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Proof step 2 from proof bits2int16-02 (previous step)

bits2int(lastn(16, bits)) < 0, 16 < # bits, bits2int(lastn(16, bits)) < ~32768 ⊦ 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)

Rule argument

name: bits2int-range subst: [bits] → [lastn(16, bits)]

Additional information

Used simplifier rules: ⊦ lastn(n, bits) = [] ↔ n = 0;% ⊦ # lastn(n, bits) = n;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: lastn(16, bits)