proposition: Lemma fusc_is_even n: (odd (fusc n)) = (n %%3 !=0).
proof: Proof. have lt3 : 0 < 3 by []. elim/fusc_ind:n => //. move => n Hr; rewrite fusc_even Hr -addnn - modnDm. by move: (ltn_pmod n lt3); case (n %% 3) => // [] [] // []. move => n Hr1 Hr2; rewrite fusc_odd oddD Hr1 Hr2 -addnn -addnS -modnDm. rewrite - (add1n n) - modnDm. move: (ltn_pmod n lt3); case (n %% 3) => // [] [] // [] //. 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)