{ 
[M:Type 
Type]
[nat2msg:
pMsg(P.M[P])]. [loc2msg:Id pMsg(P.M[P])].
[env:pEnvType(P.M[P])]. [S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg)
supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
pRunType: pRunType(T.M[T]),
member: t 
T,
so_lambda: 
x.t[x],
all: x:A. B[x],
pi2: snd(t),
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
ifthenelse: if b then t else f fi ,
implies: P 
Q,
btrue: tt,
bfalse: ff,
prop: 
,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
nat: ,
and: P 
Q,
pEnvType: pEnvType(T.M[T]),
nat_plus: 
,
top: Top,
cand: A c B,
spreadn: spread3,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
int_seg: {i..j
},
let: let,
lelt: i j < k,
Id: Id,
subtype: S 
T,
squash: 
T,
true: True,
system-equiv: system-equiv(T.M[T];S1;S2),
length: ||as||,
create-component: create-component(t;P;x;Cs;L),
select: l[i],
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
process-equiv: process-equiv,
component: component(P.M[P]),
rev_implies: P 
Q,
iff: P Q,
unit: Unit,
bool: 
,
System: System(P.M[P]),
lg-is-source: lg-is-source(g;i),
or: P 
Q,
sq_type: SQType(T),
guard: {T},
pInTransit: pInTransit(P.M[P]),
pi1: fst(t),
decidable: Dec(P),
it: 
,
fulpRunType: fulpRunType(T.M[T])
Lemmas :
nat_wf,
pRun_wf2,
system-equiv_wf,
System_wf,
pEnvType_wf,
Id_wf,
pMsg_wf,
strong-type-continuous_wf,
eq_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
not_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
nat_properties,
ge_wf,
le_wf,
it_wf,
system-equiv-implies-equal,
int_seg_wf,
subtype_rel_function,
unit_wf,
top_wf,
ldag_wf,
pInTransit_wf,
subtype_rel_self,
pRunType_wf,
pRun_wf,
pi2_wf,
subtype_rel_simple_product,
lg-is-source_wf_dag,
btrue_neq_bfalse,
assert_elim,
not_assert_elim,
lg-remove_wf_dag,
lg-label_wf_dag,
lg-size_wf_dag,
lt_int_wf,
le_int_wf,
bfalse_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
pi1_wf_top,
pCom_wf,
atom2_subtype_base,
atom_subtype_base,
eq_atom_wf,
com-kind_wf,
assert_of_eq_atom,
comm-msg_wf,
deliver-msg_functionality,
squash_wf,
deliver-msg_wf,
decidable__equal_int,
int_subtype_base,
comm-create_wf,
Process_wf,
Process-stream_wf,
select_cons_tl,
component_wf,
process-equiv_wf,
equal-top,
do-chosen-command_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[nat2msg:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[loc2msg:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[env:pEnvType(P.M[P])].
\mforall{}[S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg)
supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-06_56_06
Last ObjectModification:
2011_06_18-AM-11_10_14
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