Used simplifier rules: psh-03: ⊦ m ≠ 0 → (m -1 = n ↔ m = n +1);%succ: ⊦ m +1 = m + 1;%eq-01: ⊦ m + n = m + n0 ↔ n = n0;%a: ⊦ (m + n0) + n1 = m + n0 + n1;%c: ⊦ m + n = n + m;