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;

theorem ::Theorem 2.3 (1) iff (2)
  L is continuous iff for J, K 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 Lm8,Lm9;
