proposition: Lemma S_INR : forall {R : ConstructiveReals} (n:nat), INR (S n) == @INR R n + 1.
proof: Proof. intros R n. unfold INR. rewrite <- CR_of_Q_plus. apply CR_of_Q_morph. rewrite Qinv_plus_distr. unfold Qeq, Qnum, Qden. do 2 rewrite Z.mul_1_r. fold (1 + n)%nat. rewrite (Nat2Z.inj_add 1 n). rewrite Z.add_comm. reflexivity. Qed.
imports: List Permutation Orders Sorted Mergesort QArith Qpower ConstructiveReals ConstructiveAbs ConstructiveMinMax ConstructiveSum ConstructivePower ConstructiveLimits ConstructiveDiagonal