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Proof step 44 from proof band-011x-pos (previous step)

bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2))) = (j / 2) % 2 ^ i0, 0 < j, 0 ≤ j, 0 ≤ i0, ∀ 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 ⊦ j = 1, ~1 = i0, bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) + (j % 2 = 1)') = j % (2 ^ i0 * 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ ¬ boolvar ∧ bits ≠ [] → bits2int(bits + boolvar ') = bits2int(bits) * 2 subst: [boolvar, bits] → [j % 2 = 1, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2))] rotate: F spec: int2bits inst: name: bits2int-rec-02

Additional information

Used terms: j % 2 = 1, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2))