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Proof step 23 from proof short-2bytes (previous step)

band(b2i(by0), 255) + 256 * 127 < 32767, 0 < band(b2i(by0), 255) + 256 * b2i(by), 32767 < band(b2i(by0), 255) + 256 * b2i(by) ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 24:
⊦ i < j ∧ j < j0 → i < j0

Rule argument

seq: ⊦ i < j ∧ j < j0 → i < j0 subst: [i, j, j0] → [band(b2i(by0), 255) + 256 * 127, 32767, band(b2i(by0), 255) + 256 * b2i(by)] rotate: F spec: int-basic1 inst: name: trans-01

Additional information

Used simplifier rules: ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i * j = j * i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ ¬ 127 < b2i(by);% ⊦ i * j * j0 = (i * j) * j0; Used terms: band(b2i(by0), 255) + 256 * 127, 32767, band(b2i(by0), 255) + 256 * b2i(by)