theorem :: VECTSP_8:11

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 ) ) ;