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 Th5:
  id the carrier of U1 is_homomorphism
proof
  thus U1,U1 are_similar;
  let n;
  assume n in dom the charact of(U1);
  let o1,o2 be operation of U1;
  assume
A1: o1=(the charact of U1).n & o2=(the charact of U1).n;
  set f = id the carrier of U1;
  let x be FinSequence of U1;
  assume x in dom o1;
  then o1.x in rng o1 by FUNCT_1:def 3;
  then reconsider u = o1.x as Element of U1;
  f.u = u;
  hence thesis by A1,Th3;
end;
