+theorem nplus_ass: \forall p1, p2, r1. (p1 + p2 == r1) \to
+ \forall p3, s1. (r1 + p3 == s1) \to
+ \forall r3. (p2 + p3 == r3) \to
+ \forall s3. (p1 + r3 == s3) \to s1 = s3.
+ intros 4. elim H; clear H p2 r1;
+ [ lapply linear nplus_inv_zero_1 to H2. subst.
+ lapply nplus_mono to H1, H3. subst. autobatch
+ | lapply linear nplus_inv_succ_1 to H3. decompose. subst.
+ lapply linear nplus_inv_succ_1 to H4. decompose. subst.
+ lapply linear nplus_inv_succ_2 to H5. decompose. subst. autobatch
+ ].
+qed.
+