"""Format a positive integer as a sequence of lowercase letters.

This function converts a positive integer into a string representation using lowercase letters (a-z). The conversion follows a base-26 numbering system where 'a' corresponds to 1, 'b' to 2, ..., 'z' to 26, 'aa' to 27, 'ab' to 28, and so on.

Args:
    value (int): A positive integer to be formatted. Must be greater than 0.

Returns:
    str: The formatted string representation of the integer using lowercase letters.

Raises:
    AssertionError: If `value` is not a positive integer.
"""
You should write code starting with:
import string

def format_int_alpha(value: int) -> str:
    # TODO: Implement this function
    pass

