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Proof step 125 from proof uint2bits-add-high (previous step)

1 = (i1 * 2 + j0) + j, 2 ^ (i - 1) + j ≤ 2 ^ i, 2 ^ (i - 1) + j ≤ 0, j < j0, 2 ^ (i - 1) + j < j0, 1 < 2 ^ i, j ≤ 1, j0 < 2, 0 ≤ j0, j < 0, j ≤ 2 ^ i, 0 ≤ j + 2 ^ i, 0 ≤ 2 ^ i, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 < i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 0 < j + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 0 < 2 ^ i, 2 ^ (i - 1) + j ≤ j0, 2 ^ (i - 1) ≤ 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) ⊦ j = 0, i = 1, uint2bits(2 ^ (i - 1) + (j - 1) / 2) + (j % 2 ≠ 0)' = sgn(int2bits(j).rest), j + 2 ^ i = 1, ¬ 2 ^ (i - 1) < i1 ∧ ¬ i1 ≤ 2 ^ (i - 2)

User applied rule cut formula

And obtained the following new goals

Proof step 126:
j0 = 1, 1 = (i1 * 2 + j0) + j, 2 ^ (i - 1) + j ≤ 2 ^ i, 2 ^ (i - 1) + j ≤ 0, j < j0, 2 ^ (i - 1) + j < j0, 1 < 2 ^ i, j ≤ 1, j0 < 2, 0 ≤ j0, j < 0, j ≤ 2 ^ i, 0 ≤ j + 2 ^ i, 0 ≤ 2 ^ i, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 < i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 0 < j + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 0 < 2 ^ i, 2 ^ (i - 1) + j ≤ j0, 2 ^ (i - 1) ≤ 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) ⊦ j = 0, i = 1, uint2bits(2 ^ (i - 1) + (j - 1) / 2) + (j % 2 ≠ 0)' = sgn(int2bits(j).rest), j + 2 ^ i = 1, ¬ 2 ^ (i - 1) < i1 ∧ ¬ i1 ≤ 2 ^ (i - 2)
Proof step 143:
1 = (i1 * 2 + j0) + j, 2 ^ (i - 1) + j ≤ 2 ^ i, 2 ^ (i - 1) + j ≤ 0, j < j0, 2 ^ (i - 1) + j < j0, 1 < 2 ^ i, j ≤ 1, j0 < 2, 0 ≤ j0, j < 0, j ≤ 2 ^ i, 0 ≤ j + 2 ^ i, 0 ≤ 2 ^ i, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 < i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 0 < j + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 0 < 2 ^ i, 2 ^ (i - 1) + j ≤ j0, 2 ^ (i - 1) ≤ 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) ⊦ j0 = 1, j = 0, i = 1, uint2bits(2 ^ (i - 1) + (j - 1) / 2) + (j % 2 ≠ 0)' = sgn(int2bits(j).rest), j + 2 ^ i = 1, ¬ 2 ^ (i - 1) < i1 ∧ ¬ i1 ≤ 2 ^ (i - 2)

Rule argument

fma: j0 = 1

Additional information

Used formulas: j0 = 1