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Proof step 1 from proof int2int-neg (conclusion)

⊦ j < 0 → bits2int(int2bits(j)) = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 3:
¬ 0 ≤ 2 ^ n→i(# int2bits(~ j)) + j ⊦ j < 0 → bits2int(int2bits(j)) = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)
Proof step 11:
0 ≤ 2 ^ n→i(# int2bits(~ j)) + j ⊦ j < 0 → bits2int(int2bits(j)) = bits2int(uint2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

Rule argument

name: int2bits-pos rotate: F subst: [i] → [2 ^ n→i(# int2bits(~ j)) + j]

Additional information

Used terms: 2 ^ n→i(# int2bits(~ j)) + j