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Proof step 15 from proof int2bits-restsgn (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 16:
0 < i, 0 ≤ j, 2 ^ i < j, j < 2 * 2 ^ i ⊦ sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest
Proof step 17:
0 < 2 ^ (i + 2), 0 ≤ 2 ^ (i + 2), j ≤ 2 ^ (i + 2), 0 < 2 ^ i, 0 < j, j < 2 ^ i * 2, 2 ^ i ≤ j, 0 ≤ i ⊦ 0 < i ∧ 0 ≤ j ∧ 2 ^ i < j ∧ j < 2 * 2 ^ i, sgn(uint2bits(2 ^ (i + 2) - j).rest) = uint2bits(2 ^ (i + 2) - j).rest, 0 = j, 2 ^ (i + 2) = j, ∃ i. 2 ^ i = j

Rule argument

name: uint2bits-restsgn subst: [i, j] → [i, j]

Additional information

Used terms: i, j