reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for C being U-small Category holds C opp is U-small Category
  proof
    let C be U-small Category;
A1: C is U-element;
    C opp = CatStr (# the carrier of C, the carrier' of C,
                      the Target of C, the Source of C, ~the Comp of C#)
      by OPPCAT_1:def 1;
    then C opp is U-element by A1;
    hence thesis;
  end;
