proposition: Theorem ratHalf_ne_0 : forall r, ~ r == 0 -> ~ (ratHalf r) == 0.
proof: Proof. intuition. unfold ratHalf in *. apply ratMult_0 in H0. destruct H0; intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms