
theorem Th4:
  OddNAT is denumerable
  proof
    now
      let m be Nat;
      reconsider n = 2 * m + 1 as Element of NAT by ORDINAL1:def 12;
      now
        1 * m <= 2 * m by NAT_1:4;
        hence n >= m by NAT_1:12;
        m is Element of NAT by ORDINAL1:def 12;
        hence n in OddNAT by FIB_NUM2:def 4;
      end;
      hence ex n be Nat st n >= m & n in OddNAT;
    end;
    then OddNAT is infinite by PYTHTRIP:9;
    hence thesis;
  end;
