Nuprl Lemma : loop-class-memory-size-zero
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(#(init loc(e)) = 0 ∈ ℤ;#(loop-class-memory(X;init)(e)) = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Lemmas :
decidable__equal_int,
equal-wf-T-base,
bag-size_wf,
es-loc_wf,
event-ordering+_subtype,
nat_wf,
class-ap_wf,
loop-class-memory_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
loop-class-memory-size,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\#(init loc(e)) = 0;\#(loop-class-memory(X;init)(e)) = 0)
Date html generated:
2015_07_21-PM-02_35_08
Last ObjectModification:
2015_01_27-PM-09_44_47
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