Nuprl Lemma : rec-dataflow_wf2
∀[S,A,B:Type ─→ Type].
(let Proc = corec(P.A[P] ─→ (P × B[P])) in
∀s0:S[Proc]. ∀next:∩T:{T:Type| Proc ⊆r T} . (S[A[T] ─→ (T × B[T])] ─→ A[T] ─→ (S[T] × B[T])).
(rec-dataflow(s0;s,m.next[s;m]) ∈ Proc)) supposing
(Continuous+(T.B[T]) and
Continuous+(T.A[T]) and
Continuous+(T.S[T]))
Proof
Definitions occuring in Statement :
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
corec: corec(T.F[T]),
strong-type-continuous: Continuous+(T.F[T]),
let: let,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
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 :
nat_wf,
fix_wf_corec_parameter3,
top_wf,
bool_wf,
subtype_rel_wf,
corec_wf,
strong-type-continuous_wf
Latex:
\mforall{}[S,A,B:Type {}\mrightarrow{} Type].
(let Proc = corec(P.A[P] {}\mrightarrow{} (P \mtimes{} B[P])) in
\mforall{}s0:S[Proc]. \mforall{}next:\mcap{}T:\{T:Type| Proc \msubseteq{}r T\} . (S[A[T] {}\mrightarrow{} (T \mtimes{} B[T])] {}\mrightarrow{} A[T] {}\mrightarrow{} (S[T] \mtimes{} B[T])).
(rec-dataflow(s0;s,m.next[s;m]) \mmember{} Proc)) supposing
(Continuous+(T.B[T]) and
Continuous+(T.A[T]) and
Continuous+(T.S[T]))
Date html generated:
2015_07_23-AM-11_05_28
Last ObjectModification:
2015_01_28-PM-11_35_20
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