Proof conj prod_sum_distrib_l prod_sum_distrib_r.

(* Specifications: *)
(** Proves that 0 times every number equals 0.  0 x = 0 x (0 + 0) x = 0 x 0 x + 0 x = 0 x 0 x = 0 *)
Theorem prod_0_l
:  forall x : E, 0 # x = 0.