Nuprl Lemma : State-loc-comb-invariant
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:Id ⟶ 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-loc-class(f;init;X)(e') ⇒ P[s] ⇒ P[f loc(e') a s]))))
⇒ v ∈ State-loc-comb(init;f;X)(e)
⇒ P[v])
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
Memory-loc-class: Memory-loc-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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
sq_stable: SqStable(P),
iff: P ⇐⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s],
squash: ↓T,
so_lambda: λ2x.t[x]
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:Id {}\mrightarrow{} 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-loc-class(f;init;X)(e') {}\mRightarrow{} P[s] {}\mRightarrow{} P[f loc(e') a s]))))
{}\mRightarrow{} v \mmember{} State-loc-comb(init;f;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2016_05_17-AM-10_03_09
Last ObjectModification:
2016_01_17-PM-11_03_53
Theory : classrel!lemmas
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