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Proof step 158 from proof bytes2int-int2bytes-len-eq (previous step)

(b2i(by0) - 1) * 256 + band(b2i(by), 255) < 0, (b2i(by0) - 1) * 256 + band(b2i(by), 255) = i, 256 * b2i(by0) + band(b2i(by), 255) = i + 256, 0 ≤ b2i(by0), ~129 < i, i < 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(0), by0 ' + by ' = i2b(0) ' + i2b(i) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 159:
⊦ 0 < i ∧ abs(j0) < j → ¬ i * j + j0 < 0
Proof step 160:
¬(0 < b2i(by0) - 1 ∧ abs(band(b2i(by), 255)) < 256), (b2i(by0) - 1) * 256 + band(b2i(by), 255) < 0, (b2i(by0) - 1) * 256 + band(b2i(by), 255) = i, 256 * b2i(by0) + band(b2i(by), 255) = i + 256, 0 ≤ b2i(by0), ~129 < i, i < 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(0), by0 ' + by ' = i2b(0) ' + i2b(i) '

Rule argument

seq: ⊦ 0 < i ∧ abs(j0) < j → ¬ i * j + j0 < 0 subst: [j0, j, i] → [band(b2i(by), 255), 256, b2i(by0) - 1] rotate: F spec: int-mult inst: name: modzero

Additional information

Used terms: band(b2i(by), 255), 256, b2i(by0) - 1