Nuprl Lemma : pv11_p1_bnum_p2a
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
∀accpts,ldrs,reps:bag(Id). ∀b:pv11_p1_Ballot_Num(). ∀i,l:Id. ∀s:ℤ. ∀c:Cmd.
(pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e)
⇒ (∃n:ℤ. (↑(pv11_p1_eq_bnums() b (pv11_p1_mk_bnum() n l)))))
Proof
Definitions occuring in Statement :
pv11_p1_p2a'send: pv11_p1_p2a'send(Cmd;f),
pv11_p1_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_eq_bnums: pv11_p1_eq_bnums(),
pv11_p1_mk_bnum: pv11_p1_mk_bnum(),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
msg-interface: Interface,
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
int: ℤ,
bag: bag(T)
Lemmas :
make-Msg-as-mk-msg,
pv11_p1-p2a,
bfalse_wf,
sq_stable__assert,
pv11_p1_eq_bnums_wf,
subtype_rel_sum,
unit_wf2,
pv11_p1_mk_bnum_wf,
pv11_p1_eq_bnums-assert,
and_wf,
equal_wf,
outl_wf,
Id_wf,
assert_wf,
isl_wf,
pi2_wf,
squash_wf,
exists_wf,
pv11_p1_ldr_fun_loc_bnum,
bag-member-sq-list-member,
pv11_p1_LeaderStateFun_wf,
bool_wf,
list_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}ldrs$_\mbackslash{}ff7\000Cbuid}$:Id {}\mrightarrow{} \mBbbZ{}.
\mforall{}accpts,ldrs,reps:bag(Id). \mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}i,l:Id. \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
(pv11\_p1\_p2a'send(Cmd;f) i <l, b, s, c> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid}\000C$;reps;f)(e)
{}\mRightarrow{} (\mexists{}n:\mBbbZ{}. (\muparrow{}(pv11\_p1\_eq\_bnums() b (pv11\_p1\_mk\_bnum() n l)))))
Date html generated:
2015_07_23-PM-04_48_58
Last ObjectModification:
2015_01_29-AM-09_50_33
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