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Proof step 1 from proof uint2bits-restsgn (conclusion)

0 < i, 0 ≤ j, 2 ^ i < j, j < 2 * 2 ^ i ⊦ sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest

User applied rule induction

And obtained the following new goals

Proof step 2:
0 < i ∧ 0 ≤ j ∧ 2 ^ i < j ∧ j < 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

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)