proposition: Lemma mult_compat : forall n p, FS n * FS p = FS (n * p + n + p)%nat.
proof: Proof. cbn; intros; f_equal; ring. 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)