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Proof step 2 from proof int2bits-len-neg-01 (previous step)

i < 0 ⊦ # int2bits(i) = # int2bits(~(i + 1))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1))
Proof step 4:
0 < ~(i + 1) → (∃ i0. 0 ≤ i0 ∧ 2 ^ i0 ≤ ~(i + 1) ∧ ~(i + 1) < 2 ^ (i0 + 1)), i < 0 ⊦ # int2bits(i) = # int2bits(~(i + 1))

Rule argument

seq: ⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1)) subst: [j] → [~(i + 1)] rotate: F spec: int-pot inst: name: exin2pot

Additional information

Used terms: ~(i + 1)