-----Description----- 
This task requires writing a Lean 4 method that determines whether a list of integers follows a peak-valley pattern.

A list follows this pattern if:
A. It strictly increases at first,
B. Then strictly decreases,
C. Both parts are non-empty.

Examples:
- [1, 3, 5, 4, 2] -> true
- [1, 2, 3] -> false
- [5, 4, 3] -> false
- [1, 2, 2, 1] -> false

-----Input-----
The input consists of a list of integers:

-----Output-----
The output is an integer:
Returns true if the list has a peak-valley structure, false otherwise.

