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Proof step 97 from proof int2bits-rec-2pot-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n → fillsgn(n, sgn(bits)) = fillsgn(n, bits) subst: [bits, n] → [bitsinvert(uint2bits(~(j % 2 ^ i))) +1, i→n(i) + 1] rotate: F spec: bitopsaux inst: name: fill-sgn-01

Additional information

Used simplifier rules: ⊦ m + n = n + m; Used terms: bitsinvert(uint2bits(~(j % 2 ^ i))) +1, i→n(i) + 1