reserve UA for Universal_Algebra,
  f, g for Function of UA, UA;

theorem Th1:
  id the carrier of UA is_isomorphism
proof
  set I = id the carrier of UA;
  I is_homomorphism by ALG_1:5;
  hence I is_monomorphism;
  I is_homomorphism & rng I = the carrier of UA by ALG_1:5,RELAT_1:45;
  hence I is_epimorphism;
end;
