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Proof step 3 from proof modmod-mult-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i % (j * j0)) % j = i % j
Proof step 5:
0 < j0 ⊦ (i % (j * j0)) % j = i % j, j = 0, 0 < j ∧ 0 ≤ i ∧ 0 < j0

Rule argument

spec: <toplevel> name: modmod-mult-04 seq: ⊦ 0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i % (j * j0)) % j = i % j subst: [j0, j, i] → [j0, j, i] flags: <all paths>

Additional information

Used terms: j0, j, i