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

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

User applied rule induction

And obtained the following new goals

Proof step 3:
0 ≤ j ∧ 0 ≤ j0, ∀ j1, j0, i. i→n(j1) < i→n(j) → 0 ≤ j1 ∧ 0 ≤ j0 → i ^ (j1 + j0) = i ^ j1 * i ^ j0 ⊦ i ^ (j + j0) = i ^ j * i ^ j0

Rule argument

indvar: i→n(j) wfpred: <

Additional information

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