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Proof step 13 from proof uint2bits-add-low-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 < j, j0 < 0, 0 < i, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 < 0, 2 ^ i ≤ 2 ^ (i - 1) ⊦ j = 1, uint2bits(2 ^ i * j + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Rule argument

Additional information

Used simplifier rules: ⊦ i + j ≤ i + j0 ↔ j ≤ j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;