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Proof step 2 from proof int2bits-len-neg (previous step)

j < 2 ^ i, j < 0, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i ⊦ # int2bits(j) = i→n(i + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 4:
j < 0, j < 2 ^ i, j < 0, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i ⊦ # sgn(bitsinvert(uint2bits(abs(j))) +1) = i→n(i + 2)

Rule argument

name: int2bits-neg rotate: F subst: [i] → [j]

Additional information

Used terms: j