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Proof step 43 from proof bytes2int-int2bytes-len-eq (previous step)

¬ abs(band(b2i(by), 255)) < 256, # bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1), bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) < 0, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 + by ' = int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1) + int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256).last ', bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, band(b2i(by), 255) % 256 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
# bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1), 256 ≤ abs(band(b2i(by), 255)), bytes2int(bytes1) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ band(b2i(by), 255) % 256 = 0, (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, bytes1 = [], bytes1 + by ' = int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1) + int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256).last ', b2i(by) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%0 ≤ i, i < 128 ⊦ band(b2i(by), 255) = (* i) ↔ b2i(by) = i;% ⊦ 0 < abs(i) ↔ i ≠ 0;% ⊦ 0 ≤ abs(i);% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ band(i, j) = band(j, i);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;