[isabelle] Factorial Equivalent Iterative Factorial

I have the following two primrecs (n! and a iterative version)

primrec F::"nat => nat" 
  "F         0  = 1"
| "F (Suc n) = Suc n * F n"

primrec Fi::"nat => nat => nat"
  "Fi        0  a = a"
| "Fi (Suc n) a = Fi n (Suc n * a)"

I want to prove 

F n = Fi n 1

I have not made much progress and am wondering if someone has done this already or knows of a similar proof that would give me some hints.


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