lambda calculus – Church Numerals represented as a List?

Afternoon All,

Perhaps an easy one for many, but am new to Lambda calculus:

Is the below list, Ni, a representation of the Church numerals? I think it is but how do I prove it…if not, what is it…?

The terms Ni and N’i for each natural number i are defined as follows.
(n and c are variables while i stands for a number.)

          N'0 = n
          N'i = c i N'i−1 for i > 0
          Ni = λc.λn.N'i for any i

any help much appreciated…
Kind Regards