def is_valid_deck(deck_of_cards):
    """ (list of int) -> bool
    
    A valid deck contains every integer from 1 up to the number of cards in 
    the deck. 
    Return True if and only if the deck_of_cards is a valid deck of cards. 
    
    >>> is_valid_deck([1, 4, 3, 2])
    True
    >>> is_valid_deck([])
    False
    """
    
    # If the length of deck_of_cards is less than 3, it's not a valid deck.
    if len(deck_of_cards) < 3:
        return False
    
    # Otherwise, check whether every number from 1 up to the biggest integer 
    # is in the deck_of_cards.
    else:
        for i in range(1, len(deck_of_cards) + 1):
            if not (i in deck_of_cards):
                return False
        return True