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Proof step 3 from proof pot-pot-02 (previous step)

0 ≤ j0, 0 ≤ j ⊦ i ^ (j * j0) = (i ^ j) ^ j0

User applied rule induction

And obtained the following new goals

Proof step 4:
0 ≤ j0, 0 ≤ j, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j1 ∧ 0 ≤ j → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * j0) = (i ^ j) ^ j0

Rule argument

indvar: i→n(j0) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j0)