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

theorem Th14:
  a hcf {} = a & a lcm {} = {}
proof
  reconsider e = a, c = {} as Element of omega by ORDINAL1:def 12;
A1: for b st a divides b & {} divides b holds c divides b;
  ( for n st n divides a & n divides {} holds n divides e)& a divides c by Th9;
  hence thesis by A1,Def4,Def5;
end;
