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Proof step 74 from proof bor-2pot-plus-01 (previous step)

¬ false ∈ mklist(true, i→n(i) - # int2bits(j0)) ∧ mklist(true, i→n(i) - # int2bits(j0)) ≠ [], 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)) * ((2 ^ n→i(# mklist(true, i→n(i) - # int2bits(j0))) - 1) + 1) + j * 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
# int2bits(j0) < i→n(i), j < 0, j + 1 < i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i ⊦ i→n(i) = # int2bits(j0), (j + 1) * 2 ^ (n→i(i→n(i) - # int2bits(j0)) + n→i(# int2bits(j0))) = j * 2 ^ i + 2 ^ n→i(i→n(i) - # int2bits(j0)) * 2 ^ n→i(# int2bits(j0)), i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], mklist(true, i→n(i) - # int2bits(j0)) + bitsinvert(int2bits(j0)) = []

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ ¬ false ∈ mklist(true, n);% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ m ≤ n → (n - m = 0 ↔ n = m);% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i) = j;% ⊦ # mklist(boolvar, n) = n;