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Proof step 20 from proof uint2bits-add-low (previous step)

(j - 1) / 2 < 0 ∧ 0 < i - 1 ∧ abs((j - 1) / 2) ≤ 2 ^ (i - 1 - 1) → uint2bits((j - 1) / 2 + 2 ^ (i - 1)) = false ' + fillsgn(i→n(i - 1), int2bits((j - 1) / 2)), j ≤ 2 ^ (i - 1), j ≤ 2 ^ i, 0 ≤ 2 ^ (i - 1), 1 < j + 2 ^ i, j < 2 ^ (i - 1), j + 1 < i, 0 < 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ j + 2 ^ (i - 1), j < i, j + 1 < 2 ^ (i - 1), j ≤ 0, 0 < j + 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 ≤ j + 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ abs(j) ≤ 2 ^ (i0 - 1) → uint2bits(j + 2 ^ i0) = false ' + fillsgn(i→n(i0), int2bits(j)) ⊦ uint2bits(2 ^ (i - 1) + (j - 1) / 2) + (~1 = j % 2)' = false ' + fillsgn(i→n(i), int2bits(j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
j ≤ 2 ^ (i - 1), j ≤ 2 ^ i, 0 ≤ 2 ^ (i - 1), 1 < j + 2 ^ i, j < 2 ^ (i - 1), j + 1 < i, 0 < 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ j + 2 ^ (i - 1), j < i, j + 1 < 2 ^ (i - 1), j ≤ 0, 0 < j + 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 ≤ j + 2 ^ i, j ≠ 0 ∧ i ≠ 1 ∧ ¬ 2 ^ (i - 2) < abs(j - 1) / 2 → uint2bits((j - 1) / 2 + 2 ^ (i - 1)) = false ' + fillsgn(i→n(i) - 1, int2bits((j - 1) / 2)), ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ abs(j) ≤ 2 ^ (i0 - 1) → uint2bits(j + 2 ^ i0) = false ' + fillsgn(i→n(i0), int2bits(j)) ⊦ uint2bits(2 ^ (i - 1) + (j - 1) / 2) + (~1 = j % 2)' = false ' + fillsgn(i→n(i), int2bits(j))

Rule argument

Additional information

Used simplifier rules: ⊦ n -1 = n - 1;% ⊦ 0 < i ∧ i ≠ 1 → i→n(i - 1) = i→n(i) -1;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i - j - i0 = i - j + i0;%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;