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;

theorem
  X misses Y implies (Z "/\" X) misses (Z "/\" Y)
proof
  assume
A1: X misses Y;
  (Z "/\" X) "/\" (Z "/\" Y) = Z "/\" (X "/\" (Y "/\" Z)) by LATTICES:def 7
    .= Z "/\" ((X "/\" Y) "/\" Z) by LATTICES:def 7
    .= Z "/\" Bottom L by A1
    .= Bottom L;
  hence thesis;
end;
