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Proof step 22 from proof band-011x-is-unsigned (previous step)

# int2bits(j) ≤ i→n(i), 0 ≤ 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ i ⊦ j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(i→n(i)), fillsgn(i→n(i), int2bits(j)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# int2bits(j) ≤ i→n(i), 0 ≤ 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ i ⊦ fillsgn(i→n(i), int2bits(j)) = [], j = bits2int(fillsgn(i→n(i), int2bits(j)))

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ 0 < i → n→i(i→n(i)) = i;