reserve U0 for Universal_Algebra,
  U1 for SubAlgebra of U0,
  o for operation of U0;

theorem Th20:
  for U0 being with_const_op strict Universal_Algebra for U1 be
  SubAlgebra of U0 for H be Subset of U0 st H = the carrier of U0 holds
  GenUnivAlg(H) "\/" U1 = GenUnivAlg(H)
proof
  let U0 be with_const_op strict Universal_Algebra;
  let U1 be SubAlgebra of U0, H be Subset of U0;
  assume H = the carrier of U0;
  then H \/ the carrier of U1 = H by Th3,XBOOLE_1:12;
  hence thesis by UNIALG_2:20;
end;
