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Proof step 11 from proof div-le-same-neg (previous step)

i0 * (i1 + 1) + j0 < 0, j0 ≤ 0, i0 ≤ 0, abs(j0) ≤ i1, 0 ≤ i1 ⊦ 0 ≤ i1 * i0 + j0 ↔ i0 * (i1 + 1) + j0 = 0 ∨ 0 = i1, i1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i0 * (i1 + 1) + j0 < 0, i0 < i1, j0 < i1, 0 < i1, abs(j0) ≤ i1, i0 ≤ 0, j0 ≤ 0 ⊦ 0 ≤ i1 * i0 + j0 ↔ i0 * (i1 + 1) + j0 = 0, i1 = 0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)