{ [Info,A,B:Type].
    X:EClass(A). Y:EClass(B). es:EO+(Info). e:E.
      (e  (X&Y)
       ((e  X)  ((e  Y)  (e  Prior(Y))))
           ((e  Y)  ((e  X)  (e  Prior(X))))) }

{ Proof }



Definitions occuring in Statement :  latest-pair: (X&Y) primed-class: Prior(X) in-eclass: e  X eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E assert: b uall: [x:A]. B[x] all: x:A. B[x] iff: P  Q or: P  Q and: P  Q universe: Type
Definitions :  eq_knd: a = b fpf-dom: x  dom(f) cand: A c B so_apply: x[s] guard: {T} l_member: (x  l) bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o} axiom: Ax bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x) natural_number: $n real: grp_car: |g| bag-only: only(bs) pair: <a, b> single-bag: {x} empty-bag: {} nat: bag-size: bag-size(bs) void: Void true: True rev_implies: P  Q fpf: a:A fp-B[a] strong-subtype: strong-subtype(A;B) set: {x:A| B[x]}  le: A  B ge: i  j  less_than: a < b false: False limited-type: LimitedType prop: bfalse: ff btrue: tt decide: case b of inl(x) =s[x] | inr(y) =t[y] uimplies: b supposing a uiff: uiff(P;Q) eq_bool: p =b q lt_int: i <z j le_int: i z j eq_int: (i = j) null: null(as) set_blt: a < b grp_blt: a < b infix_ap: x f y dcdr-to-bool: [d] bl-all: (xL.P[x])_b bl-exists: (xL.P[x])_b b-exists: (i<n.P[i])_b eq_type: eq_type(T;T') not: A qeq: qeq(r;s) q_less: q_less(r;s) q_le: q_le(r;s) deq-member: deq-member(eq;x;L) deq-disjoint: deq-disjoint(eq;as;bs) deq-all-disjoint: deq-all-disjoint(eq;ass;bs) eq_id: a = b eq_lnk: a = b es-eq-E: e = e' es-bless: e <loc e' es-ble: e loc e' bimplies: p  q band: p  q bor: p q bnot: b int: unit: Unit bool: assert: b primed-class: Prior(X) eclass-compose4: eclass-compose4(f;X;Y;Z;V) in-eclass: e  X latest-pair: (X&Y) lambda: x.A[x] subtype: S  T subtype_rel: A r B atom: Atom apply: f a top: Top es-base-E: es-base-E(es) token: "$token" ifthenelse: if b then t else f fi  record-select: r.x bag: bag(T) dep-isect: Error :dep-isect,  eq_atom: x =a y eq_atom: eq_atom$n(x;y) record+: record+ equal: s = t member: t  T event_ordering: EO es-E: E uall: [x:A]. B[x] isect: x:A. B[x] iff: P  Q and: P  Q product: x:A  B[x] implies: P  Q or: P  Q union: left + right universe: Type eclass: EClass(A[eo; e]) so_lambda: x y.t[x; y] event-ordering+: EO+(Info) function: x:A  B[x] all: x:A. B[x] MaAuto: Error :MaAuto,  Repeat: Error :Repeat,  CollapseTHEN: Error :CollapseTHEN,  Try: Error :Try,  RepUR: Error :RepUR,  CollapseTHENA: Error :CollapseTHENA
Lemmas :  bag-size_wf ifthenelse_wf bag_wf single-bag_wf bag-only_wf primed-class_wf eq_int_wf assert_wf true_wf assert_witness bool_wf es-interface-top subtype_rel_wf eclass_wf member_wf in-eclass_wf not_wf bnot_wf assert_of_bnot eqff_to_assert uiff_transitivity eqtt_to_assert event-ordering+_wf event-ordering+_inc subtype_rel_self es-base-E_wf es-E_wf nat_wf top_wf empty-bag_wf false_wf rev_implies_wf iff_wf

\mforall{}[Info,A,B:Type].
    \mforall{}X:EClass(A).  \mforall{}Y:EClass(B).  \mforall{}es:EO+(Info).  \mforall{}e:E.
        (\muparrow{}e  \mmember{}\msubb{}  (X\&Y)
        \mLeftarrow{}{}\mRightarrow{}  ((\muparrow{}e  \mmember{}\msubb{}  X)  \mwedge{}  ((\muparrow{}e  \mmember{}\msubb{}  Y)  \mvee{}  (\muparrow{}e  \mmember{}\msubb{}  Prior(Y))))  \mvee{}  ((\muparrow{}e  \mmember{}\msubb{}  Y)  \mwedge{}  ((\muparrow{}e  \mmember{}\msubb{}  X)  \mvee{}  (\muparrow{}e  \mmember{}\msubb{}  Prior(X)))))


Date html generated: 2011_08_16-PM-05_36_31
Last ObjectModification: 2011_01_20-PM-03_41_00

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