Nuprl Lemma : pv11_p1_on_p1b_wf
∀[Cmd:ValueAllType]
(pv11_p1_on_p1b(Cmd) ∈ pv11_p1_Ballot_Num()
─→ Id
─→ (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
─→ (bag(Id) × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
─→ (bag(Id) × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_on_p1b: pv11_p1_on_p1b(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
list: T List,
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 :
pv11_p1_eq_bnums_wf,
bool_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
let_wf,
bag_wf,
Id_wf,
list_wf,
pv11_p1_Ballot_Num_wf,
pv11_p1_append_news_wf,
pv11_p1_same_pvalue_wf,
bag-remove_wf,
id-deq_wf,
eqff_to_assert,
assert-bnot,
iff_transitivity,
assert_wf,
iff_weakening_uiff,
assert_of_band,
set_wf,
valueall-type_wf
Latex:
\mforall{}[Cmd:ValueAllType]
(pv11\_p1\_on\_p1b(Cmd) \mmember{} pv11\_p1\_Ballot\_Num()
{}\mrightarrow{} Id
{}\mrightarrow{} (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (bag(Id) \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (bag(Id) \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
Date html generated:
2015_07_23-PM-04_32_19
Last ObjectModification:
2015_01_29-PM-04_42_05
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