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Proof step 9 from proof pot-pot-02 (previous step)

j0 = i0 + 1, 0 < j0, 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) ^ i0 * i ^ j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 ≤ j, 0 ≤ i0, ∀ j1, j, i. i→n(j1) < i→n(i0 + 1) → 0 ≤ j1 ∧ 0 ≤ j → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * (i0 + 1)) = (i ^ j) ^ i0 * i ^ j

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)