Nuprl Lemma : disjoint-union-comb-classrel

[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E]. [v:A + B].
  uiff(v  X (+) Y(e);((isl(v))  outl(v)  X(e))  ((isl(v))  outr(v)  Y(e)))


Proof not projected




Definitions occuring in Statement :  disjoint-union-comb: X (+) Y classrel: v  X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E outr: outr(x) outl: outl(x) isl: isl(x) assert: b uiff: uiff(P;Q) uall: [x:A]. B[x] not: A squash: T or: P  Q and: P  Q union: left + right universe: Type
Definitions :  uiff: uiff(P;Q) classrel: v  X(e) disjoint-union-comb: X (+) Y squash: T or: P  Q and: P  Q assert: b isl: isl(x) outl: outl(x) outr: outr(x) uimplies: b supposing a member: t  T true: True prop: bag-member: x  bs exists: x:A. B[x] btrue: tt bfalse: ff ifthenelse: if b then t else f fi  cand: A c B so_lambda: x.t[x] so_lambda: x y.t[x; y] not: A implies: P  Q guard: {T} bnot: b sq_or: a  b uall: [x:A]. B[x] all: x:A. B[x] false: False so_apply: x[s] so_apply: x[s1;s2] sq_type: SQType(T) sq_stable: SqStable(P) rev_uimplies: rev_uimplies(P;Q) subtype: S  T
Lemmas :  classrel_wf parallel-class_wf simple-comb-1_wf lifting-1_wf squash_wf or_wf true_wf not_wf exists_wf and_wf equal_wf bag_wf bag_qinc l_member_wf false_wf disjoint-union-comb_wf es-E_wf event-ordering+_inc event-ordering+_wf eclass_wf parallel-classrel simple-comb-1-classrel assert_wf isl_wf subtype_base_sq bool_wf bool_subtype_base not_assert_elim btrue_wf outl_wf outr_wf bnot_wf sq_stable__classrel

\mforall{}[Info,A,B:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:A  +  B].
    uiff(v  \mmember{}  X  (+)  Y(e);\mdownarrow{}((\muparrow{}isl(v))  \mwedge{}  outl(v)  \mmember{}  X(e))  \mvee{}  ((\mneg{}\muparrow{}isl(v))  \mwedge{}  outr(v)  \mmember{}  Y(e)))


Date html generated: 2012_01_23-PM-01_25_30
Last ObjectModification: 2012_01_11-AM-11_18_24

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