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 \+\ Y) "\/" (X "/\" Y)
proof
  thus X "\/" Y = (Y \ X) "\/" X by Th35
    .= (Y \ X) "\/" ((X \ Y) "\/" (X "/\" Y)) by Th36
    .= (X \+\ Y) "\/" (X "/\" Y) by LATTICES:def 5;
end;
