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Proof step 11 from proof pot-dist-pos (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
(i0 + 1) + j0 = i1 +1, 0 ≤ j0, 0 ≤ i0 + j0, 0 ≤ i0, 0 ≤ i0 + 1, ∀ j1, j0, i. i→n(j1) < i→n(i0 +1) → 0 ≤ j1 ∧ 0 ≤ j0 → i ^ (j1 + j0) = i ^ j1 * i ^ j0 ⊦ i ^ i1 * 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] → [(i0 + 1) + j0, i1] flags:

Additional information

Used simplifier rules: ⊦ i = j -1 ↔ j = i +1; (elim) Used terms: (i0 + 1) + j0, i1