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Proof step 9 from proof pot-dist-pos (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
j = i0 +1, 0 < j + j0, 0 < j, 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)-1 * i = (i ^ i0 * i) * i ^ j0

Rule argument

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

Additional information

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