reserve L for D_Lattice;
reserve a, b, c for Element of L;
reserve L for B_Lattice;
reserve a, b for Element of L;

theorem Th23:
  b"/\"a = Bottom L iff b [= a`
proof
  thus b"/\"a = Bottom L implies b [= a`
  proof
    assume
A1: b"/\"a = Bottom L;
    b = b"/\"Top L
      .= b"/\"(a"\/"a`) by Th19
      .= Bottom L"\/"(b"/\"a`) by A1,Def11
      .= b"/\"a`;
    then b"\/"a` = a` by Def8;
    hence thesis;
  end;
  thus thesis
  proof
    assume b [= a`;
    then b"/\"a [= a`"/\"a by Th7;
    then
A2: b"/\"a [= Bottom L by Th18;
    Bottom L [= b"/\"a;
    hence thesis by A2,Th6;
  end;
end;
