Nuprl Lemma : pv11_p1_acc_p2a

∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
∀v:pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List). ∀b:pv11_p1_Ballot_Num(). ∀s:ℤ. ∀c:Cmd.
  (v ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e)
  ⇒ let bnum,accepted = v 
     in (<b, s, c> ∈ accepted) ⇒ (∃e':E. ∃l:Id. (e' ≤loc e  ∧ <l, b, s, c> ∈ pv11_p1_p2a'base(Cmd;f)(e'))))


Proof



Definitions occuring in Statement :  pv11_p1_AcceptorState: pv11_p1_AcceptorState(Cmd;ldrs_uid;mf),  pv11_p1_p2a'base: pv11_p1_p2a'base(Cmd;mf),  pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),  pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),  Message: Message(f),  classrel: v ∈ X(e),  event-ordering+: EO+(Info),  es-le: e ≤loc e' ,  es-E: E,  Id: Id,  l_member: (x ∈ l),  list: T List,  vatype: ValueAllType,  all: ∀x:A. B[x],  exists: ∃x:A. B[x],  implies: P ⇒ Q,  and: P ∧ Q,  function: x:A ─→ B[x],  spread: spread def,  pair: <a, b>,  product: x:A × B[x],  int: ℤ
Lemmas :  int_seg_wf,  length_wf,  name_wf,  pv11_p1_headers_wf,  l_all_iff,  l_member_wf,  equal_wf,  pv11_p1_headers_fun_wf,  cons_wf_listp,  nil_wf,  listp_wf,  cons_member,  cons_wf,  equal-wf-base,  iff_weakening_equal,  classrel_wf,  squash_wf,  true_wf,  es-E_wf,  event-ordering+_subtype,  event-ordering+_wf,  eclass_wf,  State2-state-class2,  pv11_p1_init_acceptor_wf,  Id_wf,  pv11_p1_on_p1a_wf,  pv11_p1_p1a'base_wf,  pv11_p1_on_p2a_wf,  pv11_p1_p2a'base_wf,  State-loc-comb-invariant-sv1,  exists_wf,  es-le_wf,  single-bag_wf,  disjoint-union-tr_wf,  disjoint-union-comb_wf,  single-valued-bag-single,  disjoint-union-comb-single-val,  base-headers-msg-val-single-val,  subtype_rel_weakening,  ext-eq_weakening,  base-disjoint-classrel,  iff_transitivity,  not_wf,  assert_wf,  name_eq_wf,  bnot_wf,  assert-name_eq,  iff_weakening_uiff,  assert_of_bnot,  sq_stable__encodes-msg-type,  l_all_fwd,  list_wf,  valueall-type_wf,  equal-wf-T-base,  bag-member-single,  nil_member,  bag-member_wf,  disj_un_tr_ap_inl_lemma,  disj_un_tr_ap_inr_lemma,  pv11_p1_leq_bnum_wf,  bool_cases,  subtype_base_sq,  bool_wf,  bool_subtype_base,  eqtt_to_assert,  bl-exists_wf,  pv11_p1_same_pvalue_wf,  assert-bl-exists,  eqff_to_assert,  l_exists_wf,  l_exists_iff,  member_append,  assert_of_bor,  lt_int_wf,  eq_int_wf,  assert_of_eq_int,  le_int_wf,  assert_of_lt_int,  int_subtype_base,  le_wf,  assert_of_band,  assert_of_le_int,  less_than_wf,  or_wf,  member_singleton,  subtype_rel_sum,  unit_wf2,  es-first_wf2,  pv11_p1_add_if_new_wf,  pv11_p1_Ballot_Num_wf,  bool_cases_sqequal,  assert-bnot,  State-loc-comb_wf,  es-pred_wf,  pv11_p1_AcceptorState_wf,  Message_wf,  subtype_rel_dep_function,  vatype_wf,  pv11_p1_headers_type_wf,  set_wf,  disjoint-union-comb-classrel,  and_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{}v:pv11\_p1\_Ballot\_Num()  \mtimes{}  ((pv11\_p1\_Ballot\_Num()  \mtimes{}  \mBbbZ{}  \mtimes{}  Cmd)  List).  \mforall{}b:pv11\_p1\_Ballot\_Num().  \mforall{}s:\mBbbZ{}.
\mforall{}c:Cmd.
    (v  \mmember{}  pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e)
    {}\mRightarrow{}  let  bnum,accepted  =  v 
          in  (<b,  s,  c>  \mmember{}  accepted)
                {}\mRightarrow{}  (\mexists{}e':E.  \mexists{}l:Id.  (e'  \mleq{}loc  e    \mwedge{}  <l,  b,  s,  c>  \mmember{}  pv11\_p1\_p2a'base(Cmd;f)(e'))))


Date html generated: 2015_07_23-PM-04_45_03
Last ObjectModification: 2015_02_04-AM-07_42_33

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