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Proof step 5 from proof int2bits-len-add (previous step)

0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0, 0 < j * 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 6:
⊦ i * j = j * i
Proof step 7:
0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0, 0 < 2 ^ i * j + j0 ⊦ # int2bits(~(2 ^ i * j + j0)) = # int2bits(~ j) + i→n(i)

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [2 ^ i, j] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used terms: 2 ^ i, j