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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
system-strongly-realizes: system-strongly-realizes,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
InitialSystem: InitialSystem(P.M[P]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
system-realizes: system-realizes,
let: let,
cand: A c∧ B
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:
2016_05_17-AM-11_05_28
Last ObjectModification:
2015_12_29-PM-05_16_58
Theory : process-model
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