Noticing the following:

>>> a ="nectarine"
>>> a[1]
'e'
>>> a = a[:1] + "egg" + a[1:]
>>> a
'neggectarine'
>>> 

I thought I could implement the eggy-peggy program as follows: 

sentence = "this is a test"
i = 0 # index in string 
for letter in sentence: # for every letter
    if letter in "aeiou": # if it's a vowel 
        sentence = sentence[:i] + "egg" + sentence[i:] # split and insert "egg"
    i = i + 1 # update index
print sentence

As you can see I am keeping track of the letters with an index, i, which I increment
every time I move to the next letter. I use the split and insert that I illustrated at
the beginning, and store the result in the same variable, sentence. 

Is this program correct? 

If it is: run it, to prove it correct. Then explain why it's correct. 

If it's not: provide a counterexample or explain why you think it doesn't work. How can 
it be fixed if it's wrong (with minimal effort)?