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