Nuprl Lemma : Memory-class-single-val2
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)].
∀es:EO+(Info). ∀e:E. ∀s1,s2:S.
(single-valued-classrel(es;X;A)
⇒ single-valued-bag(init loc(e);S)
⇒ s1 ∈ Memory-class(f;init;X)(e)
⇒ s2 ∈ Memory-class(f;init;X)(e)
⇒ (s1 = s2 ∈ S))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
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,
equal: s = t ∈ T,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
Memory-classrel,
iterated_classrel-single-val,
es-pred_wf,
single-valued-bag_wf,
squash_wf,
true_wf,
bag_wf,
es-pred-loc-base,
iff_weakening_equal,
classrel_wf,
Memory-class_wf,
es-loc_wf,
event-ordering+_subtype,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_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). \mforall{}e:E. \mforall{}s1,s2:S.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e);S)
{}\mRightarrow{} s1 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} s2 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} (s1 = s2))
Date html generated:
2015_07_22-PM-00_12_59
Last ObjectModification:
2015_02_04-PM-04_40_21
Home
Index