Nuprl Lemma : pv11_p1_pmax_desc_implies
∀Cmd:ValueAllType. ∀ldrs_uid:Id ─→ ℤ. ∀pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀b:pv11_p1_Ballot_Num(). ∀s:ℤ.
∀c:Cmd.
((<b, s, c> ∈ pvals) ⇒ (∃c':Cmd. (<s, c'> ∈ pv11_p1_pmax(Cmd;ldrs_uid) pvals)))
Proof
Definitions occuring in Statement :
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
Lemmas :
list_accum_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
pv11_p1_leq_bnum_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
member-mapfilter,
l_member_wf,
bnot_wf,
bl-exists_wf,
pv11_p1_lt_bnum_wf,
assert_wf,
pv11_p1_pmax_wf,
pv11_p1_Ballot_Num_wf,
list_wf,
Id_wf,
valueall-type_wf,
list_accum_invariant2,
iseg_wf,
append_wf,
cons_wf,
nil_wf,
list_accum_invariant3,
bl-exists-append,
bl-exists-singleton,
not_wf,
equal-wf-base,
int_subtype_base,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert_of_band,
pv11_p1_lt_bnum_implies_not3,
uiff_transitivity,
l_all_wf2,
not-assert-bl-exists,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
decidable__assert,
pv11_p1_leq_bnum_or,
pv11_p1_lt_bnum_trans2,
pv11_p1_lt_bnum_irrefl2,
and_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd\000C) List.
\mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<b, s, c> \mmember{} pvals) {}\mRightarrow{} (\mexists{}c':Cmd. (<s, c'> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) pv\000Cals)))
Date html generated:
2015_07_23-PM-04_44_50
Last ObjectModification:
2015_01_29-AM-09_54_39
Home
Index