End BR_FUNEXT.
Section BR_CONSTANTS.
Variable f : nat -> R.
Variable r0 c: R.
Definition br := {{ r0, plus, f}}.

(* Specifications: *)
(* Lemma 6 from paper *)
Lemma add_constant_add_br: forall `{Ring R}  (n: nat),
((toBR c) # n) +
{{r0, plus, f}} # n =
{{(r0 + c), plus, f}} # n.