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Proof step 7 from proof bor-2pot-plus-01 (previous step)

j * 2 ^ i < 0, j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, j < 0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(abs(j * 2 ^ i))) +1)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, j < 0 ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~(j * 2 ^ i))) +1)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ~ i * j = ~(i * j);% ⊦ abs(2 ^ i) = 2 ^ i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ abs(i * j) = abs(i) * abs(j);