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;

theorem ::Theorem 2.3 (1) iff (2')
  L is continuous iff for J, K being non empty set for F being Function
of [:J, K:], the carrier of L st for j being Element of J holds rng((curry F).j
  ) is directed holds Inf Sups curry F = Sup Infs Frege curry F by Lm8,Lm10;
