proposition: Lemma big_cat_nested : forall r1 r2 (P : pred I) F, let x := \big[op/idx]_(i <- r2 | P i) F i in \big[op/idx]_(i <- r1 ++ r2 | P i) F i === \big[op/x]_(i <- r1 | P i) F i.
proof: Proof. by move=> r1 r2 P F; rewrite /reducebig foldr_cat; reflexivity. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq div choice fintype finfun paths Setoid Morphisms OperationClasses bigops