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Proof step 24 from proof shiftzero-max-neg (previous step)

¬(2 ^ (i0 + 1) % 2 = 0 ∧ 0 < 2 ^ (i0 + 1)), n→i(n) = i0 + 1, 1 ≤ n, 0 < j, 2 ^ i0 ≤ (2 ^ (i0 + 1) - 1) / 2 >> (j - 1), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
n→i(n) = i0 + 1, 1 ≤ n, 0 < j, 2 ^ i0 ≤ (2 ^ (i0 + 1) - 1) / 2 >> (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, 2 ^ (i0 + 1) % 2 = 0

Rule argument

Additional information

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