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Proof step 99 from proof uint2bits-add-high (previous step)

0 ≤ i - 1 ∧ 0 ≤ i0, abs(j - 1) / 2 = 2 ^ i0, i - 1 = i0, j % 2 = 0, 2 ^ i0 + (j - 1) / 2 = 0, 2 ^ i0 + j < i0, 2 ^ i0 + j < i, j + 1 < i0, 0 < i0, j < i0, 0 < 2 ^ i, 1 < 2 ^ i, 2 ^ i0 + 1 < 2 ^ i, 0 < j + 2 ^ i, j + 1 < i, 0 < i, j < i, j + 1 < 2 ^ i, j < 2 ^ i, 0 ≤ 2 ^ i, 0 ≤ j + 2 ^ i, j ≤ 2 ^ i, j < 0, 2 ^ i0 + j < 2 ^ i, 2 ^ i0 + j < 0, j < (j - 1) / 2, (2 ^ i0 + j) + 1 < i0, (2 ^ i0 + j) + 1 < 2 ^ i, (2 ^ i0 + j) + 1 < i, ∀ 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, j = 0, j = ~1, j + 2 ^ i = 1, i0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 100:
2 ^ (i - 1) + (j - 1) / 2 = 0, j % 2 = 0, abs(j - 1) / 2 = 2 ^ (i - 1), 0 ≤ i, 0 < i, 2 + 2 ^ (i - 1) + j < i, 2 ^ (i - 1) + j < 0, j < 0, j ≤ 2 ^ i, 0 ≤ j + 2 ^ i, 0 ≤ 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 0 < j + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 1 < i, 2 + j < i, (2 ^ (i - 1) + j) + 1 < i, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < (j - 1) / 2, ∀ 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, j + 2 ^ i = 1, j = ~1, j = 0

Rule argument

Additional information

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