proposition: Lemma has_big_cat (p : pred B) xs f : has p (\big[cat/[::]]_(x <- xs) f x) = has (fun x => has p (f x)) xs.
proof: Proof. elim: xs=>[|x xs IH]; first by rewrite big_nil. by rewrite big_cons has_cat /= IH. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat seq path eqtype choice bigop) pcm(options prelude pred)