Used simplifier rules: le-def: ⊦ i ≤ j ↔ ¬ j < i;%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0);% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)