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Proof step 7 from proof modmod-mult-03 (previous step)

j < j0, j < 0, 0 < j0, j + 1 < j0 ⊦ j = 0, (i % (j * j0)) % j = i % j

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i % (j * j0)) % j = i % j
Proof step 9:
0 < ~ j ∧ 0 ≤ i ∧ 0 < j0 → (i % (~ j * j0)) % ~ j = i % ~ j, j < j0, j < 0, 0 < j0, j + 1 < j0 ⊦ j = 0, (i % (j * j0)) % j = i % j

Rule argument

spec: int-div inst: name: modmod-mult-04 seq: ⊦ 0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i % (j * j0)) % j = i % j subst: [j, i, j0] → [~ j, i, j0] flags: current, []

Additional information

Used terms: ~ j, i, j0