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Proof step 31 from proof bor-2pot-plus (previous step)

¬(¬ false ∈ mklist(true, i→n(i)) ∧ # mklist(true, i→n(i)) ≤ # bitsinvert(bits) ∧ mklist(true, i→n(i)) ≠ []), # int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(bits), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
int2bits(j0) = boolvar ' + bits, # int2bits(j0) = i→n(i) + 1, # bits < i→n(i), boolvar ∈ int2bits(j0), 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, 0 < j, j0 < 2 ^ i, 0 < i ⊦ bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(bits), mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], i = 0

Rule argument

Additional information

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