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Proof step 66 from proof bytes2int-int2bytes-len-eq (previous step)

~256 < band(b2i(by), 255) - 256 ∧ band(b2i(by), 255) - 256 < ~128, bytes1 = int2bytes(bytes2int(bytes1)), bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) < 0, 0 ≤ band(b2i(by), 255), band(b2i(by), 255) < 128, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = (i2b(~1) ' + i2b(band(b2i(by), 255) - 256) ').last, bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, band(b2i(by), 255) = 256, b2i(by) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
bytes1 = int2bytes(bytes2int(bytes1)), bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) < 0, 0 ≤ band(b2i(by), 255), band(b2i(by), 255) < 128, 0 < band(b2i(by), 255), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, band(b2i(by), 255) = 256, b2i(by) = 0, by = i2b(band(b2i(by), 255) - 256)

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);% ⊦ i * j = j * i;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ (bytes + by ').last = by;