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Proof step 8 from proof modmod-ma (previous step)

0 ≤ i, 0 ≤ i0, 0 ≤ j0, 0 < j ⊦ (i % j * i0 % j + j0) % j = ((i % j * i0 % j) % j + j0) % j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j + i0) % j = (i + i0) % j
Proof step 10:
¬(0 < j ∧ 0 ≤ i % j * i0 % j ∧ 0 ≤ j0), 0 ≤ i, 0 ≤ i0, 0 ≤ j0, 0 < j ⊦ (i % j * i0 % j + j0) % j = ((i % j * i0 % j) % j + j0) % j

Rule argument

spec: int-div inst: name: modmod-add seq: 0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j + i0) % j = (i + i0) % j subst: [i0, j, i] → [j0, j, i % j * i0 % j] flags: rewrite, current

Additional information

Used terms: j0, j, i % j * i0 % j