reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;

theorem Th18:
  b <> {} implies a hcf b <> {} & b div^ (a hcf b) <> {}
proof
  a hcf b divides b by Def5;
  then b = (a hcf b)*^(b div^ (a hcf b)) by Th7;
  hence thesis by ORDINAL2:35;
end;
