reserve a,a1,a2,v,v1,v2,x for object;
reserve V,A for set;
reserve m,n for Nat;
reserve S,S1,S2 for FinSequence;
reserve D,D1,D2 for NonatomicND of V,A;

theorem
  v in dom D implies naming(V,A,v,denaming(v,D)) = v .--> D.v
  proof
    assume
A1: v in dom D;
    ex n being Nat st D is TypeSSNominativeData of V,A\/FNDSC(V,A).n by Th33;
    then dom D c= V by RELAT_1:def 18;
    hence naming(V,A,v,denaming(v,D)) = v.-->denaming(v,D) by A1,Def13
    .= v.-->D.v by A1,Def12;
  end;
