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

0 ≤ i1, 0 ≤ j0, j0 < j, 0 ≤ i0, 0 < 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:
0 ≤ i1, 0 ≤ j0, j0 < j, 0 ≤ i0, 0 < 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