reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;

theorem Th23:
  for B1,B2 being set st B1 <N< B2 holds B1/\B2/\NAT={}
proof
  let B1,B2 be set;
  assume
A1: B1 <N< B2;
  now
    set x =the  Element of B1/\B2/\NAT;
    reconsider nx=x as Nat;
    assume B1/\ B2/\NAT <> {};
    then
A2: x in B1/\B2 by XBOOLE_0:def 4;
    then
A3: nx in B2 by XBOOLE_0:def 4;
    nx in B1 by A2,XBOOLE_0:def 4;
    hence contradiction by A1,A3;
  end;
  hence thesis;
end;
