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: List vatype: ValueAllType assert: b all: x:A. B[x] exists: x:A. B[x] iff: ⇐⇒ Q implies:  Q and: P ∧ Q apply: a function: x:A ─→ B[x] pair: <a, b> product: x:A × B[x] int:
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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