Nuprl Lemma : nysiad_MessageBagState-classrel

[M:ValueAllType]. ∀[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. ∀[deqM:EqDecider(M)].
[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List]. ∀[waitingmap:map-sig{i:l}(Id;M)].
[mf:nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr)].
[msg2m:Message(mf) ─→ M].
  ∀es:EO+(Message(mf)). ∀e:E. ∀v:(M × Id? × Id) List × map-sig-map(waitingmap).
    (v ∈
      nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m)(
      e)
    ⇐⇒ v
        nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;...;...;...;...;mf;...;es;e)
        ∈ ((M × Id? × Id) List × map-sig-map(waitingmap)))


Proof




Definitions occuring in Statement :  nysiad_MessageBagStateFun: nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m;es;e) nysiad_MessageBagState: nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;readyhdr;...;...;mf;msg2m) nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr) Message: Message(f) classrel: v ∈ X(e) event-ordering+: EO+(Info) es-E: E Id: Id deq: EqDecider(T) list: List vatype: ValueAllType uall: [x:A]. B[x] all: x:A. B[x] iff: ⇐⇒ Q unit: Unit function: x:A ─→ B[x] product: x:A × B[x] union: left right atom: Atom equal: t ∈ T map-sig-map: map-sig-map(m) map-sig: map-sig{i:l}(Key;Value)
Lemmas :  sq_stable__and equal_wf vatype_wf equal-wf-T-base sq_stable__equal squash_wf int_seg_wf length_wf name_wf nysiad_headers_wf l_all_iff l_member_wf nysiad_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 Message_wf subtype_rel_dep_function Id_wf unit_wf2 classrel-classfun nysiad_MessageBagState-functional classrel_wf list_wf map-sig-map_wf nysiad_MessageBagState_wf nysiad_MessageBagStateFun_wf es-E_wf event-ordering+_subtype event-ordering+_wf nysiad_headers_type_wf map-sig_wf deq_wf set_wf valueall-type_wf

Latex:
\mforall{}[M:ValueAllType].  \mforall{}[add2baghdr,addwaitinghdr,adeliverhdr:Atom  List].  \mforall{}[deqM:EqDecider(M)].
\mforall{}[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom  List].  \mforall{}[waitingmap:map-sig\{i:l\}(Id;M)].
\mforall{}[...



Date html generated: 2015_07_23-PM-03_43_46
Last ObjectModification: 2015_02_04-PM-04_24_24

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