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Proof step 57 from proof band-011x-pos (previous step)

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

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] → [uint2bits(j / 2), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;%0 ≤ i ⊦ uint2bits(i) ≠ [];%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: uint2bits(j / 2), boolvar, bits