proposition: Lemma doubleS_inj: injective (fun z => z.*2.+1).
proof: Proof. apply: inj_comp succn_inj double_inj. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)