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Proof step 2 from proof bits2int-le8-01 (previous step)

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

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 < bits2int(bits) → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ (i + 1)), 127 < bits2int(bits), # bits ≤ 8, 0 < bits2int(bits), 0 ≤ bits2int(bits) ⊦ bits = []

Rule argument

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

Additional information

Used terms: bits2int(bits)