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
Lemmas :
corec-subtype,
continuous-function,
strong-continuous-product,
continuous-id,
subtype_rel_weakening,
nat_wf,
strong-type-continuous_wf
\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:
2015_07_17-AM-11_19_35
Last ObjectModification:
2015_01_28-AM-07_36_19
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