fact: Definition carry_reduce n (s:Z) (c:list (Z * Z)) (index:nat) (p : list Z) := from_associational n (Associational.reduce s c (to_associational (S n) (@carry n (S n) index p))).
imports: Coq.ZArith.ZArith Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.QArith.QArith_base Coq.QArith.Qreduction Coq.QArith.Qround