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Proof step 17 from proof int2bits-restsgn (previous step)

0 < 2 ^ (i + 2), 0 ≤ 2 ^ (i + 2), j ≤ 2 ^ (i + 2), 0 < 2 ^ i, 0 < j, j < 2 ^ i * 2, 2 ^ i ≤ j, 0 ≤ i ⊦ 0 < i ∧ 0 ≤ j ∧ 2 ^ i < j ∧ j < 2 * 2 ^ i, sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest, 0 = j, 2 ^ (i + 2) = j, ∃ i. 2 ^ i = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
1 < 2 ^ (i + 2), j < 2 ^ (i + 2), 0 ≤ i, 2 ^ i ≤ j, j < 2 ^ i * 2, 0 < j, 0 < 2 ^ i, 0 < 2 ^ (i + 2), 0 ≤ 2 ^ (i + 2) ⊦ 2 ^ (i + 2) = j, 0 = j, sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest, 0 ≠ i ∧ 2 ^ i ≠ j, ∃ i. 2 ^ i = j

Rule argument

Additional information

Used simplifier rules: ⊦ (* i) < j ∧ 0 < i → 0 ≤ j ∧ 0 < j; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i < i * j ↔ 1 < j);% ⊦ i ≤ i;% ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < i + j ↔ 0 < j;% ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0);% ⊦ 0 ≤ j → 2 ^ j ≠ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * j = j * i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j = j + i;