Nuprl Lemma : rec-process_wf
∀[S,M,E:Type ─→ Type].
(∀[s0:S[process(P.M[P];P.E[P])]]. ∀[next:∩T:{T:Type| process(P.M[P];P.E[P]) ⊆r T}
(S[M[T] ─→ (T × E[T])] ─→ M[T] ─→ (S[T] × E[T]))].
(RecProcess(s0;s,m.next[s;m]) ∈ process(P.M[P];P.E[P]))) supposing
(Continuous+(T.E[T]) and
Continuous+(T.M[T]) and
Continuous+(T.S[T]))
Proof
Definitions occuring in Statement :
rec-process: RecProcess(s0;s,m.next[s; m]),
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[s1;s2],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
isect: ∩x:A. B[x],
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
fix_wf_corec_parameter3,
top_wf,
subtype_rel_wf,
corec_wf,
bool_wf,
process_wf,
strong-type-continuous_wf
\mforall{}[S,M,E:Type {}\mrightarrow{} Type].
(\mforall{}[s0:S[process(P.M[P];P.E[P])]]. \mforall{}[next:\mcap{}T:\{T:Type| process(P.M[P];P.E[P]) \msubseteq{}r T\}
(S[M[T] {}\mrightarrow{} (T \mtimes{} E[T])] {}\mrightarrow{} M[T] {}\mrightarrow{} (S[T] \mtimes{} E[T]))].
(RecProcess(s0;s,m.next[s;m]) \mmember{} process(P.M[P];P.E[P]))) supposing
(Continuous+(T.E[T]) and
Continuous+(T.M[T]) and
Continuous+(T.S[T]))
Date html generated:
2015_07_17-AM-11_19_52
Last ObjectModification:
2015_01_28-AM-07_36_29
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