proposition: Lemma lt_plus_r: forall {a b c : T1} {n:nat}, ~ lt (a + cons b n c) a.
proof: Proof. induction a; simpl; intros * H. - now apply not_lt_zero in H. - compare destruct a1 b as Hcomp. + apply lt_inv_coeff in H; lia. + now apply lt_inv_head, le_not_gt in H. + now apply lt_inv_tail, IHa2 in H. 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)