proposition: Lemma leq_prod I r (P : pred I) (E1 E2 : I -> nat) : (forall i, P i -> E1 i <= E2 i) -> \prod_(i <- r | P i) E1 i <= \prod_(i <- r | P i) E2 i.
proof: Proof. by move=> leE12; elim/big_ind2: _ => // m1 m2 n1 n2; apply: leq_mul. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)