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

# bits ≤ n, 2 ^ n→i(n) + bits2int(bits) ≤ 0 ⊦ bits = []

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
bits ≠ [] ⊦ ~(2 ^ n→i(# bits - 1)) ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ n→i(# bits - 1)
Proof step 4:
~(2 ^ n→i(# bits - 1)) ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ n→i(# bits - 1), # bits ≤ n, 2 ^ n→i(n) + bits2int(bits) ≤ 0 ⊦ bits = []

Rule argument

name: bits2int-range subst: [bits] → [bits]

Additional information

Used terms: bits