Nuprl Lemma : pv11_p1_leader_adopted_wf
∀[Cmd:ValueAllType]. ∀[ldrs_uid:Id ─→ ℤ].
(pv11_p1_leader_adopted(Cmd;ldrs_uid) ∈ Id
─→ (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
─→ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List))
─→ bag(pv11_p1_Ballot_Num() × ℤ × Cmd))
Proof
Definitions occuring in Statement :
pv11_p1_leader_adopted: pv11_p1_leader_adopted(Cmd;ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
list: T List,
vatype: ValueAllType,
bool: 𝔹,
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,
map_wf,
pv11_p1_Ballot_Num_wf,
pv11_p1_update_proposals_wf,
pv11_p1_pmax_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nil_wf,
list-subtype-bag,
subtype_rel_self,
list_wf,
Id_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}].
(pv11\_p1\_leader\_adopted(Cmd;ldrs$_{uid}$) \mmember{} Id
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbB{} \mtimes{} ((\mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} bag(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd))
Date html generated:
2015_07_23-PM-04_33_32
Last ObjectModification:
2015_01_29-PM-04_38_38
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