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Proof step 8 from proof modmod-mult-03 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used terms: ~ j, i, j0