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Proof step 15 from proof short-2bytes (previous step)

~32768 < band(b2i(by0), 255) + 256 * ~128, band(b2i(by0), 255) + 256 * b2i(by) < ~32768 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < j ∧ j < j0 → i < j0 subst: [i, j, j0] → [band(b2i(by0), 255) + 256 * b2i(by), ~32768, band(b2i(by0), 255) + 256 * ~128] rotate: F spec: int-basic1 inst: name: trans-01

Additional information

Used simplifier rules: i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ band(i, j) = band(j, i);% ⊦ i * j = j * i;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j < j ↔ i < 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ ¬ b2i(by) < ~128;% ⊦ i * j * j0 = (i * j) * j0; Used terms: band(b2i(by0), 255) + 256 * b2i(by), ~32768, band(b2i(by0), 255) + 256 * ~128