Nuprl Lemma : Accum-class-invariant
∀[Info,B,A:Type].
∀P:B ─→ ℙ. ∀f:A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
((∀s:B. SqStable(P[s]))
⇒ (∀a:A. ∀e':E. (e' ≤loc e ⇒ a ∈ X(e') ⇒ (∀s:B. (P[s] ⇒ P[f a s]))))
⇒ (∀v:B. (v ↓∈ init loc(e) ⇒ P[v]))
⇒ v ∈ Accum-class(f;init;X)(e)
⇒ P[v])
Proof
Definitions occuring in Statement :
Accum-class: Accum-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
sq_stable: SqStable(P),
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,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
Accum-classrel-Memory,
Memory-class-invariant,
es-le_weakening,
classrel_wf,
es-locl_wf,
es-le-self,
Accum-class_wf,
all_wf,
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
es-E_wf,
es-le_wf,
sq_stable_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type].
\mforall{}P:B {}\mrightarrow{} \mBbbP{}. \mforall{}f: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.
((\mforall{}s:B. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} (\mforall{}s:B. (P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} (\mforall{}v:B. (v \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[v]))
{}\mRightarrow{} v \mmember{} Accum-class(f;init;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2015_07_22-PM-00_18_14
Last ObjectModification:
2015_01_28-AM-10_43_08
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