{ 
[A,B,S1,S2:Type]. [next1:S1 
A (S1 
B)]. [next2:S2 A (S2 B)].
[s1:S1]. [s2:S2].
rec-dataflow(s1;s,a.next1[s;a]) = rec-dataflow(s2;s,a.next2[s;a])
supposing 
R:S1 S2 
(R[s1;s2]
(s1:S1. s2:S2.
(R[s1;s2] 
(a:A. R[fst(next1[s1;a]);fst(next2[s2;a])])))
(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],
exists: x:A. B[x],
implies: P Q,
and: P Q,
function: x:A B[x],
product: x:A B[x],
universe: Type,
equal: s = t
Definitions :
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,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
void: Void,
lambda: x.A[x],
pi2: snd(t),
limited-type: LimitedType,
subtype: S T,
top: Top,
pi1: fst(t),
axiom: Ax,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
member: t 
T,
universe: Type,
prop: ,
uall: [x:A]. B[x],
so_lambda: x.t[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
dataflow: dataflow(A;B),
exists: x:A. B[x],
and: P Q,
product: x:A B[x],
equal: s = t,
apply: f a,
implies: P Q,
all: x:A. B[x],
function: x:A B[x],
so_apply: x[s1;s2],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
RepeatFor: Error :RepeatFor,
tactic: Error :tactic
Lemmas :
uall_wf,
dataflow_wf,
member_wf,
top_wf,
pi2_wf,
pi1_wf_top,
rec-dataflow-equal
\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].
rec-dataflow(s1;s,a.next1[s;a]) = rec-dataflow(s2;s,a.next2[s;a])
supposing \mexists{}R:S1 {}\mrightarrow{} S2 {}\mrightarrow{} \mBbbP{}
(R[s1;s2]
\mwedge{} (\mforall{}s1:S1. \mforall{}s2:S2. (R[s1;s2] {}\mRightarrow{} (\mforall{}a:A. R[fst(next1[s1;a]);fst(next2[s2;a])])))
\mwedge{} (\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_51
Last ObjectModification:
2011_05_12-AM-12_24_56
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