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Proof step 76 from proof uint2bits-add-high (previous step)

¬ 0 ≤ 2 ^ (i - 1) - 2 ^ i0, 2 ^ i0 + (j - 1) / 2 = 0, j % 2 = 0, uint2bits(2 ^ (i - 1) - 2 ^ i0) = false ', 2 ^ (i - 2) < 2 ^ (i - 1), 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) < 2 ^ 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, 2 ^ (i - 1) + 1 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 2 ^ (i - 2) < 2 ^ i, j < i0, 2 ^ (i - 1) + j < i0, 0 < i0, j + 1 < i0, (2 ^ (i - 1) + j) + 1 < 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 77:
2 ^ i0 + (j - 1) / 2 = 0, j % 2 = 0, 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

Rule argument

Additional information

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