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Proof step 9 from proof bytes2int-2-le-32767 (previous step)

256 * 128 ≤ band(b2i(by1), 255) + 256 * b2i(by), 0 < band(b2i(by1), 255) + 256 * b2i(by), 0 ≤ band(b2i(by1), 255) + 256 * b2i(by) ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 10:
j * i ≤ j * i0 + j0, abs(j0) < j ⊦ i ≤ i0
Proof step 11:
256 * 128 ≤ band(b2i(by1), 255) + 256 * b2i(by), 0 < band(b2i(by1), 255) + 256 * b2i(by), 0 ≤ band(b2i(by1), 255) + 256 * b2i(by) ⊦ 256 * 128 ≤ 256 * b2i(by) + band(b2i(by1), 255) ∧ abs(band(b2i(by1), 255)) < 256

Rule argument

seq: j * i ≤ j * i0 + j0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [256, 128, b2i(by), band(b2i(by1), 255)] rotate: F spec: int-mult inst: name: modlep-01

Additional information

Used simplifier rules: i ≥ 128 ⊦ ¬ (* i) ≤ b2i(by); Used terms: 256, 128, b2i(by), band(b2i(by1), 255)