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Proof step 45 from proof shiftzero-max-neg (previous step)

m = 0, 1 < j, 0 < j, i < 0, i < ~1, # int2bits(i) ≤ m + 1, 2 ^ n→i(m) ≤ >>>(m, (i - 1) / 2, j - 1), ¬ m < # int2bits((i - 1) / 2) ∧ j ≠ 1 ∧ m ≠ 0 → >>>(m, (i - 1) / 2, j - 1) < 2 ^ (n→i(m) - 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) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
1 < j, 0 < j, i < 0, i < ~1, # int2bits(i) ≤ 1, 0 < >>>(0, (i - 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) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ 0 < n ↔ n ≠ 0;% ⊦ 1 ≤ i ↔ 0 < i;