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Proof step 48 from proof int2bits-add-high (previous step)

0 ≤ 2 ∧ 0 ≤ i0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 2 ^ i0 ≤ 2 ^ (1 + i0), 0 ≤ j0 + 2 ^ i, 2 ^ i0 ≤ 2 ^ 2 * 2 ^ i0, 0 < i0, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 ≤ 2 ^ i * (2 ^ (1 + i0) + 1 - 2 ^ i0) + j0 ⊦ true ' + mklist(false, i→n(i0)) = sgn(uint2bits(2 ^ 2 * 2 ^ i0 - 2 ^ i0).rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 0 ≤ j0 + 2 ^ i, 0 < i0, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 ≤ i0, 0 ≤ 2 ^ i0, 0 ≤ (2 ^ i0 + 1) * 2 ^ i + j0 ⊦ true ' + mklist(false, i→n(i0)) = sgn(uint2bits(2 ^ i0 * 3).rest)

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i * (* j) + j0 - i = i * (j - 1) + j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ 1 * i = i;% ⊦ j ≤ (* i1) * j ↔ 0 ≤ (i1 - 1) * j;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j - i = i * (j - 1);