proposition: Lemma bigID I r (a P : pred I) F : \big[*%M/1]_(i <- r | P i) F i = \big[*%M/1]_(i <- r | P i && a i) F i * \big[*%M/1]_(i <- r | P i && ~~ a i) F i.
proof: Proof. exact/bigID_idem/mul1m. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)