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Proof step 60 from proof bytes2int-int2bytes-len-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
bytes1 = int2bytes(bytes2int(bytes1)), band(b2i(by), 255) < 256, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) < 0, 0 ≤ band(b2i(by), 255), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = int2bytes(band(b2i(by), 255) - 256).last, bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, band(b2i(by), 255) = 256, b2i(by) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);% ⊦ i * j = j * i;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + by ' = bytes0 + by0 ' ↔ bytes = bytes0 ∧ by = by0;