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

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used terms: j