Nuprl Lemma : State-comb-invariant
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[P:S ─→ ℙ]. ∀[e:E].
∀v:S
((∀s:S. SqStable(P[s]))
⇒ (∀s:S. (s ↓∈ init loc(e) ⇒ P[s]))
⇒ (∀a:A. ∀e':E. (e' ≤loc e ⇒ a ∈ X(e') ⇒ (∀s:S. (s ∈ Memory-class(f;init;X)(e') ⇒ P[s] ⇒ P[f a s]))))
⇒ v ∈ State-comb(init;f;X)(e)
⇒ P[v])
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
Memory-class: Memory-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 :
iterated_classrel_invariant3,
Memory-classrel,
prior_iterated_classrel_wf,
classrel_wf,
es-le_wf,
State-comb-classrel,
State-comb_wf,
all_wf,
es-E_wf,
event-ordering+_subtype,
Memory-class_wf,
bag-member_wf,
es-loc_wf,
sq_stable_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_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{}[P:S {}\mrightarrow{} \mBbbP{}]. \mforall{}[e:E].
\mforall{}v:S
((\mforall{}s:S. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}s:S. (s \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E.
(e' \mleq{}loc e {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} (\mforall{}s:S. (s \mmember{} Memory-class(f;init;X)(e') {}\mRightarrow{} P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} v \mmember{} State-comb(init;f;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2015_07_22-PM-00_22_21
Last ObjectModification:
2015_01_28-AM-10_11_17
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