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Proof step 49 from proof bytes2int-int2bytes-len-eq (previous step)

¬ band(b2i(by), 255) < 0, # bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1), band(b2i(by), 255) < 256, 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, b2i(by) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
# bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1), band(b2i(by), 255) < 256, 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, b2i(by) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i < 0 ∧ j0 < j ∧ 0 ≤ j → i * j + j0 < 0;% ⊦ band(i, j) = band(j, i);