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Proof step 55 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)) = [], bits2uint(uint2bits(j)) * 2 ^ n→i(# bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) + bits2uint(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 56:
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)) = [], bits2uint(bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) + 2 ^ n→i(# bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i)))) * j = j * 2 ^ i + j0, bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))) = []

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ j → ¬ uint2bits(j).first;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ # bits = 0 ↔ bits = [];% ⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i;% ⊦ # bitsinvert(bits) = # bits;