theorem
  Hom(C) c= V implies (Obj (hom-?(V,a))).b = Hom(b,a)
proof
  assume
A1: Hom(C) c= V;
  Hom(b,a) in Hom(C);
  then reconsider A = Hom(b,a) as Element of V by A1;
  set d = @A;
  (hom-?(V,a)).(id b) = (hom-?(a)).(id b) by A1,Def25
    .= id d by A1,Lm10;
  hence thesis by OPPCAT_1:30;
end;
