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Proof step 87 from proof int2bits-rec-2pot-neg-02 (previous step)

¬ i→n(i) + 1 - # uint2bits(~(j % 2 ^ i)) ≠ 0, sgn(bitsinvert(uint2bits(~(j / 2 ^ i)))) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1), j / 2 ^ i < i, j / 2 ^ i ≤ 0, 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i, true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, false ∈ uint2bits(~(j / 2 ^ i)), true ∈ uint2bits(~(j / 2 ^ i)), j % 2 ^ i < 0, # uint2bits(~(j % 2 ^ i)) ≤ i→n(i) + 1 ⊦ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))) = [], bitsinvert(uint2bits(1 - j / 2 ^ i)) +1 = [], j % 2 ^ i = 0, true ' + bitsinvert ((mklist(bitsinvert(uint2bits(~(j % 2 ^ i))).first, i→n(i) + 1 - # uint2bits(~(j % 2 ^ i))) + bitsinvert(uint2bits(~(j % 2 ^ i)))).rest) = fillsgn(i→n(i) + 1, sgn(bitsinvert(uint2bits(~(j % 2 ^ i))) +1)).rest, false ∈ (mklist(bitsinvert(uint2bits(~(j % 2 ^ i))).first, i→n(i) + 1 - # uint2bits(~(j % 2 ^ i))) + bitsinvert(uint2bits(~(j % 2 ^ i)))).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
i→n(i) + 1 = # uint2bits(~(j % 2 ^ i)), sgn(bitsinvert(uint2bits(~(j / 2 ^ i)))) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1), j % 2 ^ i < 0, true ∈ uint2bits(~(j / 2 ^ i)), false ∈ uint2bits(~(j / 2 ^ i)), true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, 0 ≤ i, j < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 < i, j / 2 ^ i ≤ 0, j / 2 ^ i < i ⊦ j % 2 ^ i = 0, bitsinvert(uint2bits(1 - j / 2 ^ i)) +1 = [], fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))) = [], true ' + uint2bits(~(j % 2 ^ i)).rest = fillsgn(i→n(i) + 1, sgn(bitsinvert(uint2bits(~(j % 2 ^ i))) +1)).rest, true ∈ uint2bits(~(j % 2 ^ i)).rest

Rule argument

Additional information

Used simplifier rules: uint2bits-empty-01: ⊦ i < 0 → uint2bits(~ i) ≠ [];% ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ bitsinvert(bitsinvert(bits)) = bits;%bits ≠ [] ⊦ bitsinvert(bits).rest = bitsinvert(bits.rest);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m - m = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n - n + n1 = m - n1;% ⊦ m + n = n + m;% ⊦ m ≤ n → (n - m = 0 ↔ n = m);