proposition: Lemma big_cond_seq : forall (I : eqType) r (P : pred I) F, \big[op/idx]_(i <- r | P i) F i === \big[op/idx]_(i <- r | P i && (i \in r)) F i.
proof: Proof. move=> I r P F; rewrite <- !(big_filter r). apply congr_big=> [|i|]; try reflexivity. by apply: eq_in_filter => i ->; rewrite andbT. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq div choice fintype finfun paths Setoid Morphisms OperationClasses bigops