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Proof step 7 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 < band(b2i(by0), 255) + 256 * 127

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i + j = j + i
Proof step 9:
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)

Rule argument

seq: ⊦ i + j = j + i subst: [j, i] → [256 * 127, band(b2i(by0), 255)] rotate: F spec: int-basic2 inst: name: add-c

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i); Used terms: 256 * 127, band(b2i(by0), 255)