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Proof step 65 from proof bor-2pot-plus-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
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, 2 ^ n→i(# fillsgn(i→n(i), bitsinvert(int2bits(j0)))) * (j + 1) = 1 + bits2uint(fillsgn(i→n(i), bitsinvert(int2bits(j0)))) + j * 2 ^ i + j0, fillsgn(i→n(i), bitsinvert(int2bits(j0))) = []

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ false ∈ mklist(true, n);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ j → bitsinvert(int2bits(j)).first;% ⊦ # bitsinvert(bits) = # bits;% ⊦ int2bits(j) ≠ [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ # mklist(boolvar, n) = n;