reserve L for Lattice;
reserve X,Y,Z,V for Element of L;
reserve L for D_Lattice;
reserve X,Y,Z for Element of L;
reserve L for 0_Lattice;
reserve X,Y,Z for Element of L;
reserve L for B_Lattice;
reserve X,Y,Z,V for Element of L;

theorem
  X "\/" Y = (X \ Y) "\/" Y
proof
  thus X "\/" Y = (X "\/" Y) "/\" Top L
    .= (X "\/" Y) "/\" (Y` "\/" Y) by LATTICES:21
    .= (X \ Y) "\/" Y by LATTICES:11;
end;
