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Proof step 59 from proof band-011x-pos (previous step)

bits2int(bitsand(false ' + mklist(true, i→n(i0)), true ' + bits)) = (j / 2) % 2 ^ i0, j % 2 = 1, uint2bits(j / 2) = true ' + bits, 0 < j, 0 ≤ j, 0 ≤ i0, bitsand(false ' + mklist(true, i→n(i0)), true ' + bits).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)), true ' + bits) + 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] → [bitsand(false ' + mklist(true, i→n(i0)), true ' + bits), boolvar, bits0] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: and-notempty-06: ⊦ bitsand(boolvar ' + bits, boolvar0 ' + bits0) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bitsand(false ' + mklist(true, i→n(i0)), true ' + bits), boolvar, bits0