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Proof step 4 from proof modeq-pos-02 (previous step)

0 ≤ j1, j1 < j, 0 ≤ i1 + i0, 0 ≤ i1, 0 < j ⊦ (j * (i1 + i0) + j1) % j = j1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i * j = j * i
Proof step 6:
0 ≤ j1, j1 < j, 0 ≤ i1 + i0, 0 ≤ i1, 0 < j ⊦ ((i1 + i0) * j + j1) % j = j1

Rule argument

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

Additional information

Used terms: i1 + i0, j