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