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

theorem
  a[x]b,b[x]a are_isomorphic
proof
  thus Hom(a[x]b,b[x]a)<>{} & Hom(b[x]a,a[x]b)<>{} by Th31;
  take Switch(a,b), Switch(b,a);
  thus thesis by Th32;
end;
