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Proof step 71 from proof bor-2pot-plus-01 (previous step)

# bitsinvert(int2bits(j0)) ≠ 0, 0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0, # int2bits(j0) ≤ i→n(i) ⊦ bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, (j + 1) * 2 ^ (n→i(i→n(i) - # int2bits(j0)) + n→i(# int2bits(j0))) = 1 + j * 2 ^ i + (bits2uint(mklist(true, i→n(i) - # int2bits(j0))) * 2 ^ n→i(# bitsinvert(int2bits(j0))) + bits2uint(bitsinvert(int2bits(j0)))) + j0, mklist(true, i→n(i) - # int2bits(j0)) + bitsinvert(int2bits(j0)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0, # int2bits(j0) ≤ i→n(i) ⊦ mklist(true, i→n(i) - # int2bits(j0)) + bitsinvert(int2bits(j0)) = [], bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, (j + 1) * 2 ^ (n→i(i→n(i) - # int2bits(j0)) + n→i(# int2bits(j0))) = 2 ^ n→i(# int2bits(j0)) * (bits2uint(mklist(true, i→n(i) - # int2bits(j0))) + 1) + j * 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j + i = i * (j + 1);% ⊦ i + (j - i) = j;% ⊦ # bitsinvert(bits) = # bits;%⊦ 0 ≤ i → bits2uint(bitsinvert(int2bits(i))) = 2 ^ n→i(# int2bits(i)) - i + 1;