{ 
[A,B,S1,S2:Type]. [next1:S1 
A (S1 
B)]. [next2:S2 A (S2 B)].
[s1:S1]. [s2:S2]. [R:S1 S2 
].
(rec-dataflow(s1;s,a.next1[s;a])
= rec-dataflow(s2;s,a.next2[s;a])) supposing
(R[s1;s2] and
(s1:S1. s2:S2.
(R[s1;s2] 
(a:A. R[fst(next1[s1;a]);fst(next2[s2;a])]))) and
(s1:S1. s2:S2.
(R[s1;s2] (a:A. ((snd(next1[s1;a])) = (snd(next2[s2;a]))))))) }
{ Proof }
Definitions occuring in Statement :
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
dataflow: dataflow(A;B),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
pi1: fst(t),
pi2: snd(t),
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
product: x:A B[x],
universe: Type,
equal: s = t
Definitions :
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
list: type List,
let: let,
lambda: 
x.A[x],
so_lambda: 
x.t[x],
pi2: snd(t),
limited-type: LimitedType,
void: Void,
subtype: S 
T,
top: Top,
pi1: fst(t),
so_lambda: x y.t[x; y],
pair: <a, b>,
fpf: a:A fp-> B[a],
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,
axiom: Ax,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
dataflow: dataflow(A;B),
apply: f a,
so_apply: x[s1;s2],
implies: P Q,
all: x:A. B[x],
prop: ,
uimplies: b supposing a,
equal: s = t,
universe: Type,
product: x:A B[x],
function: x:A B[x],
member: t 
T,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
exists: 
x:A. B[x],
tl: tl(l),
hd: hd(l),
nil: [],
cons: [car / cdr],
append: as @ bs,
iter_df_nil: iter_df_nil{iter_df_nil_compseq_tag_def:o}(P),
guard: {T},
Complete: Error :Complete,
Try: Error :Try,
ExRepD: Error :ExRepD,
spread: spread def,
nat: 
,
primrec: primrec(n;b;c),
corec: corec(T.F[T]),
sq_type: SQType(T),
iter_df_cons: iter_df_cons{iter_df_cons_compseq_tag_def:o}(as; a; P),
sqequal: s ~ t,
D: Error :D,
RepUR: Error :RepUR,
HypSubst: Error :HypSubst,
CollapseTHENA: Error :CollapseTHENA,
it: 
,
rec_dataflow_ap: rec_dataflow_ap_compseq_tag_def,
THENM: Error :THENM,
RepeatFor: Error :RepeatFor,
AssertBY: Error :AssertBY,
tactic: Error :tactic
Lemmas :
isect_subtype_base,
nat_wf,
primrec_wf,
subtype_base_sq,
pi1_wf,
iterate-dataflow-append,
dataflow-ap_wf,
last_induction,
append_wf,
iterate-dataflow_wf,
dataflow_wf,
pi1_wf_top,
top_wf,
member_wf,
pi2_wf,
dataflow-equal,
rec-dataflow_wf
\mforall{}[A,B,S1,S2:Type]. \mforall{}[next1:S1 {}\mrightarrow{} A {}\mrightarrow{} (S1 \mtimes{} B)]. \mforall{}[next2:S2 {}\mrightarrow{} A {}\mrightarrow{} (S2 \mtimes{} B)]. \mforall{}[s1:S1]. \mforall{}[s2:S2].
\mforall{}[R:S1 {}\mrightarrow{} S2 {}\mrightarrow{} \mBbbP{}].
(rec-dataflow(s1;s,a.next1[s;a]) = rec-dataflow(s2;s,a.next2[s;a])) supposing
(R[s1;s2] and
(\mforall{}s1:S1. \mforall{}s2:S2. (R[s1;s2] {}\mRightarrow{} (\mforall{}a:A. R[fst(next1[s1;a]);fst(next2[s2;a])]))) and
(\mforall{}s1:S1. \mforall{}s2:S2. (R[s1;s2] {}\mRightarrow{} (\mforall{}a:A. ((snd(next1[s1;a])) = (snd(next2[s2;a])))))))
Date html generated:
2011_08_10-AM-08_19_44
Last ObjectModification:
2011_05_03-PM-02_23_18
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