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Proof step 167 from proof uint2bits-restsgn (previous step)

2 ^ i = i0 + 1, 2 ^ (i - 1) ≤ i0 + 1, ~2 ≤ i0, false ∈ uint2bits(i0 + 1).rest, i0 < 2 * (i0 + 1), 0 ≤ i0, 0 ≤ i, i0 * 2 + 1 < 4 * (i0 + 1), 0 < i, 2 ^ (i - 1) < 2 * (i0 + 1), 0 < i0, 2 ^ (i - 1) ≤ i0, ~1 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i0 * 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(i0 + 1).rest) = uint2bits(i0 + 1).rest, i = 1, i0 = 1

User applied rule insert equation

And obtained the following new goals

Proof step 168:
2 ^ i = i0 + 1, 2 ^ (i - 1) ≤ 2 ^ i, ~2 ≤ i0, false ∈ uint2bits(2 ^ i).rest, i0 < 2 * 2 ^ i, 0 ≤ i0, 0 ≤ i, i0 * 2 + 1 < 4 * 2 ^ i, 0 < i, 2 ^ (i - 1) < 2 * 2 ^ i, 0 < i0, 2 ^ (i - 1) ≤ i0, ~1 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i0 * 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 ^ i).rest) = uint2bits(2 ^ i).rest, i = 1, i0 = 1

Rule argument

pos: left 1 flags: rotate

Proof step 167 from proof uint2bits-restsgn (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information