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

0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0 ⊦ # int2bits(~(j * 2 ^ i + j0)) = # int2bits(~ j) + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 4:
¬ 0 ≤ ~(j * 2 ^ i + j0), 0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0 ⊦ # int2bits(~(j * 2 ^ i + j0)) = # int2bits(~ j) + i→n(i)
Proof step 9:
0 ≤ ~(j * 2 ^ i + j0), 0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0 ⊦ # uint2bits(~(j * 2 ^ i + j0)) = # int2bits(~ j) + i→n(i)

Rule argument

name: int2bits-pos rotate: F subst: [i] → [~(j * 2 ^ i + j0)]

Additional information

Used terms: ~(j * 2 ^ i + j0)