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Proof step 107 from proof int2bits-rec-2pot-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j subst: [j0, j, i] → [0, j % 2 ^ i, 2 ^ i] rotate: F spec: int-abs inst: name: numle-03

Additional information

Used terms: 0, j % 2 ^ i, 2 ^ i