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Proof step 34 from proof bib-neg-low (previous step)

i0 < 0, 256 * i0 + j < 0, j < 0, ~256 < j, 256 * i0 + j < ~128, j < ~128 ⊦ 8 = # fillsgn(8, int2bits(j).rest), b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 36:
¬ # int2bits(j).rest ≤ 8, i0 < 0, 256 * i0 + j < 0, j < 0, ~256 < j, 256 * i0 + j < ~128, j < ~128 ⊦ 8 = # fillsgn(8, int2bits(j).rest), b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(j).rest, 8] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: int2bits(j).rest, 8