Nuprl Lemma : pv11_p1_commander_output_wf
∀[Cmd:ValueAllType]. ∀[accpts,reps:bag(Id)]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)].
(pv11_p1_commander_output(Cmd;accpts;reps;mf) ∈ (pv11_p1_Ballot_Num() × ℤ × Cmd)
─→ Id
─→ (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num())
─→ bag(Id)
─→ bag(Interface))
Proof
Definitions occuring in Statement :
pv11_p1_commander_output: pv11_p1_commander_output(Cmd;accpts;reps;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
msg-interface: Interface,
Id: Id,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
bag: bag(T)
Lemmas :
sq_stable__and,
equal_wf,
cons_wf_listp,
nil_wf,
listp_wf,
vatype_wf,
cons_wf,
pv11_p1_Ballot_Num_wf,
list_wf,
equal-wf-T-base,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
pv11_p1_headers_wf,
l_all_iff,
l_member_wf,
pv11_p1_headers_fun_wf,
cons_member,
equal-wf-base,
iff_weakening_equal,
subtype_rel_dep_function,
pv11_p1_eq_bnums_wf,
bool_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
eq_int_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert_of_eq_int,
lt_int_wf,
bag-size_wf,
nat_wf,
pv11_p1_threshold_wf,
assert_of_lt_int,
pv11_p1_decision'broadcast_wf,
eqff_to_assert,
assert-bnot,
less_than_wf,
empty-bag_wf,
msg-interface_wf,
single-bag_wf,
pv11_p1_preempted'send_wf,
iff_transitivity,
assert_wf,
int_subtype_base,
iff_weakening_uiff,
assert_of_band,
pv11_p1_headers_type_wf,
bag_wf,
Id_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[accpts,reps:bag(Id)]. \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)].
(pv11\_p1\_commander\_output(Cmd;accpts;reps;mf) \mmember{} (pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd)
{}\mrightarrow{} Id
{}\mrightarrow{} (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num())
{}\mrightarrow{} bag(Id)
{}\mrightarrow{} bag(Interface))
Date html generated:
2015_07_23-PM-04_32_00
Last ObjectModification:
2015_02_04-AM-07_22_45
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