
theorem Th13:
  for W being with_non-empty_element set for L being LATTICE holds
  L is Object of W-INF_category iff
  L is strict complete & the carrier of L in W
proof
  let W be with_non-empty_element set;
  ex a being non empty set st a in W by SETFAM_1:def 10;
  hence thesis by Def4;
end;
