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Proof step 8 from proof bytes2int-len-one-02 (previous step)

0 ≤ bytes2int(i2b(0) ' + by '), bytes2int(i2b(0) ' + by ') < 128, b2i(by) < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by, i2b(0) ']

Additional information

Used simplifier rules: bytes2int-zero: ⊦ bytes2int(i2b(0) ') = 0;% ⊦ by ' ≠ [];% ⊦ i < 0 → band(i, 255) = (i + 1) % 256 + 255;% ⊦ (b2i(by) + 1) % 256 = b2i(by) + 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ b2i(by) < ~128; Used terms: by, i2b(0) '