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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i * j = j * i
Proof step 10:
i0 * j + j0 < j, j0 < j, i1 + 1 < j, 0 < j, i0 * j + j0 < 0, 1 + i1 * j < j, i1 ≤ 0, i1 < 0, i1 < j, abs(j0) < j, j0 ≤ 0, (i0 * j + j0) + 1 < j ⊦ ((i1 + i0) * j + j0) % j = j0

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [i1 + i0, j] flags: rewrite

Additional information

Used terms: i1 + i0, j