Nuprl Lemma : new_23_sig_rounds_inc

Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
e1,e2:E. ∀n,round1,round2:ℤ.
  ((e1 <loc e2)
   round1 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e1)
   round2 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e2)
   (round1 ≤ round2))


Proof




Definitions occuring in Statement :  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-locl: (e <loc e') es-E: E list: List vatype: ValueAllType le: A ≤ B all: x:A. B[x] implies:  Q apply: a int: atom: Atom
Lemmas :  int_seg_wf length_wf name_wf new_23_sig_headers_wf l_all_iff l_member_wf equal_wf new_23_sig_headers_fun_wf cons_member cons_wf cons_wf_listp listp_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 squash_wf true_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot Id_wf classrel_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf Memory1-memory-class1 new_23_sig_update_round_wf new_23_sig_RoundInfo_wf Memory-loc-class-trans-refl le_wf single-bag_wf le_weakening le_transitivity sq_stable__le eq_int_wf assert_of_eq_int lt_int_wf assert_of_lt_int less_than_wf neg_assert_of_eq_int parallel-class-single-val new_23_sig_retry'base_wf eclass0_wf new_23_sig_vote'base_wf new_23_sig_vote2retry_wf disjoint-classrel-symm eclass0-disjoint-classrel base-disjoint-classrel iff_transitivity not_wf assert_wf bnot_wf iff_weakening_uiff assert_of_bnot sq_stable__encodes-msg-type l_all_fwd list_wf valueall-type_wf subtype_rel_weakening ext-eq_weakening eclass0-single-val single-valued-bag-single base-headers-msg-val-single-val es-le_weakening new_23_sig_NewRoundsState_wf es-locl_wf Message_wf subtype_rel_dep_function vatype_wf new_23_sig_headers_type_wf set_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{}e1,e2:E.  \mforall{}n,round1,round2:\mBbbZ{}.
    ((e1  <loc  e2)
    {}\mRightarrow{}  round1  \mmember{}  new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f)  n(e1)
    {}\mRightarrow{}  round2  \mmember{}  new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f)  n(e2)
    {}\mRightarrow{}  (round1  \mleq{}  round2))



Date html generated: 2015_07_23-PM-03_51_26
Last ObjectModification: 2015_02_04-PM-01_56_51

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