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 implies Y = X "\/" (Y \ X)
proof
  assume
A1: X [= Y;
  Y = Y "/\" Top L
    .= Y "/\" ( X "\/" X`) by LATTICES:21
    .= (Y "/\" X) "\/" ( Y "/\" X`) by LATTICES:def 11
    .= X "\/" (Y \ X) by A1,LATTICES:4;
  hence thesis;
end;
