proposition: Theorem ratAdd_nz : forall r1 r2, ~(r1 + r2 == 0) <-> (~r1 == 0) \/ (~r2 == 0).
proof: Proof. intuition. destruct (eq_Rat_dec r1 0); intuition. destruct (eq_Rat_dec r2 0); intuition. exfalso. eapply H. apply ratAdd_0; eauto. apply H1. specialize (ratAdd_0 r1 r2); intuition. apply H1. specialize (ratAdd_0 r1 r2); intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms