Nuprl Lemma : memory-classrel1-sv
∀[Info,A1,S:Type].
∀init:Id ─→ S. ∀tr1:Id ─→ A1 ─→ S ─→ S. ∀X1:EClass(A1). ∀es:EO+(Info). ∀e:E. ∀v:S.
(single-valued-classrel(es;X1;A1)
⇒ (v ∈ memory-class1(initially init
applying tr1
on X1)(e)
⇐⇒ prior-iterated-classrel(es;A1;S;v;X1;tr1 loc(e);λloc.{init loc};e)))
Proof
Definitions occuring in Statement :
memory-class1: memory-class1,
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
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],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
single-bag: {x}
Lemmas :
single-valued-classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
prior-iterated-classrel_wf,
single-bag_wf,
es-loc_wf,
Memory-loc-classrel-single-val,
single-valued-bag-single,
classrel_wf,
Memory-loc-class_wf,
iff_wf,
squash_wf,
true_wf,
Memory1-memory-class1,
iff_weakening_equal
Latex:
\mforall{}[Info,A1,S:Type].
\mforall{}init:Id {}\mrightarrow{} S. \mforall{}tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S. \mforall{}X1:EClass(A1). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:S.
(single-valued-classrel(es;X1;A1)
{}\mRightarrow{} (v \mmember{} memory-class1(initially init
applying tr1
on X1)(e)
\mLeftarrow{}{}\mRightarrow{} prior-iterated-classrel(es;A1;S;v;X1;tr1 loc(e);\mlambda{}loc.\{init loc\};e)))
Date html generated:
2015_07_22-PM-00_26_48
Last ObjectModification:
2015_02_04-PM-05_12_38
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