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Proof step 6 from proof pot-pot-02 (previous step)

0 < j0, 0 ≤ j, 0 ≤ j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * j0) = (i ^ j) ^ j0 -1 * i ^ j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 ≤ j, 0 ≤ j0, 0 < j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * j0) = (i ^ j) ^ (j0 - 1) * i ^ j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%sub-pred: ⊦ i -1 = i - 1; from specification int-abs