
theorem
  for m,n being Nat st n<m holds nat_interval(m,n)={}
proof
  let m,n be Nat;
  assume
A1: n<m;
  now
    let e be object;
    assume e in nat_interval(m,n);
    then ex i being Nat st e=i & m<=i & i<=n;
    hence contradiction by A1,XXREAL_0:2;
  end;
  hence thesis by XBOOLE_0:def 1;
end;
