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Proof step 26 from proof shiftzero-max-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
i < 0, 2 ^ (n→i(n) - 1) ≤ >>>(n, i, 1), # int2bits(i) ≤ n, ∀ n, i, j0. i→n(j0) < i→n(1) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0, i = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ 1 ≤ i ↔ 0 < i;