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Proof step 8 from proof div-add-neg (previous step)

i2 < j, 1 + i2 * j < j, i2 ≤ 0, i2 < 0, j0 < j, i1 * j + j0 < j, (i1 * j + j0) + 1 < j, j0 ≤ 0, abs(j0) < j, 0 < j, i1 * j + j0 < 0, i2 + 1 < j ⊦ (j * (i2 + i1) + j0) / j = i1 + i2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i * j = j * i
Proof step 10:
i2 < j, 1 + i2 * j < j, i2 ≤ 0, i2 < 0, j0 < j, i1 * j + j0 < j, (i1 * j + j0) + 1 < j, j0 ≤ 0, abs(j0) < j, 0 < j, i1 * j + j0 < 0, i2 + 1 < j ⊦ ((i2 + i1) * j + j0) / j = i1 + i2

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [i2 + i1, j] flags: rewrite

Additional information

Used terms: i2 + i1, j