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Proof step 6 from proof pot-pot (previous step)

0 < j0, 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 -1 * i ^ j = i ^ (j * j0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
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)

Rule argument

spec: int-basic1 name: elim-pred seq: ⊦ i = j -1 ↔ j = i +1 subst: [j, i] → [j0, i0]

Additional information

Used simplifier rules: ⊦ i = j -1 ↔ j = i +1; (elim) Used terms: j0, i0