### Nuprl Lemma : simple-comb1-classrel

`∀[Info,B,C:Type]. ∀[f:B ─→ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  uiff(v ∈ λa.lifting1(f;a)|X|(e);↓∃b:B. (b ∈ X(e) ∧ (v = (f b) ∈ C)))`

Proof

Definitions occuring in Statement :  simple-comb1: `λx.F[x]|X|` 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` lifting1: `lifting1(f;b)`
Lemmas :  int_seg_wf bag_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 bag-member_wf lifting1_wf false_wf lelt_wf squash_wf exists_wf all_wf bag-member-combine single-bag_wf bag-member-single subtype_rel-equal select-cons-hd decidable__le not-le-2 less-iff-le condition-implies-le add-commutes minus-add minus-zero zero-add add_functionality_wrt_le add-associates le-add-cancel2 decidable__equal_int subtype_base_sq int_subtype_base classrel_wf simple-comb_wf le_wf eclass_wf es-E_wf event-ordering+_subtype event-ordering+_wf es-interface-subtype_rel2 and_wf equal_wf

Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[f:B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:C].
uiff(v  \mmember{}  \mlambda{}a.lifting1(f;a)|X|(e);\mdownarrow{}\mexists{}b:B.  (b  \mmember{}  X(e)  \mwedge{}  (v  =  (f  b))))

Date html generated: 2015_07_22-PM-00_10_33
Last ObjectModification: 2015_01_28-AM-11_42_32

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