theorem
  Hom(C) c= V implies (Obj (hom?-(V,a))).b = Hom(a,b)
proof
  assume
A1: Hom(C) c= V;
  Hom(a,b) in Hom(C);
  then reconsider A = Hom(a,b) as Element of V by A1;
  set d = @A;
  (hom?-(V,a)).(id b) = (hom?-(a)).(id b) by A1,Def24
    .= id d by A1,Lm9;
  hence thesis by CAT_1:67;
end;
