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Proof step 38 from proof getInt-theorem (previous step)

0 ≤ band(b2i(by2), 255), band(b2i(by1), 255) < 256, 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 16777216, 0 ≤ band(b2i(by1), 255) ⊦ bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), 16777216 * b2i(by3)) = (bytes2int(by3 ' + by2 ') * 256 + band(b2i(by1), 255)) * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), bor(band(b2i(by0), 255), 16777216 * b2i(by3))) = bor((bytes2int(by3 ' + by2 ') * 256 + band(b2i(by1), 255)) * 256, band(b2i(by0), 255)), 65536 * bytes2int(by3 ' + by2 ') = 16777216 * b2i(by3) + 65536 * band(b2i(by2), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by2, by3 ']

Additional information

Used simplifier rules: bytes2int-one: ⊦ bytes2int(by ') = b2i(by);% ⊦ by ' ≠ [];% ⊦ band(i, j) = band(j, i);% ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: by2, by3 '