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 implies X \ Y [= Z
proof
  assume X [= Y "\/" Z;
  then X "/\" Y` [= (Y "\/" Z) "/\" Y` by LATTICES:9;
  then X "/\" Y` [= (Y "/\" Y`) "\/" (Z "/\" Y`) by LATTICES:def 11;
  then
A1: X \ Y [= Bottom L "\/" (Z "/\" Y`) by LATTICES:20;
  Z "/\" Y` [= Z by LATTICES:6;
  hence thesis by A1,LATTICES:7;
end;
