reserve n,k,b for Nat, i for Integer;

theorem Th7:
  EvenNAT misses OddNAT
  proof
    thus EvenNAT /\ OddNAT c= {}
    proof
      let n be object;
      assume n in EvenNAT /\ OddNAT;
      then A1: n in EvenNAT & n in OddNAT by XBOOLE_0:def 4;
      consider e being Nat such that
      A2: e=n & e is even by A1;
      consider o being Nat such that
      A3: o=n & o is odd by A1;
      thus thesis by A2,A3;
    end;
    thus {} c= EvenNAT /\ OddNAT by XBOOLE_1:2;
  end;
