
theorem
  for S being compact Hausdorff TopLattice st for x being Element of S
  holds x"/\" is continuous holds S is meet-continuous
proof
  let S be compact Hausdorff TopLattice;
  assume
A1: for x being Element of S holds x "/\" is continuous;
  then
  for N being net of S st N is eventually-directed holds ex_sup_of N & sup
  N in Lim N by Th38;
  hence thesis by A1,Th37;
end;
