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Proof step 52 from proof bor-2pot-plus (previous step)

¬(# bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i)))) ≠ 0 ∧ # uint2bits(j) ≠ 0 ∧ ¬ uint2bits(j).first), int2bits(j0) = false ' + bitsinvert(bits), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, # int2bits(j0) ≤ i→n(i), false ∈ int2bits(j0) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))) = [], int2bits(j0) = false ' + bitsinvert(bits), false ∈ int2bits(j0), # int2bits(j0) ≤ i→n(i), 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, 0 ≤ i, j0 < 2 ^ i, 0 < j ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], j = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ j → bits2int(uint2bits(j)) = j;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ bitsinvert([]) = [];% ⊦ 0 ≤ j → ¬ uint2bits(j).first;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ # bitsinvert(bits) = # bits;