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Proof step 2 from proof bits2int-le8 (previous step)

bits2int(bits) < ~128, # bits ≤ 8, bits2int(bits) < 0 ⊦ bits = []

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ j < 0 → (∃ i. ~1 ≤ i ∧ j < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ j)
Proof step 4:
bits2int(bits) < 0 → (∃ i. ~1 ≤ i ∧ bits2int(bits) < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ bits2int(bits)), bits2int(bits) < ~128, # bits ≤ 8, bits2int(bits) < 0 ⊦ bits = []

Rule argument

seq: ⊦ j < 0 → (∃ i. ~1 ≤ i ∧ j < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ j) subst: [j] → [bits2int(bits)] rotate: F spec: int-pot inst: name: exin2pot-neg

Additional information

Used terms: bits2int(bits)