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Proof step 11 from proof ls-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i * j0 = i1 + i0 * j, 0 < j, 0 < j0 ⊦ j0 = 0, j = 0, i1 < 0 ↔ ¬ i0 * j ≤ i * j0

Rule argument

Additional information

Used simplifier rules: ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j = j * i;