proposition: Lemma leqif_sum (I : finType) (P C : pred I) (E1 E2 : I -> nat) : (forall i, P i -> E1 i <= E2 i ?= iff C i) -> \sum_(i | P i) E1 i <= \sum_(i | P i) E2 i ?= iff [forall (i | P i), C i].
proof: Proof. move=> leE12; rewrite -big_andE. by elim/big_rec3: _ => // i Ci m1 m2 /leE12; apply: leqif_add. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)