reserve x, y, i for object,
  L for up-complete Semilattice;

theorem ::Theorem 2.1 (1) iff (2)
  L is continuous iff for x being Element of L holds waybelow x is Ideal
  of L & x <= sup waybelow x & for I being Ideal of L st x <= sup I holds
  waybelow x c= I by Lm1,Lm2;
