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Proof step 25 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 26:
⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 27:
# bitsinvert(byte2bits(by)) ≠ 0, bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], (bits2uint(bitsinvert(bytes2bits(bytes))) + 1) * 256 = ((bits2uint(bitsinvert(bytes2bits(bytes))) * 2 ^ n→i(# bitsinvert(byte2bits(by))) + bits2uint(bitsinvert(byte2bits(by)))) + band(b2i(by), 255)) + 1

Rule argument

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

Additional information

Used simplifier rules: byte2bits-length: ⊦ # byte2bits(by) = 8;% ⊦ # bitsinvert(bits) = # bits; Used terms: bitsinvert(byte2bits(by)), bitsinvert(bytes2bits(bytes))