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Proof step 5 from proof uint2bits-restsgn (previous step)

¬(0 < 2 ^ (i + 2) - j ∧ 2 ^ (i + 2) - j ≠ 1), j < 2 * 2 ^ i, 2 ^ i < j, 0 < i, 2 < j, 0 ≤ 2 ^ i, 1 < j, 0 ≤ j, 0 < j, 1 < 2 ^ i, 0 < 2 ^ i, ∀ j0, i. i→n(j0) < i→n(j) → 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 + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
j < 2 * 2 ^ i, 2 ^ i < j, 0 < i, 2 < j, 0 ≤ 2 ^ i, 1 < j, 0 ≤ j, 0 < j, 1 < 2 ^ i, 0 < 2 ^ i, ∀ j0, i. i→n(j0) < i→n(j) → 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 + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest, ¬ 2 ^ (i + 2) ≤ j ∧ 2 ^ (i + 2) ≠ 1 + j

Rule argument

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i < j - i0 ↔ i + i0 < j;