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 \ X implies X = Bottom L
proof
A1: X "/\" (Y "/\" X`) = Y "/\" (X` "/\" X) by LATTICES:def 7
    .= Y "/\" Bottom L by LATTICES:20
    .= Bottom L;
  assume X [= Y \ X;
  hence thesis by A1,LATTICES:4;
end;
