proposition: Lemma succ_is_plus_one (a : T1) : succ a = a + 1.
proof: Proof. induction a as [ |a IHa n b IHb]; [trivial |]. - destruct a; cbn. + now rewrite <- plus_n_O. + rewrite IHb; f_equal. 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)