The definition of factorial (fac for short) can be broken down as

    succ = \n\f\x. n f (f x) -- the successor function for Church numerals
    F   = \c\n. n (c (succ n))
    fac = \n\f. n F (\x.f) id

As you can see there is no use of a decrement function. Instead, numbers 1..n are recreated by the iterated successor function.

We can follow the reduction of fac 3 as

    0 = \f\x. x
    1 = \f\x. f x
    2 = \f\x. f(f x)
    3 = \f\x. f(f(f x))
    fac 3 = \f. F (F (F (\x.f))) 1
          = \f. 1 (F (F (\x.f))  2)
          = \f. 1 (2 (F (\x.f)   3))
          = \f. 1 (2 (3 ((\x.f)  4)))
          = \f. 1 (2 (3 f))