Used simplifier rules: lrec: ⊦ m +1 < n +1 ↔ m < n;%ref-1: ⊦ ¬ n < n;%neq-01: ⊦ m ≠ n → (¬ m < n ↔ n < m);%s: ⊦ m < n +1 ↔ ¬ n < m;