Nuprl Lemma : simple-loc-comb1-concat-classrel

[Info,A,B:Type]. [f:Id  A  bag(B)]. [X:EClass(A)]. [es:EO+(Info)]. [e:E]. [v:B].
  uiff(v  simple-loc-comb1(l,a.concat-lifting1-loc(f;a;l);X)(e);a:A. (a  X(e)  bag-member(B;v;f loc(e) a)))


Proof not projected




Definitions occuring in Statement :  concat-lifting1-loc: concat-lifting1-loc(f;bag;loc) simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X) classrel: v  X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id uiff: uiff(P;Q) uall: [x:A]. B[x] exists: x:A. B[x] squash: T and: P  Q apply: f a function: x:A  B[x] universe: Type bag-member: bag-member(T;x;bs) bag: bag(T)
Definitions :  uall: [x:A]. B[x] nat: member: t  T le: A  B not: A implies: P  Q false: False length: ||as|| ge: i  j  label: ...$L... t ycomb: Y top: Top so_lambda: x y.t[x; y] select: l[i] ifthenelse: if b then t else f fi  le_int: i z j bnot: b lt_int: i <z j bfalse: ff btrue: tt int_seg: {i..j} all: x:A. B[x] lelt: i  j < k and: P  Q iff: P  Q rev_implies: P  Q squash: T exists: x:A. B[x] lifting-gen-list-rev: lifting-gen-list-rev(n;bags) eq_int: (i = j) prop: so_lambda: x.t[x] true: True cand: A c B concat-lifting1-loc: concat-lifting1-loc(f;bag;loc) 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) simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X) uimplies: b supposing a so_apply: x[s] so_apply: x[s1;s2] decidable: Dec(P) or: P  Q sq_type: SQType(T) guard: {T} sq_stable: SqStable(P) rev_uimplies: rev_uimplies(P;Q) subtype: S  T
Lemmas :  simple-loc-comb-concat-classrel le_wf select_wf length_wf1 length_nil length_wf_nat top_wf length_cons non_neg_length int_seg_wf es-E_wf event-ordering+_inc event-ordering+_wf eclass_wf Id_wf bag_wf decidable__equal_int subtype_base_sq int_subtype_base concat-lifting1-loc_wf bag-member-union bag-combine_wf single-bag_wf bag-member-combine bag-member-single bag-member_wf sq_stable__bag-member squash_wf classrel_wf es-loc_wf simple-loc-comb_wf

\mforall{}[Info,A,B:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:B].
    uiff(v  \mmember{}  simple-loc-comb1(l,a.concat-lifting1-loc(f;a;l);X)(e);\mdownarrow{}\mexists{}a:A
                                                                                                                                      (a  \mmember{}  X(e)
                                                                                                                                      \mwedge{}  bag-member(B;v;f  loc(e)  a)))


Date html generated: 2011_10_20-PM-03_42_15
Last ObjectModification: 2011_08_16-PM-03_48_18

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