proposition: Lemma big_fsetID (B : pred I) (A : {fset I}) (F : I -> R) : \big[op/idx]_(i <- A) F i = op (\big[op/idx]_(i <- [fset x in A | B x]) F i) (\big[op/idx]_(i <- [fset x in A | ~~ B x]) F i).
proof: Proof. by rewrite !big_fset; apply: bigID. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop)