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Proof step 18 from proof divides-prime (previous step)

2 ≤ i0 * i, i < 0, i0 < 0, 1 < abs(i0) ∧ abs(i0) < i0 * i → ¬ abs(i0) | i0 * i, ∀ i1. 1 < i1 ∧ i1 < i0 * i → ¬ i1 | i0 * i ⊦ i0 = 0, ~1 = i, i = 0, ~1 = i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
2 ≤ i0 * i, i < 0, i0 < 0, ∀ i1. 1 < i1 ∧ i1 < i0 * i → ¬ i1 | i0 * i, 1 < ~ i0 ∧ ~ i0 < i0 * i → ¬ ~ i0 | i0 * i ⊦ i0 = 0, ~1 = i, i = 0, ~1 = i0

Rule argument

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs