Nuprl Lemma : Memory-loc-class-invariant-sv1
∀[Info,B,A:Type].
∀P:B ─→ ℙ. ∀f:Id ─→ A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
(single-valued-classrel(es;X;A)
⇒ single-valued-bag(init loc(e);B)
⇒ (∀v:B. (v ↓∈ init loc(e) ⇒ P[v]))
⇒ (∀a:A. ∀e':E. ∀s:B.
((e' <loc e) ⇒ a ∈ X(e') ⇒ s ∈ Memory-loc-class(f;init;X)(e') ⇒ P[s] ⇒ P[f loc(e') a s]))
⇒ v ∈ Memory-loc-class(f;init;X)(e)
⇒ P[v])
Proof
Definitions occuring in Statement :
Memory-loc-class: Memory-loc-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-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
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-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
Memory-classrel-loc,
Memory-class-invariant-sv1,
and_wf,
equal_wf,
Id_wf,
Memory-class_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
classrel_wf,
es-locl_wf,
Memory-loc-class_wf,
all_wf,
es-loc_wf,
bag-member_wf,
single-valued-bag_wf,
single-valued-classrel_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type].
\mforall{}P:B {}\mrightarrow{} \mBbbP{}. \mforall{}f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B. \mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:B.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e);B)
{}\mRightarrow{} (\mforall{}v:B. (v \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[v]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. \mforall{}s:B.
((e' <loc e)
{}\mRightarrow{} a \mmember{} X(e')
{}\mRightarrow{} s \mmember{} Memory-loc-class(f;init;X)(e')
{}\mRightarrow{} P[s]
{}\mRightarrow{} P[f loc(e') a s]))
{}\mRightarrow{} v \mmember{} Memory-loc-class(f;init;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2015_07_22-PM-00_14_02
Last ObjectModification:
2015_01_28-AM-10_46_07
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