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Proof step 2 from proof bits2int16-01 (previous step)

# bits = 16, 0 < bits2int(bits), 32767 < bits2int(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] → [bits]

Additional information

Used simplifier rules: ⊦ # [] = 0;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: bits