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Proof step 9 from proof uint2bits-add-high (previous step)

j = 1 - 2 ^ i, j + 2 ^ i = 1, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 < i, j < 0, 2 ^ (i - 1) < 2 ^ i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, 0 < 2 ^ i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 2 ^ (i - 1) + j ≤ 0, j ≤ 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 ' + true ' = sgn(int2bits(j).rest)

User applied rule insert equation

And obtained the following new goals

Proof step 10:
(1 - 2 ^ i) + 2 ^ i = 1, (2 ^ (i - 1) + (1 - 2 ^ i)) + 1 < 2 ^ i, 1 - 2 ^ i < 2 ^ i, (1 - 2 ^ i) + 1 < 2 ^ i, 1 - 2 ^ i < i, 2 ^ (i - 1) + (1 - 2 ^ i) < 0, 0 < i, 1 - 2 ^ i < 0, 2 ^ (i - 1) < 2 ^ i, (2 ^ (i - 1) + (1 - 2 ^ i)) + 1 < i, 2 ^ (i - 1) + (1 - 2 ^ i) < i, 0 < 2 ^ i, (1 - 2 ^ i) + 1 < i, 2 ^ (i - 1) + (1 - 2 ^ i) < 2 ^ i, 2 ^ (i - 1) + (1 - 2 ^ i) ≤ 0, 1 - 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 ' + true ' = sgn(int2bits(1 - 2 ^ i).rest)

Rule argument

pos: left 1 flags: discard

Proof step 9 from proof uint2bits-add-high (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information