Proof by induction would work here.
Let be the statement that:
Base case: True.
Inductive step: Assuming is true, it remains to show that is also true, that is:
Modifying it a bit just to see what we're working with:
(I just expanded the '...' a bit and noticed that is 'in' there)
Now we have to show that the right hand side of and are the same.
Simplify and notice that in :
And now it is a matter of simplifying the inside the brackets.