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Proof step 9 from proof short-2bytes-03 (previous step)

256 * b2i(by) ≤ 256 * 127, 0 < band(b2i(by0), 255) + 256 * b2i(by), 32768 < band(b2i(by0), 255) + 256 * b2i(by) ⊦ 32768 < 256 * 127 + band(b2i(by0), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < j + i0 ∧ ¬ j0 < j → i < j0 + i0 subst: [i, j, i0, j0] → [32768, 256 * b2i(by), band(b2i(by0), 255), 256 * 127] rotate: F spec: int-basic2 inst: name: lst-02

Additional information

Used simplifier rules: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 ≤ (* j) ↔ i0 ≤ j / i);% ⊦ b2i(by) ≤ 127;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 ≤ i ∧ i ≤ i0 → ¬ i0 < band(i, j);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ ¬ 127 < b2i(by);% ⊦ band(i, j) = band(j, i); Used terms: 32768, 256 * b2i(by), band(b2i(by0), 255), 256 * 127