Nuprl Lemma : system-realizes_wf
∀[M:Type ⟶ Type]
∀[S:InitialSystem(P.M[P])]. ∀[n2m:ℕ ⟶ pMsg(P.M[P])]. ∀[l2m:Id ⟶ pMsg(P.M[P])]. ∀[A:pEnvType(P.M[P])
⟶ pRunType(P.M[P])
⟶ ℙ].
∀[B:EO+(pMsg(P.M[P])) ⟶ ℙ].
(assuming(env,r.A[env;r])
S |- eo.B[eo] ∈ ℙ)
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-realizes: system-realizes,
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],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
system-realizes: system-realizes,
let: let,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
InitialSystem: InitialSystem(P.M[P]),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[S:InitialSystem(P.M[P])]. \mforall{}[n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[l2m:Id {}\mrightarrow{} pMsg(P.M[P])].
\mforall{}[A:pEnvType(P.M[P]) {}\mrightarrow{} pRunType(P.M[P]) {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:EO+(pMsg(P.M[P])) {}\mrightarrow{} \mBbbP{}].
(assuming(env,r.A[env;r])
S |- eo.B[eo] \mmember{} \mBbbP{})
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-11_03_26
Last ObjectModification:
2015_12_29-PM-05_23_35
Theory : process-model
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