i0 = j + i0, ∀ j. i0 = i0 + j → j = 0 ⊦ j = 0
Used simplifier rules: add-pred: ⊦ i + j -1 = (i + j)-1;%add-a: ⊦ i + j + i0 = (i + j) + i0;%add-c: ⊦ i + j = j + i;% ⊦ i -1 = j -1 ↔ i = j; (s)