### Nuprl Lemma : simple-comb2-concat-classrel

`∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  uiff(v ∈ λa,b.concat-lifting2(f;a;b)|X;Y|(e);↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Y(e) ∧ v ↓∈ f a b))`

Proof

Definitions occuring in Statement :  simple-comb2: `λx,y.F[x; y]|X;Y|` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` 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` concat-lifting2: `concat-lifting2(f;abag;bbag)` bag-member: `x ↓∈ bs` bag: `bag(T)`
Lemmas :  simple-comb-concat-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 concat-lifting2_wf bag_wf classrel_wf simple-comb2_wf squash_wf exists_wf bag-member_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf all_wf bag-member-union bag-combine_wf single-bag_wf bag-member-combine bag-member-single and_wf true_wf iff_weakening_equal simple-comb_wf

Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}[v:C].
uiff(v  \mmember{}  \mlambda{}a,b.concat-lifting2(f;a;b)|X;Y|(e);\mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  (a  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  a  b))

Date html generated: 2015_07_22-PM-00_10_27
Last ObjectModification: 2015_02_04-PM-04_41_57

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