Step
*
of Lemma
member-loop-class-memory
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  (e ∈b loop-class-memory(X;init) ~ 0 <z #(init loc(e)))
BY
{ ((UnivCD THENA Auto)
   THEN VrBoolCase ⌈e ∈b loop-class-memory(X;init)⌉⋅
   THEN VrBoolCase ⌈0 <z #(init loc(e))⌉⋅
   THEN (RWO "loop-class-memory-member<" (-2) THEN Auto)
   THEN RW assert_pushdownC (-1)
   THEN Auto) }
Latex:
Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    (e  \mmember{}\msubb{}  loop-class-memory(X;init)  \msim{}  0  <z  \#(init  loc(e)))
By
Latex:
((UnivCD  THENA  Auto)
  THEN  VrBoolCase  \mkleeneopen{}e  \mmember{}\msubb{}  loop-class-memory(X;init)\mkleeneclose{}\mcdot{}
  THEN  VrBoolCase  \mkleeneopen{}0  <z  \#(init  loc(e))\mkleeneclose{}\mcdot{}
  THEN  (RWO  "loop-class-memory-member<"  (-2)  THEN  Auto)
  THEN  RW  assert\_pushdownC  (-1)
  THEN  Auto)
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