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Proof step 5 from proof modeq-pos-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i * j = j * i
Proof step 7:
0 < j, j1 < j, 0 ≤ i1 + i0, 0 ≤ i1, 0 ≤ j1 ⊦ ((i1 + i0) * j + j1) % j = j1

Rule argument

spec: int-mult name: commutativity seq: ⊦ i * j = j * i subst: [i, j] → [i1 + i0, j] flags: <rotated> <all paths>

Additional information

Used terms: i1 + i0, j