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Proof step 12 from proof pot-pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [j, i0 * j, i] flags: <all paths>

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * j + i = i * (j + 1); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 ≤ i → (0 ≤ i * j ↔ i = 0 ∨ 0 ≤ j); (s) Used terms: j, i0 * j, i