proposition: Lemma sorted_ggenS s : all even s -> sorted gtn s -> sorted ggen s.
proof: Proof. case: s => // n s; elim: s n => //= m s Ihs n /andP [on ha] /andP [lnm hb]. rewrite Ihs //; case/andP:ha => /negbTE => om _; move: lnm. by rewrite (evenE(negbTE on)) (evenE om) - doubleS leq_double ltn_double andbT. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)