proposition: Lemma big_cat_int n m p (P : pred int) F : m <= n -> n <= p -> \big[op/idx]_(m <= i < p :> int | P i) F i = op (\big[op/idx]_(m <= i < n :> int | P i) F i) (\big[op/idx]_(n <= i < p :> int | P i) F i).
proof: Proof. by move=> le_mn le_np; rewrite -big_cat /= index_iotaz_add. Qed.
imports: mathcomp(all_ssreflect all_algebra) extra_mathcomp