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Proof step 13 from proof bytes2int-rec (previous step)

(bytes2bits(bytes) + byte2bits(by)).first ⊦ bytes2bits(bytes) + byte2bits(by) = [], bytes = [], bits2uint((bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)))+1) + bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1
Proof step 15:
bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) ≠ [], (bytes2bits(bytes) + byte2bits(by)).first ⊦ bytes2bits(bytes) + byte2bits(by) = [], bytes = [], (bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + 1) + bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255) = 0

Rule argument

seq: ⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1 subst: [bits] → [bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))] rotate: F spec: int2bits inst: name: bits2uint-succ

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))