Nuprl Lemma : Memory-class-single-val
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)].
∀es:EO+(Info)
(single-valued-classrel(es;X;A)
⇒ (∀l:Id. single-valued-bag(init l;S))
⇒ single-valued-classrel(es;Memory-class(f;init;X);S))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
all_wf,
Id_wf,
single-valued-bag_wf,
single-valued-classrel_wf,
event-ordering+_wf,
classrel_wf,
Memory-class_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
bag_wf,
Memory-classrel-single-val,
iterated-classrel-single-val,
es-pred_wf,
es-loc_wf
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)].
\mforall{}es:EO+(Info)
(single-valued-classrel(es;X;A)
{}\mRightarrow{} (\mforall{}l:Id. single-valued-bag(init l;S))
{}\mRightarrow{} single-valued-classrel(es;Memory-class(f;init;X);S))
Date html generated:
2015_07_22-PM-00_12_57
Last ObjectModification:
2015_01_28-AM-11_40_16
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