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.

(* Lemma 7 *)
(* Here is where I need a module :( nat -> R forms a module over R *)
Lemma mul_constant_add_br: forall `{Ring R} (n: nat),
((toBR c) # n) * ((mkBR r0 plus f) # n) =
(mkBR (c * r0) plus (scaleLoopVariantFn c f)) # n.