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 "/\" Z = Bottom L implies X [= Y
proof
  assume that
A1: X [= (Y "\/" Z) and
A2: X "/\" Z = Bottom L;
  X "/\" (Y "\/" Z) = X by A1,LATTICES:4;
  then (X "/\" Y) "\/" Bottom L = X by A2,LATTICES:def 11;
  hence thesis by LATTICES:4;
end;
