Nuprl Lemma : pv11_p1_ldr_active2

∀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() × 𝔹 × ((ℤ × Cmd) List).
  (v ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e)
  ⇒ let bnum,active,proposals1 = v in 
     (↑active)
     ⇒ (↓∃e':E
           ∃pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List
            ∃proposals:(ℤ × Cmd) List
             ∃b:𝔹
              ((e' <loc e)
              ∧ <bnum, pvals> ∈ pv11_p1_adopted'base(Cmd;f)(e')
              ∧ <bnum, b, proposals> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e'))))


Proof



Definitions occuring in Statement :  pv11_p1_LeaderState: pv11_p1_LeaderState(Cmd;ldrs_uid;mf),  pv11_p1_adopted'base: pv11_p1_adopted'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-locl: (e <loc e'),  es-E: E,  Id: Id,  list: T List,  vatype: ValueAllType,  assert: ↑b,  bool: 𝔹,  spreadn: spread3,  all: ∀x:A. B[x],  exists: ∃x:A. B[x],  squash: ↓T,  implies: P ⇒ Q,  and: P ∧ Q,  function: x:A ─→ B[x],  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,  list_wf,  classrel_wf,  squash_wf,  true_wf,  es-E_wf,  event-ordering+_subtype,  event-ordering+_wf,  eclass_wf,  pv11_p1_Ballot_Num_wf,  bool_wf,  Memory3-memory-class3,  pv11_p1_init_leader_wf,  pv11_p1_on_propose_wf,  pv11_p1_propose'base_wf,  pv11_p1_when_adopted_wf,  pv11_p1_adopted'base_wf,  pv11_p1_when_preempted_wf,  pv11_p1_preempted'base_wf,  Memory-loc-class-invariant-sv1,  assert_wf,  exists_wf,  es-locl_wf,  pv11_p1_LeaderState_wf,  disjoint-union-tr_wf,  single-bag_wf,  Id_wf,  disjoint-union-comb_wf,  disjoint-union-comb-single-val,  base-headers-msg-val-single-val,  subtype_rel_weakening,  ext-eq_weakening,  base-disjoint-classrel,  iff_transitivity,  not_wf,  name_eq_wf,  bnot_wf,  assert-name_eq,  iff_weakening_uiff,  assert_of_bnot,  sq_stable__encodes-msg-type,  l_all_fwd,  valueall-type_wf,  equal-wf-T-base,  disjoint-classrel-symm,  disjoint-union-comb-disjoint-classrel,  single-valued-bag-single,  es-loc_wf,  bag-member-single,  bag-member_wf,  disj_un_tr_ap_inl_lemma,  disj_un_tr_ap_inr_lemma,  pv11_p1_eq_bnums_wf,  eqtt_to_assert,  pv11_p1_eq_bnums-assert,  eqff_to_assert,  bool_cases_sqequal,  subtype_base_sq,  bool_subtype_base,  assert-bnot,  pv11_p1_is_bnum_wf,  pv11_p1_lt_bnum_wf,  false_wf,  Memory-loc-class_wf,  Message_wf,  subtype_rel_dep_function,  vatype_wf,  pv11_p1_headers_type_wf,  set_wf,  disjoint-union-comb-classrel,  union_subtype_base,  unit_wf2,  product_subtype_base,  int_subtype_base,  atom2_subtype_base,  unit_subtype_base
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{}  \mBbbB{}  \mtimes{}  ((\mBbbZ{}  \mtimes{}  Cmd)  List).
    (v  \mmember{}  pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e)
    {}\mRightarrow{}  let  bnum,active,proposals1  =  v  in 
          (\muparrow{}active)
          {}\mRightarrow{}  (\mdownarrow{}\mexists{}e':E
                      \mexists{}pvals:(pv11\_p1\_Ballot\_Num()  \mtimes{}  \mBbbZ{}  \mtimes{}  Cmd)  List
                        \mexists{}proposals:(\mBbbZ{}  \mtimes{}  Cmd)  List
                          \mexists{}b:\mBbbB{}
                            ((e'  <loc  e)
                            \mwedge{}  <bnum,  pvals>  \mmember{}  pv11\_p1\_adopted'base(Cmd;f)(e')
                            \mwedge{}  <bnum,  b,  proposals>  \mmember{}  pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e\000C'))))


Date html generated: 2015_07_23-PM-04_45_42
Last ObjectModification: 2015_02_04-AM-08_29_02

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