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Proof step 149 from proof uint2bits-restsgn (previous step)

1 < 2 ^ i, 0 ≤ 2 ^ i, false ∈ uint2bits(2 * (2 ^ i - 1)).rest, 0 < 2 ^ i, 0 < i, 2 ^ i ≤ 2, 1 < 2 ^ (i - 1), 0 < 2 ^ (i - 1), 0 ≤ 2 ^ (i - 1), ∀ j0, i. i→n(j0) < i→n(1 * 2 + 1) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ sgn(uint2bits(2 * (2 ^ i - 1)).rest) = uint2bits(2 * (2 ^ i - 1)).rest, i = 0, i = 1

User applied rule cut formula

And obtained the following new goals

Proof step 150:
1 < 2 ^ i, 0 ≤ 2 ^ i, false ∈ uint2bits(2 * (2 ^ i - 1)).rest, 0 < 2 ^ i, 0 < i, 2 ^ i ≤ 2, 1 < 2 ^ (i - 1), 0 < 2 ^ (i - 1), 0 ≤ 2 ^ (i - 1), ∀ j0, i. i→n(j0) < i→n(1 * 2 + 1) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ i = 1, sgn(uint2bits(2 * (2 ^ i - 1)).rest) = uint2bits(2 * (2 ^ i - 1)).rest, i = 0, i = 1

Rule argument

fma: i = 1

Additional information

Used formulas: i = 1