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 Th36:
  (X "/\" Y) "\/" (X \ Y) = X
proof
  (X "/\" Y) "\/" (X \ Y) =((X "/\" Y) "\/" X) "/\" ((X "/\" Y) "\/" Y`)
  by LATTICES:11
    .= X "/\" ((X "/\" Y) "\/" Y`) by LATTICES:def 8
    .= X "/\" ((X "\/" Y`) "/\" (Y "\/" Y`)) by LATTICES:11
    .= X "/\" ((X "\/" Y`) "/\" Top L) by LATTICES:21
    .= X by LATTICES:def 9;
  hence thesis;
end;
