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Proof step 52 from proof int2bits-add-low (previous step)

2 ^ i + j0 ≤ 0 ∧ 0 ≤ j0 + 2 ^ (i - 1) → 2 ^ i + j0 ≤ j0 + 2 ^ (i - 1), 0 < 2 ^ (i - 1) + j0, j0 < 0, j < 0, 0 < i, i < n→i(# int2bits(~(j * 2 ^ i + j0))), j * 2 ^ i + j0 < 0, 0 < j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i), 0 ≤ (j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)) * 2 ^ i + j0, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 ≤ 0 ⊦ sgn(uint2bits(j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i) - 1).rest + fillsgn(i→n(i), int2bits(j0))) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0)), j * 2 ^ i + j0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
0 < 2 ^ (i - 1) + j0, j0 < 0, j < 0, 0 < i, i < n→i(# int2bits(~(j * 2 ^ i + j0))), j * 2 ^ i + j0 < 0, 0 < j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i), 0 ≤ (j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)) * 2 ^ i + j0, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 ≤ 0, 2 ^ i ≤ 2 ^ (i - 1) ⊦ sgn(uint2bits(j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i) - 1).rest + fillsgn(i→n(i), int2bits(j0))) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0)), j * 2 ^ i + j0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j ≤ i + j0 ↔ j ≤ j0;% ⊦ i < j → ¬ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;