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 misses Y implies (X "\/" Y) \ Y = X
proof
  assume X "/\" Y = Bottom L;
  then X` "\/" (X "/\" Y) = X`;
  then (X` "\/" X) "/\" (X` "\/" Y) = X` by LATTICES:11;
  then Top L "/\" (X` "\/" Y) = X` by LATTICES:21;
  then (X` "\/" Y)` = X;
  then
A1: X`` "/\" Y` = X by LATTICES:24;
  (X "\/" Y) \ Y = (X "/\" Y`) "\/" (Y "/\" Y`) by LATTICES:def 11
    .= (X "/\" Y`) "\/" Bottom L by LATTICES:20
    .= X "/\" Y`;
  hence thesis by A1;
end;
