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Proof step 33 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256 - 1), 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 - 1) + int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256).last ', bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i % j = 0 ∧ i + i0 < 0 ∧ i0 % j = 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j subst: [j, i0, i] → [256, band(b2i(by), 255), bytes2int(bytes1) * 256] rotate: F spec: int-div inst: name: div-add1-negpos-neg

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;%j ≠ 0 ⊦ (i * j) / j = i;% ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%⊦ i % j = 0 ∧ i + i0 < 0 ∧ 0 ≤ i ∧ i0 < 0 ∧ 0 < j → (i + i0) % j = i0 % j;% ⊦ by '.last = by; Used terms: 256, band(b2i(by), 255), bytes2int(bytes1) * 256