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Proof step 29 from proof bytes2int-len-one-01 (previous step)

0 ≤ band(b2i(by), 255) + 256 * bytes2int(by0 ' + bytes), bytes2int(by0 ' + bytes) < 0, band(b2i(by), 255) + 256 * bytes2int(by0 ' + bytes) < 128, 0 ≤ band(b2i(by), 255) ⊦ bytes2int(by0 ' + bytes) = 0, by0 = i2b(0)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 30:
⊦ 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(by0 ' + bytes), band(b2i(by), 255), 256] rotate: F spec: int-mult inst: name: modzero-03

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: bytes2int(by0 ' + bytes), band(b2i(by), 255), 256