proposition: Lemma fusc_monotone n: odd n -> n = 1 \/ fusc n.+1 < fusc n.
proof: Proof. move => on; rewrite (oddE on) - doubleS fusc_even fusc_odd. by case:(n./2) ; [ left | move => k; right; rewrite ltn_paddl // fusc_gt0 ]. 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)