### 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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