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Proof step 28 from proof shiftzero-max-neg (previous step)

2 ^ (i0 + 1) % 2 = 0, n→i(n) = i0 + 1, 1 ≤ n, 0 < j, 2 ^ i0 ≤ (2 ^ (i0 + 1) / 2 - 1) >> (j - 1), ~1 ≤ i0, ∀ n, i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j0 ∧ n ≠ 0 → >>>(n, i, j0) < 2 ^ (n→i(n) - 1) ⊦ j = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 30:
0 < i0 + 1, (2 ^ (i0 + 1)-1 * 2) % 2 = 0, n→i(n) = i0 + 1, 1 ≤ n, 0 < j, 2 ^ i0 ≤ ((2 ^ (i0 + 1)-1 * 2) / 2 - 1) >> (j - 1), ~1 ≤ i0, ∀ n, i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j0 ∧ n ≠ 0 → >>>(n, i, j0) < 2 ^ (n→i(n) - 1) ⊦ j = 0, n = 0

Rule argument

seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0 + 1, 2] rotate: F spec: int-pot inst: name: Pot-pos

Additional information

Used simplifier rules: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < 0 → (n→i(m) = i + 1 ↔ m = 0 ∧ i = ~1); Used terms: i0 + 1, 2