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
  U1,U1 are_isomorphic
proof
  set i = id the carrier of U1;
  i is_homomorphism & rng i = the carrier of U1 by Th5;
  then i is_isomorphism by Th7;
  hence thesis;
end;
