Nuprl Lemma : simple-loc-comb1-classrel

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


Proof not projected




Definitions occuring in Statement :  lifting1-loc: lifting1-loc(f;loc;b) 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 equal: s = t
Definitions :  member: t  T so_lambda: x y.t[x; y] so_lambda: x.t[x] and: P  Q nat: int_seg: {i..j} le: A  B not: A implies: P  Q false: False select: l[i] length: ||as|| lelt: i  j < k ge: i  j  label: ...$L... t ycomb: Y ifthenelse: if b then t else f fi  le_int: i z j bnot: b lt_int: i <z j bfalse: ff btrue: tt all: x:A. B[x] subtype: S  T suptype: suptype(S; T) lifting1-loc: lifting1-loc(f;loc;b) top: Top iff: P  Q rev_implies: P  Q funtype: funtype(n;A;T) primrec: primrec(n;b;c) eq_int: (i = j) true: True uall: [x:A]. B[x] exists: x:A. B[x] squash: T bag-member: x  bs simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X) uimplies: b supposing a guard: {T} so_apply: x[s] uiff: uiff(P;Q) so_apply: x[s1;s2] prop: decidable: Dec(P) or: P  Q sq_type: SQType(T) uncurry-rev: uncurry-rev(n;f) uncurry-gen: uncurry-gen(n)
Lemmas :  classrel_wf simple-loc-comb1_wf lifting1-loc_wf bag_wf Id_wf squash_wf exists_wf and_wf equal_wf es-loc_wf event-ordering+_inc es-E_wf event-ordering+_wf eclass_wf simple-loc-comb-classrel le_wf select_wf length_wf length_nil length_wf_nil length_cons non_neg_length length_wf_nat int_seg_wf decidable__equal_int subtype_base_sq int_subtype_base lelt_wf lifting-loc-member-simple ycomb-unroll lifting-loc-gen-rev_wf bag-member_wf uall_wf iff_wf all_wf iff_weakening_uiff uiff_functionality_wrt_uiff2

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


Date html generated: 2012_01_23-PM-01_08_20
Last ObjectModification: 2011_12_30-PM-08_40_05

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