Section BR_CONSTANTS.
Variable f : nat -> R.
Variable r0 c: R.
Definition br := {{ r0, plus, f}}.
Hint Resolve add_constant_add_br : Recurrence.
Hint Rewrite @add_constant_add_br : Recurrence.
Hint Resolve mul_constant_add_br : Recurrence.
Hint Rewrite @mul_constant_add_br : Recurrence.

(* (* Lemma 8 *)
Lemma pow_constant_add_br: forall `{Ring R} (n: nat),
pow_N c ((mkBR r0 plus f) # n) =
(mkBR (pow_N c r0) mult (fun n => pow_N c (f # n))) # n.