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Proof step 14 from proof mod-pot-pot (previous step)

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 15:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 16:
0 ≤ i2, 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 * i |%| j) |%| j = (i ^ i2 |%| j * i |%| j) |%| j

Rule argument

spec: int-pot inst: name: succ seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i2, i |%| j] flags: rewrite

Additional information

Used terms: i2, i |%| j