| n ≠ # fillsgn(n, sgn(bits)), # sgn(bits) < # bits, # sgn(bits) < n, n < # bits, # sgn(bits) + 1 < # bits ⊦ lastn(n, fillsgn(n, sgn(bits))) = lastn(n, bits), bits = [], n = # bits |
# sgn(bits) + 1 < # bits, n < # bits, # sgn(bits) < n, # sgn(bits) < # bits ⊦ n = # fillsgn(n, sgn(bits)), n = # bits, bits = [], lastn(n, fillsgn(n, sgn(bits))) = lastn(n, bits)