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

theorem Th8:
  EvenNAT \/ OddNAT = NAT
  proof
    thus EvenNAT \/ OddNAT c= NAT;
    let n be object;
    assume A1: n in NAT & not n in (EvenNAT \/ OddNAT);
    then reconsider n as Nat;
    n in NAT & not n in EvenNAT & not n in OddNAT by A1, XBOOLE_0:def 3;
    then not n is even & not n is odd;
    hence contradiction;
  end;
