Nuprl Lemma : simple-loc-comb-3-concat-single-val

[Info:Type]. [es:EO+(Info)]. [A,B,C,D:Type]. [F:Id  A  B  C  bag(D)]. [X:EClass(A)]. [Y:EClass(B)].
[Z:EClass(C)].
  single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D) 
  supposing (i:Id. a:A. b:B. c:C.  (bag-size(F i a b c)  1))
   single-valued-classrel(es;X;A)
   single-valued-classrel(es;Y;B)
   single-valued-classrel(es;Z;C)


Proof not projected




Definitions occuring in Statement :  concat-lifting-loc-3: concat-lifting-loc-3(f),  simple-loc-comb-3: F|Loc, X, Y, Z|,  single-valued-classrel: single-valued-classrel(es;X;T),  eclass: EClass(A[eo; e]),  event-ordering+: EO+(Info),  Id: Id,  uimplies: b supposing a,  uall: [x:A]. B[x],  le: A  B,  all: x:A. B[x],  and: P  Q,  apply: f a,  function: x:A  B[x],  natural_number: $n,  universe: Type,  bag-size: bag-size(bs),  bag: bag(T)
Definitions :  eclass: EClass(A[eo; e]),  and: P  Q,  all: x:A. B[x],  single-valued-classrel: single-valued-classrel(es;X;T),  implies: P  Q,  member: t  T,  prop: ,  cand: A c B,  so_lambda: x.t[x],  uall: [x:A]. B[x],  uimplies: b supposing a,  lifting-gen-list-rev: lifting-gen-list-rev(n;bags),  select: l[i],  ycomb: Y,  ifthenelse: if b then t else f fi ,  eq_int: (i = j),  btrue: tt,  bfalse: ff,  le_int: i z j,  bnot: b,  lt_int: i <z j,  le: A  B,  or: P  Q,  not: A,  false: False,  iff: P  Q,  squash: T,  true: True,  rev_implies: P  Q,  classrel: v  X(e),  simple-loc-comb-3: F|Loc, X, Y, Z|,  concat-lifting-loc-3: concat-lifting-loc-3(f),  simple-loc-comb: F|Loc; Xs|,  concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),  concat-lifting: concat-lifting(n;f;bags),  concat-lifting-list: concat-lifting-list(n;bags),  uiff: uiff(P;Q),  so_apply: x[s],  nat: ,  exists: x:A. B[x],  subtype: S  T
Lemmas :  bag-member-union,  classrel_wf,  simple-loc-comb-3_wf,  concat-lifting-loc-3_wf,  es-E_wf,  event-ordering+_inc,  all_wf,  Id_wf,  le_wf,  bag-size_wf,  nat_wf,  implies-wf,  equal_wf,  event-ordering+_wf,  bag_wf,  bag-combine_wf,  single-bag_wf,  es-loc_wf,  bag-member-combine,  bag-member-single,  bag-size-zero,  bag-member_wf,  squash_wf,  true_wf,  bag-member-empty-iff,  bag-size-one,  bag-only_wf,  and_wf

\mforall{}[Info:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[A,B,C,D:Type].  \mforall{}[F:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  C  {}\mrightarrow{}  bag(D)].  \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)].  \mforall{}[Z:EClass(C)].
    single-valued-classrel(es;concat-lifting-loc-3(F)|Loc,  X,  Y,  Z|;D) 
    supposing  (\mforall{}i:Id.  \mforall{}a:A.  \mforall{}b:B.  \mforall{}c:C.    (bag-size(F  i  a  b  c)  \mleq{}  1))
    \mwedge{}  single-valued-classrel(es;X;A)
    \mwedge{}  single-valued-classrel(es;Y;B)
    \mwedge{}  single-valued-classrel(es;Z;C)


Date html generated: 2012_01_23-PM-01_15_20
Last ObjectModification: 2011_11_11-AM-11_22_30

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