Nuprl Lemma : system-strongly-realizes-and1
∀[M:Type ─→ Type]
∀[A:pEnvType(P.M[P]) ─→ pRunType(P.M[P]) ─→ ℙ]
∀n2m:ℕ ─→ pMsg(P.M[P]). ∀l2m:Id ─→ pMsg(P.M[P]). ∀S1,S2:InitialSystem(P.M[P]).
∀[B1,B2:EO+(pMsg(P.M[P])) ─→ ℙ].
(assuming(env,r.A[env;r])
S1 |= eo.B1[eo]
⇒ assuming(env,r.A[env;r])
S2 |= eo.B2[eo]
⇒ (∀S:InitialSystem(P.M[P])
(sub-system(P.M[P];S1;S)
⇒ sub-system(P.M[P];S2;S)
⇒ assuming(env,r.A[env;r])
S |= eo.B1[eo] ∧ B2[eo])))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-strongly-realizes: system-strongly-realizes,
sub-system: sub-system(P.M[P];S1;S2),
InitialSystem: InitialSystem(P.M[P]),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
pMsg: pMsg(P.M[P]),
event-ordering+: EO+(Info),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
nat_wf,
sub-system_wf,
InitialSystem_wf,
system-strongly-realizes_wf,
pRunType_wf,
pEnvType_wf,
event-ordering+_wf,
pMsg_wf,
Id_wf,
strong-type-continuous_wf,
sub-system_transitivity,
pRun_wf2
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[A:pEnvType(P.M[P]) {}\mrightarrow{} pRunType(P.M[P]) {}\mrightarrow{} \mBbbP{}]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}S1,S2:InitialSystem(P.M[P]).
\mforall{}[B1,B2:EO+(pMsg(P.M[P])) {}\mrightarrow{} \mBbbP{}].
(assuming(env,r.A[env;r])
S1 |= eo.B1[eo]
{}\mRightarrow{} assuming(env,r.A[env;r])
S2 |= eo.B2[eo]
{}\mRightarrow{} (\mforall{}S:InitialSystem(P.M[P])
(sub-system(P.M[P];S1;S)
{}\mRightarrow{} sub-system(P.M[P];S2;S)
{}\mRightarrow{} assuming(env,r.A[env;r])
S |= eo.B1[eo] \mwedge{} B2[eo])))
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_20_30
Last ObjectModification:
2015_01_28-PM-11_17_25
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