Proof
fun H : E_1 = E_0
=> distinct_0_1 (eq_sym H).
(** A predicate that accepts one element, x, and asserts that x is nonzero. *)
Definition nonzero
: E -> Prop
:= Ring.nonzero ring.

(** Proves that 0 is the right identity element. *)
Theorem sum_id_r
:  sum_is_id_r 0.