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Proof step 9 from proof pot-pot-02 (previous step)

0 ≤ j, 0 ≤ i0, ∀ j1, j, i. i→n(j1) < i→n(i0 + 1) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * (i0 + 1)) = (i ^ j) ^ i0 * i ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 11:
0 ≤ j, 0 ≤ i0, ∀ j1, j, i. i→n(j1) < i→n(i0 + 1) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (i0 * j + 1 * j) = (i ^ j) ^ i0 * i ^ j

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, 1, i0] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, 1, i0