Definition nfloor1 x pr := proj1_sig (nfloor1_ex x pr).

(* Specifications: *)
Lemma INRp1_pos : forall n, 0 < INR n + 1.
Lemma Rlt_nat (x : R) : (exists n : nat, x = INR (S n)) -> 0 < x.
Lemma Rle_pow_lin (a : R) (n : nat) : 0 <= a -> 1 + INR n * a <= (1 + a) ^ n.
Lemma C_n_n: forall n, C n n = 1.
Lemma C_n_0: forall n, C n 0 = 1.