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Proof step 1 from proof mod-nls-04 (conclusion)

⊦ i0 - 1 ≤ ~ abs(j) ∧ j ≠ 0 → ¬ i % j < i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i % j < i0, i0 + abs(j) ≤ 1 ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs