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Proof step 117 from proof int2bits-rec-2pot-neg-02 (previous step)

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 ⊦ bits2int(sgn(bitsinvert(uint2bits(~(j / 2 ^ i))))) = bits2int(sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1)), 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, sgn(bitsinvert(uint2bits(~(j % 2 ^ i))) +1)).rest, j % 2 ^ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ bits2int(sgn(bits)) = bits2int(bits)
Proof step 119:
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 ⊦ bits2int(bitsinvert(uint2bits(~(j / 2 ^ i)))) = bits2int(sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1)), 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, sgn(bitsinvert(uint2bits(~(j % 2 ^ i))) +1)).rest, j % 2 ^ i = 0

Rule argument

name: bits2int-sgn rotate: F subst: [bits] → [bitsinvert(uint2bits(~(j / 2 ^ i)))]

Additional information

Used terms: bitsinvert(uint2bits(~(j / 2 ^ i)))