proposition: Lemma lucas_is_even_mod3 n: odd (lucas n) = (n %%3 !=0).
proof: Proof. rewrite - fib_is_even_mod3; case:n => // n. by rewrite lucasS oddD odd_double addbF. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)