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Proof step 7 from proof pot-pot (previous step)

j0 = i0 +1, 0 < j0, 0 ≤ i, 0 ≤ j, 0 ≤ j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j1 ∧ 0 ≤ j ∧ 0 ≤ i → (i ^ j) ^ j1 = i ^ (j * j1) ⊦ (i ^ j) ^ i0 * i ^ j = i ^ (j * j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
~1 ≤ i0, 0 ≤ j, 0 ≤ i, 0 ≤ i0, ∀ j1, j, i. i→n(j1) < i→n(i0 +1) → 0 ≤ j1 ∧ 0 ≤ j ∧ 0 ≤ i → (i ^ j) ^ j1 = i ^ (j * j1) ⊦ (i ^ j) ^ i0 * i ^ j = i ^ (j * (i0 + 1))

Rule argument

Additional information

Used simplifier rules: ⊦ ~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)% ⊦ i +1 = i + 1; (s)