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Proof step 68 from proof band-011x-pos (previous step)

bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) = boolvar + bits, 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)) = [], boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
bits2uint(bits) = (j / 2) % 2 ^ i0, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) = false ' + bits, j % 2 = 1, 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, bits2uint(bits) * 2 + 1 = j % (2 ^ i0 * 2)

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ' + bits ≠ [];% ⊦ bits2int(false ' + bits) = bits2uint(bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;