proposition: Lemma inv_INR_fact_pos : forall n, (/INR (fact n)) > 0.
proof: Proof. intros n. assert (INR (fact n) > 0). induction n. simpl. lra. simpl. rewrite plus_INR. replace 0 with (0 + 0) by intuition. apply Rplus_gt_ge_compat. apply IHn. intuition. apply Rinv_0_lt_compat. intuition. Qed.
imports: PeanoNat Rseries_facts Rsequence_facts Rsequence_subsequence Rpser_usual Reals Rsequence_tactics Rtactic Lra