qed.
theorem divides_gcd_aux: \forall p,m,n,d. O < n \to n \le m \to n \le p \to
d \divides m \to d \divides n \to d \divides gcd_aux p m n.
intro.
elim p
qed.
theorem divides_gcd_aux: \forall p,m,n,d. O < n \to n \le m \to n \le p \to
d \divides m \to d \divides n \to d \divides gcd_aux p m n.
intro.
elim p