| 0 ≤ i0, # int2bits(i) = i→n(i0) * 8 + 1, # int2bits(i) / 8 = i→n(i0), 0 < i, i→n(i0) * 8 < # int2bits(i), i→n(i0) * 8 - 1 < i→n(i0) * 8, i < 2 ^ (n→i(n) * 8 - 1), n ≤ i→n(i0), 0 < i0 ⊦ n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0 |
# int2bits(i) = i→n(i0) * 8 + 1, # int2bits(i) / 8 = i→n(i0), 0 < i, i→n(i0) * 8 < # int2bits(i), i→n(i0) * 8 - 1 < i→n(i0) * 8, i < 2 ^ (n→i(n) * 8 - 1), n ≤ i→n(i0), 0 < i0 ⊦ n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0
Used simplifier rules: ⊦ m * n = n * m;% ⊦ i ≠ j → (i ≤ j ↔ i < j);