-theorem nplus_mono: \forall p,q,r1. (p + q == r1) \to
- \forall r2. (p + q == r2) \to r1 = r2.
- intros 4. elim H; clear H q r1;
- [ lapply linear nplus_gen_zero_2 to H1
- | lapply linear nplus_gen_succ_2 to H3. decompose
- ]; subst; auto.
+theorem nplus_mono: ∀p,q,r1. p ⊕ q ≍ r1 →
+ ∀r2. p ⊕ q ≍ r2 → r1 = r2.
+ intros 4; elim H; clear H q r1;
+ [ lapply linear nplus_inv_zero_2 to H1
+ | lapply linear nplus_inv_succ_2 to H3. decompose
+ ]; destruct; autobatch.