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Proof step 7 from proof uint2bits-restsgn (previous step)

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 ⊦ ¬ 2 ^ (i + 2) ≤ j, 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 8:
2 ^ (i + 2) ≤ j, 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, 2 ^ (i + 2) < 2 * 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

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)