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Proof step 3 from proof int2bits-lslen-07 (previous step)

j < 0, # int2bits(j) + 1 < # int2bits(j + 1) ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 4:
⊦ j < 0 → (∃ i. ~1 ≤ i ∧ j < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ j)
Proof step 5:
j < 0 → (∃ i. ~1 ≤ i ∧ j < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ j), j < 0, # int2bits(j) + 1 < # int2bits(j + 1) ⊦

Rule argument

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

Additional information

Used terms: j