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Proof step 2 from proof bits2int16-03 (previous step)

0 < bits2int(lastn(16, bits)), 16 < # bits, 32767 < bits2int(lastn(16, bits)) ⊦ 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 + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: lastn(16, bits)