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Proof step 42 from proof bib-neg-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits)
Proof step 44:
¬ int2bits(j).rest ≠ [], 8 = # fillsgn(8, int2bits(j).rest), j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ b2i(i2b(bits2int(fillsgn(8, int2bits(j).rest)))) = 256 + j
Proof step 48:
int2bits(j).rest ≠ [], 8 = # fillsgn(8, int2bits(j).rest), j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ b2i(i2b(bits2int(int2bits(j).rest))) = 256 + j

Rule argument

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

Additional information

Used terms: int2bits(j).rest, 8