{ 
[A,B,S:Type]. [hs:S]. [nxt:S 
A (S 
bag(B))].
rec-dataflow-halt-state(A;B;hs;s,a.nxt[s;a])
supposing a:A. (nxt[hs;a] = <hs, {}>) }
{ Proof }
Definitions occuring in Statement :
rec-dataflow-halt-state: rec-dataflow-halt-state(A;B;s0;s,a.next[s; a]),
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
all: x:A. B[x],
function: x:A B[x],
pair: <a, b>,
product: x:A B[x],
universe: Type,
equal: s = t
Definitions :
iter_df_cons: iter_df_cons{iter_df_cons_compseq_tag_def:o}(as; a; P),
rec_dataflow_ap: rec_dataflow_ap_compseq_tag_def,
iter_df_nil: iter_df_nil{iter_df_nil_compseq_tag_def:o}(P),
pair: <a, b>,
limited-type: LimitedType,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
so_lambda: 
x y.t[x; y],
axiom: Ax,
empty-bag: Error :empty-bag,
apply: f a,
so_apply: x[s1;s2],
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
pi2: snd(t),
list: type List,
lambda: x.A[x],
prop: 
,
rec-dataflow-halt-state: rec-dataflow-halt-state(A;B;s0;s,a.next[s; a]),
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
product: x:A B[x],
bag: Error :bag,
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t 
T,
all: x:A. B[x],
function: x:A B[x],
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
rationals: 
,
so_apply: x[s],
union: left + right,
or: P 
Q,
append: as @ bs,
guard: {T},
locl: locl(a),
Knd: Knd,
l_member: (x l),
so_lambda: x.t[x],
void: Void,
subtype: S T,
top: Top,
pi1: fst(t),
assert: 
b,
bool: 
,
fpf: a:A fp-> B[a],
quotient: x,y:A//B[x; y],
implies: P 
Q,
MaAuto: Error :MaAuto,
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
let: let,
Complete: Error :Complete,
dataflow: dataflow(A;B)
Lemmas :
iterate-dataflow_wf,
rec-dataflow_wf,
dataflow_wf,
dataflow-ap_wf,
subtype_base_sq,
pi1_wf_top,
top_wf,
member_wf,
pi2_wf,
Error :empty-bag_wf,
rec-dataflow-halt-state_wf,
Error :bag_wf
\mforall{}[A,B,S:Type]. \mforall{}[hs:S]. \mforall{}[nxt:S {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} bag(B))].
rec-dataflow-halt-state(A;B;hs;s,a.nxt[s;a]) supposing \mforall{}a:A. (nxt[hs;a] = <hs, \{\}>)
Date html generated:
2011_08_10-AM-08_22_37
Last ObjectModification:
2011_03_22-PM-01_57_08
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