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Proof step 26 from proof bor-2pot-plus-01 (previous step)

mklist(false, i→n(i)) ≠ [] ∧ (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, j < 0 ⊦ i = 0, bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1) + mklist(false, i→n(i))), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 0, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1)) + mklist(true, i→n(i)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0, i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i +1 = i + 1;% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bitsinvert(mklist(boolvar, n)) = mklist(¬ boolvar, n);% ⊦ bitsinvert(bits + bits0) = bitsinvert(bits) + bitsinvert(bits0);