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Proof step 32 from proof shiftzero-max-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
0 < j, 1 < j, 2 ^ (n→i(n) - j) ≤ >>>(n - 1, (i - 1) / 2, j - 1), j ≤ n→i(n), # int2bits(i) ≤ n, i < ~1, i < 0, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0, n = 1

Rule argument

Additional information

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