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Proof step 2 from proof band-011x-neg (previous step)

j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = bits2int(bitsand(false ' + mklist(true, i→n(i)), int2bits(j))) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 4:
j < 0, j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = bits2int(bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(abs(j))) +1))) + 1

Rule argument

seq: ⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1) subst: [i] → [j] rotate: F spec: int2bits inst: name: int2bits-neg

Additional information

Used terms: j