### Nuprl Lemma : simple-comb-2-classrel

`∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  uiff(v ∈ lifting-2(f)|X, Y|(e);↓∃a:A. ∃b:B. ((v = (f a b) ∈ C) ∧ b ∈ Y(e) ∧ a ∈ X(e)))`

Proof

Definitions occuring in Statement :  simple-comb-2: `F|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` equal: `s = t ∈ T` lifting-2: `lifting-2(f)`
Lemmas :  decidable__equal_int subtype_base_sq int_subtype_base select_wf cons_wf es-interface-subtype_rel2 es-E_wf event-ordering+_subtype nil_wf length_wf int_seg_wf simple-comb_wf false_wf le_wf sq_stable__le length_nil non_neg_length length_wf_nil length_cons length_wf_nat lifting2_wf lelt_wf bag_wf classrel_wf simple-comb-2_wf lifting-2_wf squash_wf exists_wf event-ordering+_wf eclass_wf simple-comb2-classrel

Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}[v:C].
uiff(v  \mmember{}  lifting-2(f)|X,  Y|(e);\mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  ((v  =  (f  a  b))  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  a  \mmember{}  X(e)))

Date html generated: 2015_07_22-PM-00_11_03
Last ObjectModification: 2015_01_28-AM-11_41_13

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