| # int2bits(i / 2) < #(mklist(false, i→n(i0)) + int2bits(i / 2) + (i % 2 = 1)'), 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2uint(firstn(# int2bits(i / 2), (mklist(false, i→n(i0)) + int2bits(i / 2) + (i % 2 = 1)').butlast)) = bits2int(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2))) |
0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2uint(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2))) = bits2int(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))
Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m + n < m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + boolvar ').butlast = bits;