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Proof step 11 from proof mod-pot-pot (previous step)

0 < j, 0 < j, 0 ≤ i2, ∀ i1, j, i. i→n(i1) < i→n(i2 + 1) → 0 ≤ i1 ∧ 0 < j → (i |%| j) ^ i1 |%| j = i ^ i1 |%| j ⊦ (i |%| j) ^ (i2 + 1) |%| j = (i ^ i2 |%| j * i |%| j) |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < j → (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j
Proof step 13:
0 < j, 0 < j, 0 < j, 0 ≤ i2, ∀ i1, j, i. i→n(i1) < i→n(i2 + 1) → 0 ≤ i1 ∧ 0 < j → (i |%| j) ^ i1 |%| j = i ^ i1 |%| j ⊦ (i |%| j) ^ (i2 + 1) |%| j = ((i ^ i2 |%| j) |%| j * (i |%| j) |%| j) |%| j

Rule argument

spec: int-mod inst: name: mod-mult-law seq: ⊦ 0 < j → (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j subst: [j, i0, i] → [j, i |%| j, i ^ i2 |%| j] flags: rewrite, current

Additional information

Used terms: j, i |%| j, i ^ i2 |%| j