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Proof step 153 from proof uint2bits-add-high (previous step)

i = 1 - i1 * 2, 1 = i + i1 * 2, i + 1 < i1, i + 1 < 4 * 2 ^ i2 + i1 * 2, i < i1, i < 4 * 2 ^ i2 + i1 * 2, i < 2 ^ i2, i < i2, i < 2 * (i1 + 1) + i2, i < 0, i < ~2, i1 + i < 0, 0 < i1, 0 ≤ i1, 0 ≤ 4 * 2 ^ i2 + i1 * 2, 0 < 4 * 2 ^ i2 + i1 * 2, 2 ^ i2 * 2 < i1, i1 * 2 < 4 * 2 ^ i2, 2 ^ i2 < i1, ~2 * 2 ^ i2 < i1 * 2, 2 < 2 * (i1 + 1) + i2, 2 * (2 ^ i2 + 1) < 2 * (i1 + 1) + i2, 2 < 4 * 2 ^ i2 + i1 * 2, 2 * (2 ^ i2 + 1) < 4 * 2 ^ i2 + i1 * 2, i1 * 2 ≤ 1 + 4 * 2 ^ i2, 2 * (2 ^ i2 + 1) < 4 * 2 ^ i2, 0 ≤ 2 ^ i2, 0 ≤ i2, 0 < 2 * (i1 + 1) + i2, 0 ≤ 2 * (i1 + 1) + i2, 1 < i1, 0 < 2 ^ i2, i < i1 + 4 * 2 ^ i2, i1 + i < 2 ^ i2, i1 + i < i2, i1 + i < 2 * (i1 + 1) + i2, i + 1 < i1 + 4 * 2 ^ i2, (i1 + i) + 1 < 2 ^ i2, i ≤ i1 + i2, ∀ i0, j. i→n(i0) < i→n(i2 + 2) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ 4 * 2 ^ i2 = i1 * 2, uint2bits(2 ^ i2 * 2 - i1) + (i % 2 ≠ 0)' = sgn(int2bits(i).rest), ~1 = i2

User applied rule insert equation

And obtained the following new goals

Rule argument

pos: left 1 flags: discard

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