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Proof step 16 from proof int2bytes-rec-pos-any (previous step)

¬(# int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8 + 1) ∧ int2bits(j % 2 ^ (i * 8)) ≠ []), 0 < j, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 1 + 8 * i→n(i), 0 ≤ i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(1 + 8 * i→n(i), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
i→n(i * 8 + 1) < # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, # int2bits(j % 2 ^ (i * 8)) ≤ 1 + 8 * i→n(i), 0 < i, 2 ^ (i * 8) ≤ j, 0 < j, i→n(i * 8 + 1) ≤ 8 * i→n(i) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(1 + 8 * i→n(i), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = n + m;% ⊦ m * n = n * m;% ⊦ i * j = j * i;