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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