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Proof step 67 from proof band-011x-pos (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)), boolvar, bits