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Proof step 2 from proof int2bits-len-pos-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

seq: ⊦ ~ i * j = ~(i * j) subst: [j, i] → [2 ^ i, j] rotate: T spec: int-mult inst: name: minus-left

Additional information

Used terms: 2 ^ i, j