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Proof step 61 from proof bytes2int-int2bytes-len-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) '
Proof step 63:
¬(~128 ≤ band(b2i(by), 255) - 256 ∧ band(b2i(by), 255) - 256 < 128), 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
Proof step 69:
~128 ≤ band(b2i(by), 255) - 256 ∧ band(b2i(by), 255) - 256 < 128, 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 = i2b(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

name: int2bytes-byte rotate: F subst: [i] → [band(b2i(by), 255) - 256]

Additional information

Used terms: band(b2i(by), 255) - 256