reserve x, y, i for object,
  L for up-complete Semilattice;
reserve L for complete LATTICE,
  a, b, c for Element of L,
  J for non empty set,
  K for non-empty ManySortedSet of J;
reserve J, K, D for non empty set,
  j for Element of J,
  k for Element of K;
reserve J for non empty set,
  K for non-empty ManySortedSet of J;

theorem Th24: ::Corollary 2.5
  for L being completely-distributive LATTICE holds L is continuous
proof
  let L be completely-distributive LATTICE;
A1: for F being DoubleIndexedSet of K, L st for j being Element of J holds
  rng(F.j) is directed holds Inf Sups F = Sup Infs Frege F by Def3;
  L is complete by Def3;
  hence thesis by A1,Lm9;
end;
