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 "/\" (Y \ Z) = X "/\" Y \ X "/\" Z
proof
  X "/\" Y \ X "/\" Z = ((X "/\" Y) \ X) "\/" ((X "/\" Y) \ Z) by Th42
    .= Bottom L "\/" ((X "/\" Y) \ Z) by Th29,LATTICES:6
    .= (X "/\" Y) \ Z;
  hence thesis by LATTICES:def 7;
end;
