Nuprl Lemma : OARcast_DelivererForSenderSeqState_wf

[M:ValueAllType]. ∀[deliverhdr:Atom List]. ∀[deqM:EqDecider(M)]. ∀[oarcasthdr,orderedhdr:Atom List].
[orderers:bag(Id)]. ∀[orderhdr:Atom List].
[mf:OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
  (OARcast_DelivererForSenderSeqState(M;deliverhdr;deqM;oarcasthdr;orderedhdr;orderers;orderhdr;mf) ∈ Id
   ─→ ℤ
   ─→ EClass(bag(Id) × ((M × ℕList)))


Proof




Definitions occuring in Statement :  OARcast_DelivererForSenderSeqState: OARcast_DelivererForSenderSeqState(M;deliverhdr;deqM;oarcasthdr;orderedhdr;orderers;orderhdr;mf) OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr) Message: Message(f) eclass: EClass(A[eo; e]) Id: Id deq: EqDecider(T) list: List nat: vatype: ValueAllType uall: [x:A]. B[x] member: t ∈ T function: x:A ─→ B[x] product: x:A × B[x] int: atom: Atom bag: bag(T)
Lemmas :  sq_stable__and equal_wf vatype_wf sq_stable__equal squash_wf int_seg_wf length_wf name_wf OARcast_headers_wf l_all_iff l_member_wf OARcast_headers_fun_wf cons_member cons_wf nil_wf equal-wf-base list_subtype_base atom_subtype_base iff_weakening_equal name_eq_wf bool_wf eqtt_to_assert assert-name_eq sq_stable__no_repeats true_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot Id_wf subtype_rel_dep_function state-class1_wf Message_wf list_wf nat_wf OARcast_init_odstate_wf OARcast_deliverer_for_sender_seq_update_wf OARcast_ordered'verify_wf OARcast_headers_type_wf bag_wf deq_wf set_wf valueall-type_wf

Latex:
\mforall{}[M:ValueAllType].  \mforall{}[deliverhdr:Atom  List].  \mforall{}[deqM:EqDecider(M)].
\mforall{}[oarcasthdr,orderedhdr:Atom  List].  \mforall{}[orderers:bag(Id)].  \mforall{}[orderhdr:Atom  List].
\mforall{}[mf:OARcast\_headers\_type\{i:l\}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
    (OARcast\_DelivererForSenderSeqState(M;deliverhdr;deqM;oarcasthdr;orderedhdr;orderers;orderhdr;mf)
      \mmember{}  Id  {}\mrightarrow{}  \mBbbZ{}  {}\mrightarrow{}  EClass(bag(Id)  \mtimes{}  ((M  \mtimes{}  \mBbbN{})  List)))



Date html generated: 2015_07_23-PM-00_33_00
Last ObjectModification: 2015_02_04-PM-04_28_37

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