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Proof step 2 from proof pot-pot (previous step)

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

User applied rule induction

And obtained the following new goals

Proof step 3:
0 ≤ j0, 0 ≤ j, 0 ≤ i, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j1 ∧ 0 ≤ j ∧ 0 ≤ i → (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)