Definition CoPrime (a b : nat) := gcd (Z_of_nat a) (Z_of_nat b) 1.
Definition prod : forall (n : nat) (x : nat -> nat), nat.
intros.
induction n as [| n Hrecn].
exact 1.
exact (x n * Hrecn).
Defined.
Definition factorial (n : nat) : nat := prod n S.

Lemma coPrime1 : forall a : nat, CoPrime 1 a.