reserve F for Field;
reserve VS for strict VectSp of F;
reserve u,e for set;
reserve x for set;
reserve Z1 for set;

theorem
  for L1,L2 being Lattice for f being Function of the carrier of L1, the
  carrier of L2 holds f is Homomorphism of L1, L2 iff f is
  sup-Semilattice-Homomorphism of L1, L2 & f is Semilattice-Homomorphism of L1,
  L2;
