[failure]SICP Exercise 2.6[λcalculus]

http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html#%_thm_2.6 for those of you who haven't memorized your sicp yet.

i can dig the idea behind church numerals. number represented by the number of times a function is applied, sure.
but i'm having trouble seeing how the substitution model is used to go from
(lambda (f) (lambda (x) (f (((lambda (f) (lambda (x) x)) f) x)))) to (lambda (f) (lambda (x) (f x))) or whatever the fuck.

halp.

[quote]
(lambda (f) (lambda (x) (f (((lambda (f) (lambda (x) x)) f) x))))[/quote]
THIS IS WHAT FUNCTIONAL PROGRAMMERS ACTUALLY BELIEVE.