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 Th3:
  (id the carrier of U1)*a = a
proof
  set f = id the carrier of U1;
A1: dom (f*a) = dom a by FINSEQ_3:120;
A2: now
    let n be Nat;
    assume
A3: n in dom(f*a);
    then reconsider u = a.n as Element of U1 by A1,FINSEQ_2:11;
    f.u = u;
    hence (f*a).n = a.n by A3,FINSEQ_3:120;
  end;
  len (f*a) = len a by FINSEQ_3:120;
  hence thesis by A2,FINSEQ_2:9;
end;
