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Proof step 58 from proof band-011x-pos (previous step)

uint2bits(j / 2) = boolvar + bits ∧ uint2bits(j / 2) ≠ [], 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, boolvar, ∀ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
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

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ boolvar + bits = boolvar ' + bits;