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Proof step 174 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes = # int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + 1, 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), bytes2int(bytes.butlast) < 0, ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) % 256).last '

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 175:
⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0

Rule argument

seq: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0 subst: [i, j0, j] → [bytes2int(bytes.butlast), band(b2i(bytes.last), 255), 256] rotate: F spec: int-mult inst: name: modzero-03

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i < j → ¬ j < i; Used terms: bytes2int(bytes.butlast), band(b2i(bytes.last), 255), 256