Lambda Calculus: Prove $m \ Succ\ n = m+n$

Question

Given $Succ = \lambda n. \lambda fx. f(n f(x))$ and

church's numeral: $n = \lambda fx.f^n(x)$

Show that $ m\ Succ\ n = m + n$

I don't get how it can be shown. I get stuck on this step:

$\lambda fx. f^m(x) \ \lambda fx.f^{n+1}(x)$

Many thanks.

Answer 1

Hint: $m\,Succ\,n=(m\,Succ)n =(Succ^m)(n)$

Ultimately, it will be a proof by induction.