proposition: Lemma big_distrlr I J rI rJ (pI : pred I) (pJ : pred J) F G : (\big[+%M/0]_(i <- rI | pI i) F i) * (\big[+%M/0]_(j <- rJ | pJ j) G j) = \big[+%M/0]_(i <- rI | pI i) \big[+%M/0]_(j <- rJ | pJ j) (F i * G j).
proof: Proof. by rewrite big_distrl; under eq_bigr do rewrite big_distrr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)