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Proof step 11 from proof bytes2int-append (previous step)

(bytes2bits(bytes) + bytes2bits(bytes0)).first ⊦ bytes0 = [], bytes = [], bits2int(bytes2bits(bytes) + bytes2bits(bytes0)) = bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(bits) +1)
Proof step 13:
(bytes2bits(bytes) + bytes2bits(bytes0)).first ∧ bytes2bits(bytes) + bytes2bits(bytes0) ≠ [], (bytes2bits(bytes) + bytes2bits(bytes0)).first ⊦ bytes0 = [], bytes = [], ~ bits2uint(bitsinvert(bytes2bits(bytes) + bytes2bits(bytes0)) +1) = bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

Rule argument

seq: ⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(bits) +1) subst: [bits] → [bytes2bits(bytes) + bytes2bits(bytes0)] rotate: F spec: int2bits inst: name: bits2int-neg-03

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bytes2bits(bytes) + bytes2bits(bytes0)