
theorem Th14:
  for C being Coherence_Space, A being c=directed Subset of C
  holds union A in C
proof
  let C be Coherence_Space, A be c=directed Subset of C;
  now
    let a,b be set;
    assume a in A & b in A;
    then ex c being set st a \/ b c= c & c in A by Th5;
    hence a \/ b in C by CLASSES1:def 1;
  end;
  hence thesis by Def1;
end;
