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Proof step 40 from proof uint2bits-add-high (previous step)

(2 ^ (i - 1) + (0 - 2 ^ i)) + 1 < 2 ^ i, 0 - 2 ^ i < 2 ^ i, (0 - 2 ^ i) + 1 < 2 ^ i, 0 - 2 ^ i < i, 2 ^ (i - 1) < 2 ^ i, (2 ^ (i - 1) + (0 - 2 ^ i)) + 1 < i, (0 - 2 ^ i) + 1 < i, 2 ^ (i - 1) + (0 - 2 ^ i) < 2 ^ i, 0 < 2 ^ i, 2 ^ (i - 1) + (0 - 2 ^ i) < 0, 0 < i, 0 - 2 ^ i < 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) ⊦ false ' = sgn(int2bits(0 - 2 ^ i).rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
0 ≤ 2 ^ i + i, 0 ≤ 2 ^ i + 2 ^ i, 0 < i, 0 < 2 ^ i, 2 ^ (i - 1) < 2 ^ i + 2 ^ i, 1 < 2 ^ i + i, 2 ^ (i - 1) + 1 < 2 ^ i + i, 2 ^ (i - 1) < 2 ^ i, 1 < 2 ^ i + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i + 2 ^ 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) ⊦ false ' = sgn(mklist(false, i→n(i)))

Rule argument

Additional information

Used simplifier rules: int2bits-2pot-01: 0 ≤ i ⊦ int2bits(~(2 ^ i)) = true ' + mklist(false, i→n(i));% ⊦ (* i) < j ∧ 0 < i → 0 ≤ j ∧ 0 < j; (forward)% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ i + 0 = i;% ⊦ 0 < i ∧ 0 < j → 0 < i + j;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i + ~ j = i - j;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ 0 - i = ~ i;