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Proof step 78 from proof bytes2int-int2bytes-len-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0 subst: [j, i] → [band(b2i(by), 255), bytes2int(bytes1) * 256] rotate: F spec: int-basic2 inst: name: pls-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i * j = j * i;% ⊦ band(i, j) = band(j, i);% ⊦ i + j = j + i; Used terms: band(b2i(by), 255), bytes2int(bytes1) * 256