reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  o1 for operation of U1,
  o2 for operation of U2,
  o3 for operation of U3,
  x,y for set;
reserve a for FinSequence of U1,
  f for Function of U1,U2;

theorem Th8:
  f is_isomorphism implies dom f = the carrier of U1 & rng f
  = the carrier of U2
proof
  assume f is_isomorphism;
  then f is_epimorphism;
  hence thesis by FUNCT_2:def 1;
end;
