{ 
[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]))].
[ext:T:Type. (E[T] M[T] T E[T])].
(recprocess(s0;s,m.next[s;m];e,m,p.ext[e;m;p])
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 :
recprocess: recprocess(s0;s,m.next[s; m];e,m,p.ext[e; m; p]),
process: process(P.M[P];P.E[P]),
strong-type-continuous: Continuous+(T.F[T]),
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3],
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
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
process: process(P.M[P];P.E[P]),
member: t T,
recprocess: recprocess(s0;s,m.next[s; m];e,m,p.ext[e; m; p]),
so_apply: x[s1;s2],
so_apply: x[s1;s2;s3],
corec: corec(T.F[T]),
isect2: T1 T2,
top: Top,
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
all: x:A. B[x],
implies: P 
Q,
bool: 
,
unit: Unit,
it: 
,
prop: 
Lemmas :
ycomb_wf_corec_parameter3,
top_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]))].
\mforall{}[ext:\mcap{}T:Type. (E[T] {}\mrightarrow{} M[T] {}\mrightarrow{} T {}\mrightarrow{} E[T])].
(recprocess(s0;s,m.next[s;m];e,m,p.ext[e;m;p]) \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:
2011_08_16-AM-09_53_49
Last ObjectModification:
2011_06_18-AM-08_35_59
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