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Proof step 13 from proof nummult-le-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 14:
i * i0 < i * (i1 + 1) + j0, j0 ≤ 0, abs(j0) < i, i * (i1 + 1) + j0 ≤ 0, 0 < i, j0 < i, i * (i1 + 1) + j0 < i ⊦ ¬ i1 < i0, i = i * (i1 + 1) + j0
Proof step 17:
¬ i1 < i0, j0 ≤ 0, abs(j0) < i, i * (i1 + 1) + j0 ≤ 0, 0 < i, j0 < i, i * (i1 + 1) + j0 < i ⊦ i * i0 < i * (i1 + 1) + j0, i = i * (i1 + 1) + j0

Rule argument

pos: right 1

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