
theorem
  for m,n,k being Nat holds k in nat_interval(m,n) iff m<=k & k<=n
proof
  let m,n,k be Nat;
  hereby
    assume k in nat_interval(m,n);
    then ex i being Nat st k=i & m<=i & i<=n;
    hence m<=k & k<=n;
  end;
  assume m <= k & k <= n;
  hence thesis;
end;
