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;

theorem
  X meets Y \ Z implies X meets Y
proof
  assume X meets Y \ Z;
  then X "/\" (Y \ Z) <> Bottom L;
  then X "/\" Y "/\" Z` <> Bottom L by LATTICES:def 7;
  then X "/\" Y <> Bottom L;
  hence thesis;
end;
