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Proof step 40 from proof bytes2int-rec (previous step)

⊦ bytes2bits(bytes) + byte2bits(by) = [], bits2uint(bytes2bits(bytes) + byte2bits(by)) = bits2uint(bytes2bits(bytes)) * 256 + band(b2i(by), 255), bytes = [], (bytes2bits(bytes) + byte2bits(by)).first, bytes2bits(bytes).first

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0) subst: [bits0, bits] → [byte2bits(by), bytes2bits(bytes)] rotate: F spec: int2bits inst: name: bits2uint-split

Additional information

Used simplifier rules: byte2bits-length: ⊦ # byte2bits(by) = 8;%byte2bits-val: ⊦ bits2uint(byte2bits(by)) = band(b2i(by), 255);%byte2bits-length: ⊦ # byte2bits(by) = 8;% ⊦ i * j = j * i;% ⊦ band(i, j) = band(j, i);% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: byte2bits(by), bytes2bits(bytes)