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Proof step 17 from proof nummult-le-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
i * (i1 + 1) + j0 < i, j0 < i, 0 < i, abs(j0) < i, i * (i1 + 1) + j0 ≤ 0, j0 ≤ 0, i0 ≤ i1, i * (i1 + 1) + j0 ≤ i * i0 ⊦ i = i * (i1 + 1) + j0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)