reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem
  for a,b being Object of c1Cat*(o,m), f being Morphism of c1Cat*(o,m)
  holds f is Morphism of a,b
proof
  let a,b be Object of c1Cat*(o,m), f be Morphism of c1Cat*(o,m);
  f in Hom(a,b) by Th47;
  hence thesis by CAT_1:def 5;
end;
