proposition: Lemma FM_ltce n: (FMc (n.+4)).+1 < FMe (n.+4).
proof: Proof. rewrite ltn_neqAle; apply/andP; split. rewrite FM_rece2 FM_recc2; case (FMe n.+3 + odd n.+3) => // m. rewrite doubleS succnK; apply /negP => /eqP h. by move: (f_equal odd h); rewrite /odd -/odd !odd_double. elim:n => // n HR; move: (HR). have oe: odd (n.+4) = ~~ (odd (n.+3)) by []. rewrite (FM_recc2 n.+4) (FM_rece2 n.+2) FM_recc2 FM_rece2 oe. case: (odd _); rewrite /negb addn0 subn0 addn1 subn1 doubleS. rewrite (doubleS (FMe n.+3).*2) ! succnK !ltnS !ltn_double. by rewrite - doubleS leq_double. case: (FMe n.+3) => // k. by rewrite doubleS !succnK ltnS ltnS => /ltnW h; rewrite ltn_double ltnS. 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)