proposition: Lemma expRat_half_le_exp_exists : forall d, ~ d == 0 -> exists n, expRat (1/2) n <= d.
proof: Proof. intuition. destruct d. assert (1 <= n)%nat. destruct n. exfalso. eapply H. eapply rat_num_0. lia. exists p. rewrite expRat_terms. eapply leRat_trans. 2:{ eapply leRat_terms. eapply H0. eapply Nat.le_refl. } erewrite expnat_1. eapply leRat_terms. intuition. edestruct p. unfold natToPosnat, posnatToNat. eapply le_expnat_2. Unshelve. eapply expnat_nz. econstructor. destruct p. econstructor. intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms