proposition: Lemma idem_sub_le_big_cond (I : eqType) s s' P P' (F : I -> R) : {subset [seq i <- s | P i] <= [seq i <- s' | P' i]} -> le (\big[op/x]_(i <- s | P i) F i) (\big[op/x]_(i <- s' | P' i) F i).
proof: Proof. by move=> /(idem_sub_le_big xpredT F); rewrite !big_filter. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)