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Proof step 31 from proof bib-neg-low (previous step)

j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ 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 32:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 33:
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(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j
Proof step 42:
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

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(8, int2bits(j).rest), int2bits(i0 - 1), 8] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used terms: fillsgn(8, int2bits(j).rest), int2bits(i0 - 1), 8