
theorem :: 1.8. COROLLARY, (1) => (3), p. 182
  for L being complete LATTICE, c being closure Function of L,L holds
  Image c is directed-sups-inheriting implies corestr c is waybelow-preserving
proof
  let L be complete LATTICE, c be closure Function of L,L;
  assume Image c is directed-sups-inheriting;
  then inclusion c is directed-sups-preserving infs-preserving by Th35,Th36;
  then LowerAdj inclusion c is waybelow-preserving by Th22;
  hence thesis by Th35;
end;
