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Proof step 11 from proof band-011x-pos (previous step)

0 ≤ j, 0 < i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 13:
¬(0 < j ∧ j ≠ 1), 0 ≤ j, 0 < i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i
Proof step 32:
0 < j ∧ j ≠ 1, 0 ≤ j, 0 < i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j / 2) + (j % 2 = 1))) = j % 2 ^ i

Rule argument

seq: ⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1) subst: [i] → [j] rotate: F spec: int2bits inst: name: uint2bits-rec-01

Additional information

Used terms: j