
theorem
  for S,T being upper-bounded Semilattice
  for f being SemilatticeHomomorphism of S,T holds f.Top S = Top T
proof
  let S, T be upper-bounded Semilattice;
  let f be SemilatticeHomomorphism of S,T;
A1: f preserves_inf_of {}S by Def1;
  ex_inf_of {}S,S by YELLOW_0:43;
  then f.inf {}S = inf (f.:{}S) by A1;
  hence thesis;
end;
