proposition: Lemma coeff_lt : forall alpha n n' beta beta', (n < n')%nat -> lt (cons alpha n beta) (cons alpha n' beta').
proof: Proof. unfold lt. intros * H. rewrite compare_cons. rewrite compare_refl. now apply Nat.compare_lt_iff in H as ->. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)