
theorem Th2:
  for L, S, T being complete non empty Poset, f being
  CLHomomorphism of L, S, g being CLHomomorphism of S, T holds g*f is
  CLHomomorphism of L, T
proof
  let L, S, T be complete non empty Poset, f be CLHomomorphism of L, S, g be
  CLHomomorphism of S, T;
  f is directed-sups-preserving & g is directed-sups-preserving by
WAYBEL16:def 1;
  then
A1: g*f is directed-sups-preserving by WAYBEL20:28;
  f is infs-preserving & g is infs-preserving by WAYBEL16:def 1;
  then g*f is infs-preserving by WAYBEL20:25;
  hence thesis by A1,WAYBEL16:def 1;
end;
