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Proof step 11 from proof modmod-mult-02 (previous step)

0 < j, 0 ≤ i ⊦ (i % j * i0 % j) % j = (i * i0) % j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j * i0 % j) % j = (i * i0) % j
Proof step 13:
¬(0 < j ∧ 0 ≤ i ∧ 0 ≤ i0), 0 < j, 0 ≤ i ⊦ (i % j * i0 % j) % j = (i * i0) % j

Rule argument

spec: int-div inst: name: modmod-mult seq: 0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j * i0 % j) % j = (i * i0) % j subst: [i0, j, i] → [i0, j, i] flags: rewrite, current

Additional information

Used terms: i0, j, i