| # lastn(8, bits) = 8, firstn(# bits - 8, bits) + lastn(8, bits) = bits, b2i(i2b(bits2int(lastn(8, bits)))) < 0, bits2int(lastn(8, bits)) < 0, 8 < # bits, ~128 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(lastn(8, bits)) = sgn(bits), bits = [], false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), false ∈ firstn(# bits - 8, bits) |
# lastn(8, bits) = 8, firstn(# bits - 8, bits) + lastn(8, bits) = bits, b2i(i2b(bits2int(lastn(8, bits)))) < 0, bits2int(lastn(8, bits)) < 0, 8 < # bits, ~128 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(lastn(8, bits)) = sgn(firstn(# bits - 8, bits) + lastn(8, bits)), bits = [], false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), false ∈ firstn(# bits - 8, bits)