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Proof step 190 from proof bytes2int-int2bytes-len-eq (previous step)

bytes1 = int2bytes(bytes2int(bytes1)), 255 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 ≤ band(b2i(by), 255), 0 ≤ bytes2int(bytes1), 127 < band(b2i(by), 255), 0 < band(b2i(by), 255), band(b2i(by), 255) ≤ 255, 0 < bytes2int(bytes1), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(band(b2i(by), 255) - 256), bytes1 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 191:
band(b2i(by), 255) = i + 256, bytes1 = int2bytes(bytes2int(bytes1)), 255 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 ≤ band(b2i(by), 255), 0 ≤ bytes2int(bytes1), 127 < band(b2i(by), 255), 0 < band(b2i(by), 255), band(b2i(by), 255) ≤ 255, 0 < bytes2int(bytes1), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(i), bytes1 = []

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [band(b2i(by), 255), 256, i] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: band(b2i(by), 255), 256, i