{ [V:Type]
    A:Id List. t:. f:V List  V. v0:V. L:consensus-rcv(V;A) List.
      let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in
       archive-condition(V;A;t;f;i - 1;v;L) supposing b }

{ Proof }



Definitions occuring in Statement :  consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L) archive-condition: archive-condition(V;A;t;f;n;v;L) consensus-rcv: consensus-rcv(V;A) Id: Id assert: b nat_plus: spreadn: let a,b,c,d,e = u in v[a; b; c; d; e] uimplies: b supposing a uall: [x:A]. B[x] all: x:A. B[x] function: x:A  B[x] list: type List subtract: n - m natural_number: $n universe: Type
Definitions :  uall: [x:A]. B[x] all: x:A. B[x] spreadn: let a,b,c,d,e = u in v[a; b; c; d; e] uimplies: b supposing a prop: implies: P  Q member: t  T so_lambda: x.t[x] consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L) assert: b list_accum: list_accum(x,a.f[x; a];y;l) bfalse: ff ycomb: Y ifthenelse: if b then t else f fi  false: False and: P  Q length: ||as|| zip: zip(as;bs) subtype: S  T top: Top consensus-accum-num: consensus-accum-num(num;f;s;r) btrue: tt spreadn: spread3 let: let true: True so_lambda: x y.t[x; y] not: A guard: {T} or: P  Q cand: A c B values-for-distinct: values-for-distinct(eq;L) map: map(f;as) le: A  B cs-rcv-vote: Vote[a;i;v] filter: filter(P;l) votes-from-inning: votes-from-inning(i;L) mapfilter: mapfilter(f;P;L) rcvd-vote: rcvd-vote(x) rcvd-inning-eq: inning(r) = i squash: T outr: outr(x) band: p  q rcv-vote?: rcv-vote?(x) reduce: reduce(f;k;as) Id: Id so_apply: x[s] nat_plus: consensus-rcv: consensus-rcv(V;A) nat: rev_implies: P  Q iff: P  Q so_apply: x[s1;s2] bool: unit: Unit null: null(as) append: as @ bs decidable: Dec(P) sq_type: SQType(T) pi1: fst(t) unzip: unzip(as) pi2: snd(t) cs-initial-rcv: Init[v] it:
Lemmas :  last_induction consensus-rcv_wf consensus-accum-num-state_wf nat_plus_inc bool_wf Id_wf l_member_wf assert_wf archive-condition_wf nat_plus_wf false_wf id-deq_wf strong-subtype-deq-subtype strong-subtype-set3 strong-subtype-self consensus-accum-num-property1 append_wf top_wf eq_int_wf true_wf filter_wf rcvd-inning-gt_wf votes-from-inning_wf le_wf not_wf null_wf3 length_wf1 values-for-distinct_wf zip_wf bnot_wf archive-condition-append-init lt_int_wf nat_properties archive-condition-append-vote le_int_wf remove-repeats_wf nat_plus_properties list_accum_append iff_weakening_uiff uiff_transitivity eqtt_to_assert assert_of_eq_int eqff_to_assert assert_of_bnot not_functionality_wrt_uiff assert_of_lt_int assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int decidable__assert assert_of_null filter_wf_top member_wf subtype_base_sq int_subtype_base decidable__equal_int votes-from-inning-is-nil rcvd-innings-nil mapfilter-append rcvd-inning-eq_wf zip-append squash_wf length_wf_nat nat_wf length-map map_wf pi1_wf_top length-append unzip_zip pi2_wf list_subtype_base set_subtype_base atom2_subtype_base

\mforall{}[V:Type]
    \mforall{}A:Id  List.  \mforall{}t:\mBbbN{}\msupplus{}.  \mforall{}f:V  List  {}\mrightarrow{}  V.  \mforall{}v0:V.  \mforall{}L:consensus-rcv(V;A)  List.
        let  b,i,as,vs,v  =  consensus-accum-num-state(t;f;v0;L)  in  archive-condition(V;A;t;f;i  -  1;v;L) 
                                                                                                                          supposing  \muparrow{}b


Date html generated: 2011_08_16-AM-10_14_17
Last ObjectModification: 2011_06_18-AM-09_06_29

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