### 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) ∈ C)))`

Proof

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 ∈ T`
Definitions :  uncurry-rev: `uncurry-rev(n;f)` uncurry-gen: `uncurry-gen(n)` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` bfalse: `ff` btrue: `tt`
Lemmas :  classrel_wf simple-loc-comb1_wf lifting1-loc_wf bag_wf Id_wf squash_wf exists_wf es-loc_wf event-ordering+_subtype es-E_wf event-ordering+_wf eclass_wf simple-loc-comb-classrel false_wf le_wf select_wf cons_wf nil_wf sq_stable__le length_wf length_nil non_neg_length length_wf_nil length_cons length_wf_nat int_seg_wf decidable__equal_int subtype_base_sq int_subtype_base lelt_wf lifting-loc-member-simple subtype_rel_dep_function funtype_wf primrec1_lemma subtype_rel_self bag-member_wf all_wf lifting-loc-gen-rev_wf uall_wf iff_wf le-add-cancel2 add-associates add_functionality_wrt_le zero-add minus-zero minus-add add-commutes condition-implies-le less-iff-le not-le-2 decidable__le select-cons-hd subtype_rel-equal es-interface-subtype_rel2 simple-loc-comb_wf

Latex:
\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: 2015_07_22-PM-00_08_38
Last ObjectModification: 2015_02_02-PM-06_56_39

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