theorem Th56:
  k in GreaterOrEqualsNumbers(n) iff n <= k
  proof
    thus k in GreaterOrEqualsNumbers(n) implies n <= k
    proof
      assume k in GreaterOrEqualsNumbers(n);
      then not k in Segm n by XBOOLE_0:def 5;
      hence thesis by NAT_1:44;
    end;
A1: k in NAT by ORDINAL1:def 12;
    assume n <= k;
    then not k in Segm n by NAT_1:44;
    hence thesis by A1,XBOOLE_0:def 5;
  end;
