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Proof step 16 from proof i2np (previous step)

0 ≤ j, 0 ≤ i1, 0 ≤ j → i→n(j) * i→n(i1) + i→n(j) = i→n((i1 + 1) * j), ∀ j0. 0 ≤ j0 → i→n(j0) * i→n(i1) + i→n(j0) = i→n((i1 + 1) * j0) ⊦ i→n(i1) * i→n(j) = i→n(i1 * j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
i→n(j) * i→n(i1) + i→n(j) = i→n((i1 + 1) * j), 0 ≤ j, 0 ≤ i1, ∀ j0. 0 ≤ j0 → i→n(j0) * i→n(i1) + i→n(j0) = i→n((i1 + 1) * j0) ⊦ i→n(i1) * i→n(j) = i→n(i1 * j)

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs