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Proof step 28 from proof exin2pot (previous step)

j1 < 2, i0 < 2 ^ i * 2, 0 < i0 * 2 + j1, 0 < i0, 2 ^ (2 + i) ≤ i0 * 2 + j1, 0 ≤ j1, 0 ≤ i, 2 ^ i ≤ i0, 0 ≤ i0, ∀ j0. i→n(j0) < i→n(i0 * 2 + j1) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ i0 * 2 + j1 = 0, i0 * 2 + j1 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0
Proof step 30:
0 < i0, 0 < i0 * 2 + j1, i0 < 2 ^ i * 2, j1 < 2, 0 ≤ i0, 2 ^ i ≤ i0, 0 ≤ j1, 2 ^ 2 * 2 ^ i ≤ i0 * 2 + j1, 0 ≤ 2, 0 ≤ i, ∀ j0. i→n(j0) < i→n(i0 * 2 + j1) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ i0 * 2 + j1 = 1, i0 * 2 + j1 = 0

Rule argument

spec: <toplevel> name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i, 2, 2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: i, 2, 2