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Proof step 19 from proof int2bits-restsgn (previous step)

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 ≠ j, 2 ^ (i + 2) = j, 0 = j, sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest, ∃ i. 2 ^ i = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
1 < 2 ^ (i + 2), 0 ≤ i, 0 < 2 ^ i, 0 < 2 ^ (i + 2), 0 ≤ 2 ^ (i + 2) ⊦ 2 ^ (i + 2) = 2 ^ i, sgn(uint2bits(2 ^ (i + 2) - 2 ^ i).rest) = uint2bits(2 ^ (i + 2) - 2 ^ i).rest, ∃ i0. 2 ^ i0 = 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ 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 = j + i;% ⊦ 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;