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Proof step 151 from proof int2bytes-rec-neg-05 (previous step)

j % 2 ^ (i * 8) < ~1, # fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, ¬ 0 ≤ j % 2 ^ (i * 8) + 2 ^ (n→i(i→n(i * 8) + 1) - 1), j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ bits2bytes(fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, j % 2 ^ (i * 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 152:
# fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, j % 2 ^ (i * 8) < ~1, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i, j % 2 ^ (i * 8) < 0, 2 ^ (i * 8) + j % 2 ^ (i * 8) < 0 ⊦ bits2bytes(fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, j % 2 ^ (i * 8) = 0, fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest = []

Rule argument

Additional information

Used simplifier rules: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + 0 = i;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < j → abs(j) = j;% ⊦ abs(i * j) = abs(i) * abs(j);% ⊦ n→i(i→n(i)) = abs(i);% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;