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Proof step 8 from proof ubyte-neg (previous step)

b2i(by) < 0 ⊦ bits2int(fillsgn(8, int2bits(b2i(by)))) + 2 ^ n→i(# fillsgn(8, int2bits(b2i(by)))) = 256 + b2i(by), fillsgn(8, int2bits(b2i(by))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits)
Proof step 10:
int2bits(b2i(by)) ≠ [], b2i(by) < 0 ⊦ bits2int(int2bits(b2i(by))) + 2 ^ n→i(# fillsgn(8, int2bits(b2i(by)))) = 256 + b2i(by), fillsgn(8, int2bits(b2i(by))) = []

Rule argument

seq: ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits) subst: [bits, n] → [int2bits(b2i(by)), 8] rotate: F spec: int2bits inst: name: bits2int-fill

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(b2i(by)), 8