{ 
[A,B,S:Type]. [s0:S]. [nxt:S 
A (S 
bag(B))].
(rec-dataflow-halt-state(A;B;s0;s,a.nxt[s;a]) 
) }
{ Proof }
Definitions occuring in Statement :
rec-dataflow-halt-state: rec-dataflow-halt-state(A;B;s0;s,a.next[s; a]),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
member: t T,
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
so_lambda: 
x.t[x],
lambda: x.A[x],
let: let,
implies: P 
Q,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
empty-bag: Error :empty-bag,
so_lambda: x y.t[x; y],
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
pi2: snd(t),
limited-type: LimitedType,
list: type List,
all: x:A. B[x],
axiom: Ax,
apply: f a,
so_apply: x[s1;s2],
rec-dataflow-halt-state: rec-dataflow-halt-state(A;B;s0;s,a.next[s; a]),
prop: ,
universe: Type,
uall: [x:A]. B[x],
product: x:A B[x],
function: x:A B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
Auto: Error :Auto,
bag: Error :bag,
dataflow: dataflow(A;B),
CollapseTHEN: Error :CollapseTHEN
Lemmas :
Error :bag_wf,
member_wf,
Error :empty-bag_wf,
dataflow_wf,
iterate-dataflow_wf,
rec-dataflow_wf,
dataflow-ap_wf,
pi2_wf
\mforall{}[A,B,S:Type]. \mforall{}[s0:S]. \mforall{}[nxt:S {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} bag(B))].
(rec-dataflow-halt-state(A;B;s0;s,a.nxt[s;a]) \mmember{} \mBbbP{})
Date html generated:
2011_08_10-AM-08_20_00
Last ObjectModification:
2011_03_22-PM-01_40_41
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