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

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


Proof




Definitions occuring in Statement :  lifting-loc-2: lifting-loc-2(f) simple-loc-comb-2: (Loc,X, Y) 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: a function: x:A ─→ B[x] universe: Type equal: t ∈ T
Lemmas :  simple-loc-comb2-classrel classrel_wf simple-loc-comb-2_wf lifting-loc-2_wf squash_wf exists_wf es-loc_wf event-ordering+_subtype es-E_wf event-ordering+_wf eclass_wf Id_wf

Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:Id  {}\mrightarrow{}  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-loc-2(f)  o  (Loc,X,  Y)(e);\mdownarrow{}\mexists{}a:A
                                                                                            \mexists{}b:B.  (a  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  (v  =  (f  loc(e)  a  b))))



Date html generated: 2015_07_22-PM-00_09_01
Last ObjectModification: 2015_01_28-AM-11_41_28

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