proposition: Lemma big_mkord : forall n (P : pred nat) F, \big[op/idx]_(0 <= i < n | P i) F i === \big[op/idx]_(i < n | P i) F i.
proof: Proof. move=> n P F; rewrite /index_iota subn0; rewrite <- (big_map (@nat_of_ord n)). apply (reducebig_morph _); try reflexivity; try apply H0. by rewrite /index_enum unlock val_ord_enum. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq div choice fintype finfun paths Setoid Morphisms OperationClasses bigops