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Proof step 17 from proof int2bits-rec-2pot-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
0 ≤ i ⊦ uint2bits(i) ≠ []
Proof step 19:
¬ 0 ≤ ~(j % 2 ^ i), uint2bits(~(j % 2 ^ i)) = [], 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i ⊦ j % 2 ^ i = 0, sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) +1 + mklist(false, i→n(i))) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest

Rule argument

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

Additional information

Used terms: ~(j % 2 ^ i)