Nuprl Lemma : pv11_p1_pmax_desc_iff
∀Cmd:ValueAllType. ∀ldrs_uid:Id ─→ ℤ. ∀pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀s:ℤ. ∀c:Cmd.
((<s, c> ∈ pv11_p1_pmax(Cmd;ldrs_uid) pvals)
⇐⇒ ∃b:pv11_p1_Ballot_Num()
((<b, s, c> ∈ pvals)
∧ (∀b':pv11_p1_Ballot_Num(). ∀c':Cmd. ((<b', s, c'> ∈ pvals) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b' b))))))
Proof
Definitions occuring in Statement :
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
Lemmas :
pv11_p1_pmax_desc,
l_member_wf,
pv11_p1_pmax_wf,
member-mapfilter,
bnot_wf,
bl-exists_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
pv11_p1_lt_bnum_wf,
assert_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-bl-exists,
l_exists_iff,
equal-wf-base,
int_subtype_base,
assert_of_band,
subtype_base_sq,
exists_wf,
pv11_p1_Ballot_Num_wf,
all_wf,
pv11_p1_leq_bnum_wf,
list_wf,
Id_wf,
valueall-type_wf,
pv11_p1_lt_bnum_irrefl2,
pv11_p1_lt_bnum_trans1
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd\000C) List. \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<s, c> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) pvals)
\mLeftarrow{}{}\mRightarrow{} \mexists{}b:pv11\_p1\_Ballot\_Num()
((<b, s, c> \mmember{} pvals)
\mwedge{} (\mforall{}b':pv11\_p1\_Ballot\_Num(). \mforall{}c':Cmd.
((<b', s, c'> \mmember{} pvals) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b' b))))\000C))
Date html generated:
2015_07_23-PM-04_44_38
Last ObjectModification:
2015_01_29-AM-09_53_59
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