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Proof step 7 from proof nummult-le-03 (previous step)

i1 * i + j0 ≤ i * i0, i1 * i + j0 < i, i1 * i + j0 < 0, j0 < i, j0 ≤ 0, (i1 * i + j0) + 1 < i, 0 < i, abs(j0) < i ⊦ i1 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i1 * i + j0 ≤ i * i0, i1 * i + j0 < i, i1 * i + j0 < 0, j0 < i, j0 ≤ 0, (i1 * i + j0) + 1 < i, 0 < i, abs(j0) < i, i0 < i1 ⊦

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs