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 \+\ (X "/\" Y) = X \ Y
proof
  X \+\ (X "/\" Y) = (X "/\" (X "/\" Y)`) "\/" (Y "/\" (X "/\" X`)) by
LATTICES:def 7
    .= (X "/\" (X "/\" Y)`) "\/" (Y "/\" Bottom L) by LATTICES:20
    .= X "/\" (X` "\/" Y`) by LATTICES:23
    .= (X "/\" X`) "\/" (X "/\" Y`) by LATTICES:def 11
    .= Bottom L "\/" (X "/\" Y`) by LATTICES:20
    .= X "/\" Y`;
  hence thesis;
end;
