Re: [isabelle] Factorial Equivalent Iterative Factorial

Try proving something like this as a lemma, using induction on n:

ALL a. Fi n a = a * F n

Then F n = Fi n 1 easily follows from this.

- Brian

Quoting TIMOTHY KREMANN <twksoa262 at>:

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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