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Proof step 79 from proof uint2bits-add-high (previous step)

2 ≠ 0, 2 ^ i0 + (j - 1) / 2 = 0, ∃ j0. j = j0 * 2, uint2bits(2 ^ (i - 1) - 2 ^ i0) = false ', j < i0, 2 ^ (i - 1) + j < i0, j + 1 < i0, (2 ^ (i - 1) + j) + 1 < i0, abs(j - 1) / 2 < 2 ^ i, 2 ^ (i - 2) < abs(j - 1) / 2, abs(j - 1) / 2 ≤ 2 ^ (i - 1), j < 0, j ≤ 2 ^ i, 0 ≤ j + 2 ^ i, 0 ≤ 2 ^ i, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 ≤ i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 0 < j + 2 ^ i, i ≤ i0, 1 < 2 ^ i, 0 < 2 ^ i, 1 < i, 0 < i, 0 < i0, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ i0 = 0, j + 2 ^ i = 1, j = ~1, j = 0, i = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
uint2bits(2 ^ (i - 1) - 2 ^ i0) = false ', j0 + 2 ^ i0 = 0, j0 * 2 ≤ 2 ^ i, 0 ≤ j0 * 2 + 2 ^ i, 0 ≤ 2 ^ i, (2 ^ (i - 1) + j0 * 2) + 1 < 2 ^ i, j0 * 2 < 2 ^ i, j0 * 2 + 1 < 2 ^ i, j0 * 2 < i, 2 ^ (i - 1) + j0 * 2 < 0, 0 ≤ i, (2 ^ (i - 1) + j0 * 2) + 1 < i, 2 ^ (i - 1) + j0 * 2 < i, j0 * 2 + 1 < i, 2 ^ (i - 1) + j0 * 2 < 2 ^ i, 0 < j0 * 2 + 2 ^ i, i ≤ i0, 1 < 2 ^ i, 0 < 2 ^ i, 1 < i, 0 < i, 0 < i0, j0 * 2 < i0, 2 ^ (i - 1) + j0 * 2 < i0, j0 * 2 + 1 < i0, (2 ^ (i - 1) + j0 * 2) + 1 < i0, abs(j0 * 2 - 1) / 2 < 2 ^ i, 2 ^ (i - 2) < abs(j0 * 2 - 1) / 2, abs(j0 * 2 - 1) / 2 ≤ 2 ^ (i - 1), j0 < 0, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ i = 1, i0 = 0, j0 * 2 + 2 ^ i = 1, j0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ j < 0 → (j * 2 - 1) / 2 = j;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 2 * i ≠ ~1;