Proof
fun x H y z H0 H1
=> let H2
:  z + x = y + x
:= H1 || z + x = a @a by H0 in
let H3
:  z = y
:= op_cancel_r z y x H H2 in
H3.

(** Proves that an element's right inverse is unique. *)
Theorem op_inv_r_uniq
:  forall x : M, has_inv_l x -> forall y z : M, op_is_inv_r x y -> op_is_inv_r x z -> z = y.