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

theorem
  for U0 being with_const_op strict Universal_Algebra holds Bottom (
  UnSubAlLattice(U0)) = GenUnivAlg(Constants(U0))
proof
  let U0 be with_const_op strict Universal_Algebra;
  set L = UnSubAlLattice(U0);
  set C = Constants(U0);
  reconsider G = GenUnivAlg(C) as Element of Sub(U0) by UNIALG_2:def 14;
  reconsider l1 = G as Element of L;
  now
    let l be Element of L;
    reconsider u1 = l as Element of Sub(U0);
    reconsider U2 = u1 as strict SubAlgebra of U0 by UNIALG_2:def 14;
    thus l1 "/\" l = GenUnivAlg(C) /\ U2 by UNIALG_2:def 16
      .= l1 by Th18;
    hence l "/\" l1 = l1;
  end;
  hence thesis by LATTICES:def 16;
end;
