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Proof step 91 from proof uint2bits-add-high (previous step)

~(2 ^ i0) < 0, 0 ≤ 2 ^ i0 * 2 + 2 ^ i, 2 ^ i0 * 2 ≤ 2 ^ i, 0 ≤ 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i0 * 2 + 2 ^ i, 0 < 2 ^ i + 2 ^ i0 * 2, 1 < 2 ^ i0 * 2 + 2 ^ i, 0 < i + 2 ^ i0 * 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, i0 = 0, 2 ^ i = 1 + 2 ^ i0 * 2, ~(2 ^ i0) * 2 - 1 < 0, ~(2 ^ i0) * 2 ≤ 0 ∧ ~(2 ^ i0) * 2 ≠ 0

User applied rule simplifier

And closed the goal!

Rule argument

Additional information

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