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Proof step 17 from proof ls-def (previous step)

¬ i0 * j ≤ i * j0, i * j0 = i1 + i0 * j, 0 < j, 0 < j0 ⊦ i1 < 0, j0 = 0, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
i * j0 = i1 + i0 * j, 0 < j, 0 < j0, i * j0 < i0 * j, 0 ≤ i1 ⊦ j0 = 0, j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i * j = j * i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;