proposition: Lemma big_catr : forall r1 r2 (P : pred I) F, ~~ has P r1 -> \big[op/idx]_(i <- r1 ++ r2 | P i) F i === \big[op/idx]_(i <- r2 | P i) F i.
proof: Proof. move=> r1 r2 P F; rewrite <- big_filter, <- (big_filter r2), filter_cat. by rewrite has_count count_filter; case: filter; try reflexivity. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq div choice fintype finfun paths Setoid Morphisms OperationClasses bigops