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Proof step 22 from proof bytes2int-rec (previous step)

bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], bits2uint(bitsinvert(bytes2bits(bytes)) +1) * 256 = (bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + band(b2i(by), 255)) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1
Proof step 24:
bitsinvert(bytes2bits(bytes)) ≠ [], bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], (bits2uint(bitsinvert(bytes2bits(bytes))) + 1) * 256 = (bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + band(b2i(by), 255)) + 1

Rule argument

seq: ⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1 subst: [bits] → [bitsinvert(bytes2bits(bytes))] rotate: F spec: int2bits inst: name: bits2uint-succ

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];% ⊦ bitsinvert(bits) = [] ↔ bits = []; Used terms: bitsinvert(bytes2bits(bytes))