
theorem Th3:
  EvenNAT is denumerable
  proof
    now
      let m be Nat;
      reconsider n = 2 * m as Nat;
      now
        1 * m <= 2 * m by NAT_1:4;
        hence n >= m;
        thus n in EvenNAT by FIB_NUM2:def 3;
      end;
      hence ex n be Nat st n >= m & n in EvenNAT;
    end;
    then EvenNAT is infinite by PYTHTRIP:9;
    hence thesis;
  end;
