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Proof step 6 from proof byte2bits-val (previous step)

b2i(by) < 0 ⊦ bits2uint(fillsgn(8, int2bits(b2i(by)))) = b2i(by) + 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 8:
¬(# int2bits(b2i(by)) ≤ 8 ∧ int2bits(b2i(by)) ≠ []), b2i(by) < 0 ⊦ bits2uint(fillsgn(8, int2bits(b2i(by)))) = b2i(by) + 256
Proof step 9:
# int2bits(b2i(by)) ≤ 8 ∧ int2bits(b2i(by)) ≠ [], b2i(by) < 0 ⊦ bits2uint(mklist(int2bits(b2i(by)).first, 8 - # int2bits(b2i(by))) + int2bits(b2i(by))) = b2i(by) + 256

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [int2bits(b2i(by)), 8] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used terms: int2bits(b2i(by)), 8