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Proof step 7 from proof natpos (previous step)

i→n(i0 * j) + i→n(j0) = m0 * i→n(j) + n0, n0 < i→n(j), j0 < j, 0 < j, 0 ≤ i0, 0 ≤ i0 * j, 0 ≤ j0 ⊦ j = 0, m0 = i→n(i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i→n(i0 * j) + i→n(j0) = m0 * i→n(j) + n0, 0 < j, j0 < j, n0 < i→n(j), 0 ≤ j0, 0 ≤ i0 ⊦ j = 0, m0 = i→n(i0)

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)