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Proof step 29 from proof int2bits-rec-2pot-neg-02 (previous step)

i→n(i) < # uint2bits(~(j % 2 ^ i)), 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) +1 + uint2bits(~(j % 2 ^ i)).rest) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0, uint2bits(~(j % 2 ^ i)) = [], true ∈ uint2bits(~(j % 2 ^ i)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 0 < j → true ∈ uint2bits(j).rest
Proof step 31:
¬ 0 < ~(j % 2 ^ i), i→n(i) < # uint2bits(~(j % 2 ^ i)), 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) +1 + uint2bits(~(j % 2 ^ i)).rest) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0, uint2bits(~(j % 2 ^ i)) = [], true ∈ uint2bits(~(j % 2 ^ i)).rest

Rule argument

name: uint2bits-truein rotate: F subst: [j] → [~(j % 2 ^ i)]

Additional information

Used terms: ~(j % 2 ^ i)