proposition: Lemma sternD_nth_compare_strict u v n i (S := (sternD u v n.+1)) : 0 < u -> 0 < v -> i < 2^n -> maxn (nth 0 S (i.*2)) (nth 0 S (i.*2.+2)) < nth 0 S (i.*2.+1).
proof: Proof. move=> ap bp h. move: (sternD_nth_odd u v h); rewrite - doubleS ! sternD_nth_even => ->. move: (sternD_positive ap bp (ltnW h)) (sternD_positive ap bp h) => sa sb. by rewrite gtn_max ltn_paddl // ltn_paddr. 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)