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Proof step 184 from proof bytes2int-int2bytes-len-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 185:
0 ≤ i, i ≤ 127 ⊦ int2bytes(i) = i2b(i) '
Proof step 186:
¬(0 ≤ band(b2i(by), 255) ∧ band(b2i(by), 255) ≤ 127), bytes1 = int2bytes(bytes2int(bytes1)), band(b2i(by), 255) < 256, 255 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 ≤ band(b2i(by), 255), 0 ≤ bytes2int(bytes1), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = int2bytes(band(b2i(by), 255)).last, bytes1 = []

Rule argument

name: int2bytes-le127 rotate: F subst: [i] → [band(b2i(by), 255)]

Additional information

Used simplifier rules: ⊦ i2b(band(255, b2i(by))) = by;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ by '.last = by; Used terms: band(b2i(by), 255)