Nuprl Lemma : new_23_sig_NewRoundsState-classrel

[Cmd:ValueAllType]. ∀[notify,propose:Atom List]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
  ∀es:EO+(Message(f)). ∀e:E. ∀x,v:ℤ.
    (v ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) x(e)
    ⇐⇒ new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;x;es;e) ∈ ℤ)


Proof




Definitions occuring in Statement :  new_23_sig_NewRoundsStateFun: new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;x;es;e) new_23_sig_NewRoundsState: new_23_sig_NewRoundsState(Cmd;notify;propose;f) new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose) Message: Message(f) classrel: v ∈ X(e) event-ordering+: EO+(Info) es-E: E list: List vatype: ValueAllType uall: [x:A]. B[x] all: x:A. B[x] iff: ⇐⇒ Q apply: a int: atom: Atom equal: t ∈ T
Lemmas :  sq_stable__and equal_wf vatype_wf cons_wf_listp cons_wf nil_wf listp_wf Id_wf sq_stable__equal squash_wf int_seg_wf length_wf name_wf new_23_sig_headers_wf l_all_iff l_member_wf new_23_sig_headers_fun_wf cons_member 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 classrel-classfun new_23_sig_NewRoundsState-functional classrel_wf new_23_sig_NewRoundsState_wf equal-wf-base-T int_subtype_base new_23_sig_NewRoundsStateFun_wf es-E_wf event-ordering+_subtype event-ordering+_wf Message_wf subtype_rel_dep_function new_23_sig_headers_type_wf list_wf set_wf valueall-type_wf

Latex:
\mforall{}[Cmd:ValueAllType].  \mforall{}[notify,propose:Atom  List].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)].
    \mforall{}es:EO+(Message(f)).  \mforall{}e:E.  \mforall{}x,v:\mBbbZ{}.
        (v  \mmember{}  new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f)  x(e)
        \mLeftarrow{}{}\mRightarrow{}  v  =  new\_23\_sig\_NewRoundsStateFun(Cmd;notify;propose;f;x;es;e))



Date html generated: 2015_07_23-PM-03_51_16
Last ObjectModification: 2015_02_04-PM-01_57_41

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