(* complement for x *+ n and <= or < *)

Lemma ltr_prod I r (P : pred I) (E1 E2 : I -> R) :
has P r -> (forall i, P i -> 0 <= E1 i < E2 i) ->
\prod_(i <- r | P i) E1 i < \prod_(i <- r | P i) E2 i.