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Proof step 14 from proof bytes2int-neg (previous step)

0 ≤ bytes2int(by ' + bytes), band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes) < 0, 0 ≤ b2i(by), ∀ bytes0. # bytes0 < #(by + (bytes + by0 ')) → true → bytes0 ≠ [] → (bytes2int(bytes0) < 0 ↔ b2i(bytes0.first) < 0) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0 subst: [j, i] → [256 * bytes2int(by ' + bytes), band(255, b2i(by0))] rotate: F spec: int-abs inst: name: zero-gs

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 256 * bytes2int(by ' + bytes), band(255, b2i(by0))