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Proof step 9 from proof bytes2int-mklist-zeros (previous step)

bytes2int(mklist(i2b(0), m)) = 0 ⊦ bytes2int(mklist(i2b(0), m) + i2b(0) ') = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)

Rule argument

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

Additional information

Used simplifier rules: bytes2int-zero: ⊦ bytes2int(i2b(0) ') = 0;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ [] + bytes = bytes;% ⊦ mklist(by, 0) = [];% ⊦ mklist(by, m) = [] ↔ m = 0;% ⊦ b2i(i2b(0)) = 0;% ⊦ 0 ≤ i → band(i, 255) = i % 256;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i2b(0), mklist(i2b(0), m)