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Proof step 8 from proof int2bits-rec-2pot-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits + bitsinvert(bits0) +1
Proof step 10:
¬ 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 ⊦ sgn((bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest))+1) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0
Proof step 34:
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 ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0

Rule argument

seq: ⊦ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits + bitsinvert(bits0) +1 subst: [bits0, bits] → [fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, bitsinvert(uint2bits(~(j / 2 ^ i)))] rotate: F spec: bitopsaux inst: name: succ-zero-02

Additional information

Used terms: fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, bitsinvert(uint2bits(~(j / 2 ^ i)))