input: 
  from typing import List
  
  def element_exists(elem: int, list_int: List[int]) -> bool:
      """ Check if a given element exists within the provided list of integers.
      >>> element_exists(5, [1, 2, 3, 4, 5])
      True
      >>> element_exists(10, [1, 2, 3, 4, 5])
      False
      """
      return elem in list_int
  
output:     return elem in list_int