2 years have passed, but I want to add a little remark to this question. Originally, I asked if there is any way to tell if (λx.2*x) is equal to (λx.x+x) . Addition and multiplication on the λ-calculus can be defined as:

add = (a b c -> (a b (a b c))) mul = (a b c -> (a (b c)))

Now, if you normalize the following terms:

add_x_x = (λx . (add x x)) mul_x_2 = (mul (λf x . (f (f x)))

You get:

result = (a b c -> (a b (a b c)))