Nuprl Lemma : process-subtype
∀[M,E:Type ⟶ Type].
(process(P.M[P];P.E[P]) ⊆r (M[process(P.M[P];P.E[P])]
⟶ (process(P.M[P];P.E[P]) × E[process(P.M[P];P.E[P])]))) supposing
(Continuous+(P.E[P]) and
Continuous+(P.M[P]))
Proof
Definitions occuring in Statement :
process: process(P.M[P];P.E[P]),
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
process: process(P.M[P];P.E[P]),
so_lambda: λ2x.t[x],
so_apply: x[s],
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ
Latex:
\mforall{}[M,E:Type {}\mrightarrow{} Type].
(process(P.M[P];P.E[P]) \msubseteq{}r (M[process(P.M[P];P.E[P])]
{}\mrightarrow{} (process(P.M[P];P.E[P]) \mtimes{} E[process(P.M[P];P.E[P])]))) supposing
(Continuous+(P.E[P]) and
Continuous+(P.M[P]))
Date html generated:
2016_05_16-AM-11_42_55
Last ObjectModification:
2015_12_29-AM-09_35_33
Theory : event-ordering
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