proposition: Lemma sternD_gcd_rec u v i n (S := sternD u v n): i < 2^n -> gcdn (nth 0 S 0) (nth 0 S 1) = gcdn (nth 0 S i)(nth 0 S i.+1).
proof: Proof. elim: i => //i Hrec h1. have sa :0 < i.+1 < 2 ^ n by rewrite h1. by rewrite (Hrec (ltnW h1)) -(sternD_gcd_succ _ _ sa). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)