intro a.
apply (lt_wf_ind a).
clear a.
intros.
induction (primedec n).
exists n.
split.
assumption.
exists 1.
symmetry  in |- *.
apply mult_1_r.
induction (nonprime_witness _ H0 H1).
induction H2 as (H2, H3).
induction H3 as (H3, H4).
induction (H _ H3 H2).
exists x0.
induction H5 as (H5, H6).
split.
assumption.
eapply div_trans.
apply H6.
assumption.
Qed.

Lemma coPrimePrime :
forall a b : nat,
(forall p : nat, Prime p -> ~ Divides p a \/ ~ Divides p b) -> CoPrime a b.