{ 
[M:Type 
Type]
t:
. x:Id. m:pMsg(P.M[P]). G1,G2:LabeledDAG(pInTransit(P.M[P])).
Cs1,Cs2:component(P.M[P]) List.
((k:||Cs1||. let x,P = Cs1[k] in let z,Q = Cs2[k] in (x = z) 
P
Q)
(system-equiv(P.M[P];deliver-msg(t;m;x;Cs1;G1);
deliver-msg(t;m;x;Cs2;G2))
(deliver-msg(t;m;x;Cs1;G1)
= deliver-msg(t;m;x;Cs2;G2)))) supposing
((||Cs1|| = ||Cs2||) and
(G1 = G2))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
deliver-msg: deliver-msg(t;m;x;Cs;L),
system-equiv: system-equiv(T.M[T];S1;S2),
pInTransit: pInTransit(P.M[P]),
component: component(P.M[P]),
process-equiv: process-equiv,
pMsg: pMsg(P.M[P]),
ldag: LabeledDAG(T),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
select: l[i],
length: ||as||,
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
and: P Q,
function: x:A B[x],
spread: spread def,
product: x:A 
B[x],
list: type List,
natural_number: $n,
int: 
,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
so_apply: x[s],
all: x:A. B[x],
Id: Id,
component: component(P.M[P]),
length: ||as||,
implies: P Q,
and: P Q,
system-equiv: system-equiv(T.M[T];S1;S2),
deliver-msg: deliver-msg(t;m;x;Cs;L),
top: Top,
member: t 
T,
ext-eq: A B,
list_accum: list_accum(x,a.f[x; a];y;l),
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
ycomb: Y,
le: A 
B,
not: 
A,
false: False,
System: System(P.M[P]),
so_lambda: 
x.t[x],
prop: 
,
subtype: S 
T,
iff: P 
Q,
rev_implies: P Q,
squash: 
T,
true: True,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
cand: A c B,
pi2: snd(t),
int_seg: {i..j},
select: l[i],
process-equiv: process-equiv,
lelt: i j < k,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
pi1: fst(t),
nat: ,
sq_type: SQType(T),
guard: {T},
bool: 
,
unit: Unit,
Process-stream: Process-stream(P;msgs),
dataflow-ap: df(a),
hd: hd(l),
tl: tl(l),
decidable: Dec(P),
or: P 
Q,
it: 
,
Process-apply: Process-apply(P;m)
Lemmas :
nat_wf,
int_seg_wf,
component_wf,
System_wf,
system-equiv_wf,
top_wf,
non_neg_length,
length_wf_nat,
length_wf1,
select_wf,
Process_wf,
select_cons_tl,
process-equiv_wf,
squash_wf,
le_wf,
deliver-msg-to-comp_wf,
subtype_base_sq,
Id_wf,
atom2_subtype_base,
eq_id_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert-eq-id,
not_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
ldag_wf,
pInTransit_wf,
length_cons,
pMsg_wf,
strong-type-continuous_wf,
data-stream-cons,
Process-apply_wf,
pExt_wf,
hd_wf,
ge_wf,
tl_wf,
add-cause_wf,
lg-append_wf_dag,
true_wf,
decidable__equal_int,
int_subtype_base,
Process-stream_wf,
pi1_wf_top,
equal-top,
pi2_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}t:\mBbbN{}. \mforall{}x:Id. \mforall{}m:pMsg(P.M[P]). \mforall{}G1,G2:LabeledDAG(pInTransit(P.M[P])).
\mforall{}Cs1,Cs2:component(P.M[P]) List.
((\mforall{}k:\mBbbN{}||Cs1||. let x,P = Cs1[k] in let z,Q = Cs2[k] in (x = z) \mwedge{} P\mequiv{}Q)
{}\mRightarrow{} (system-equiv(P.M[P];deliver-msg(t;m;x;Cs1;G1);deliver-msg(t;m;x;Cs2;G2))
\mwedge{} (deliver-msg(t;m;x;Cs1;G1) = deliver-msg(t;m;x;Cs2;G2)))) supposing
((||Cs1|| = ||Cs2||) and
(G1 = G2))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-06_53_12
Last ObjectModification:
2011_06_18-AM-11_07_41
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