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Proof step 28 from proof bor-2pot-plus (previous step)

int2bits(j0) = boolvar + bits ∧ int2bits(j0) ≠ [], # int2bits(j0) = i→n(i) + 1, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ 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 29:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;