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

theorem Th5:
  a divides b iff ex c st b = a*^c
proof
  thus a divides b implies ex c st b = a*^c
  proof
    given c being Ordinal such that
A1: b = a*^c;
    per cases;
    suppose
      b = {};
      then b = a*^{} by ORDINAL2:38;
      hence thesis;
    end;
    suppose
      b <> {};
      then c is Element of omega by A1,ORDINAL3:75;
      hence thesis by A1;
    end;
  end;
  thus thesis;
end;
