Proof that, for any set, it's either true that all elements are equal or that atleast one element has a higher value than the average

proof.py

'''
Proof that, for any set, it's either true that all elements are equal or that atleast one element has a higher value than the average
'''
def avg(a):
    '''
    Calculate average over a set, list, array or similar
    '''
    return sum(a)/len(a)

def f(a):
    '''
    Test the claim for a given array
    '''
    if len(a)<2:return True
    if any([_>=avg(a) for _ in a]):return True
    return False

'''
Test the claim for n<100 (should be enough)
'''
all([f(list(range(_))) for _ in range(100)])