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Proof step 5 from proof modmod-ma (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j * i0 % j) % j = (i * i0) % j
Proof step 7:
0 < j ∧ 0 ≤ i ∧ 0 ≤ i0, 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-mult seq: 0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j * i0 % j) % j = (i * i0) % j subst: [j, i0, i] → [j, i0, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j, i0, i