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Proof step 54 from proof int2bits-rec-2pot-neg-02 (previous step)

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, j / 2 ^ i < 0 ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0, ∃ bits, bits0. uint2bits(~(j / 2 ^ i)) = bits + false ' + bits0

User applied rule exists right

And obtained the following new goals

Proof step 55:
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, j / 2 ^ i < 0 ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0, uint2bits(~(j / 2 ^ i)) = [] + false ' + uint2bits(~(j / 2 ^ i)).rest

Rule argument

pos: right 3 terms: [], uint2bits(~(j / 2 ^ i)).rest abort: F discard: T computed: F

Additional information

Used terms: [], uint2bits(~(j / 2 ^ i)).rest