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,U2 are_isomorphic & U2,U3 are_isomorphic implies U1,U3 are_isomorphic
proof
  assume U1,U2 are_isomorphic;
  then consider f such that
A1: f is_isomorphism;
  assume U2,U3 are_isomorphic;
  then consider g be Function of U2,U3 such that
A2: g is_isomorphism;
  g * f is_isomorphism by A1,A2,Th11;
  hence thesis;
end;
