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Proof step 1 from proof band-011x-neg (conclusion)

⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = bits2int(bitsand(false ' + mklist(true, i→n(i)), int2bits(j))) + 1

Rule argument

Additional information

Used simplifier rules: band-def: ⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)));%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i - j = i0 ↔ i = i0 + j;%0 ≤ i ⊦ int2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);