 0
   THEN Auto
   THEN (InstLemma `Memory-loc-class-exists` [⌜Info⌝;⌜S⌝;⌜A⌝;⌜f⌝;⌜init⌝;⌜X⌝;⌜es⌝;⌜e⌝]⋅
         THENA (Auto THEN InstHyp [⌜loc(e)⌝] (-2)⋅ THEN Auto)
         )
   THEN All(RepUR ``classrel class-ap``)
   THEN FLemma `bag-member-iff-size` [-1]
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,A,S:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(S)].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  S  {}\mrightarrow{}  S].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].
    es-total-class(es;Memory-loc-class(f;init;X))  supposing  \mforall{}l:Id.  (1  \mleq{}  \#(init  l))


By

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Latex:
((UnivCD  THENA  MaAuto)
  THEN  Unfold  `es-total-class`  0
  THEN  Auto
  THEN  (InstLemma  `Memory-loc-class-exists`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}
              THENA  (Auto  THEN  InstHyp  [\mkleeneopen{}loc(e)\mkleeneclose{}]  (-2)\mcdot{}  THEN  Auto)
              )
  THEN  All(RepUR  ``classrel  class-ap``)
  THEN  FLemma  `bag-member-iff-size`  [-1]
  THEN  Auto)

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