# Frama-C-discuss mailing list archives

This page gathers the archives of the old Frama-C-discuss archives, that was hosted by Inria's gforge before its demise at the end of 2020. To search for mails newer than September 2020, please visit the page of the new mailing list on Renater.

# [Frama-c-discuss] fact proof

```Hello,

Le 2015-03-15 20:23, Fritjof Bornebusch a ?crit :
> I have a question about the proof of recursion functions, like this one:
>
> As far as I understand this correct, the values of the inductive proof are:
> a = 1
> b = n
> n = \result
>
> But 3! is 6 and not (b*n) = 2 * 6 = 12
>
> Or do I missunderstand the proof?

I think you misunderstood the proof, or more exactly the is_prod predicate.

Take fact(3), by its contracts it ensures is_prod(1,3,\result).

By inductive definition of is_prod, we have:
forall k:integer. is_prod(1,3-1,k) && 1 <= 3 ==> is_prod(1,3,\result)
(with \result == 3*k).

By inductive definition of is_prod, we have:
forall k':integer. is_prod(1,2-1,k') && 1 <= 2 ==> is_prod(1,2,2*k')
(with 2*k'==k)

By inductive definition of is_prod, we have:
forall k'':integer. is_prod(1,1-1,k'') && 1 <= 1 ==>
is_prod(1,1,1*k'') (with 1*k''==k')

By inductive definition of is_prod, we have:
is_prod(1,1-1,1) because 1 > 0.

Therefore we have:
is_prod(1,0,1)
==>
is_prod(1,1,1) (i.e. k''==1)
==>
is_prod(1,1,2) (i.e. k'==1)
==>
is_prod(1,3,6) (i.e. k=2, \result==3*k=3*2)

Best regards,
david

```