(**********************************************************************)
 
Inductive is_gcd (a b c : nat) : Prop :=
    is_gcd_intro :
      divides c a ->
      divides c b ->
      (forall d : nat, divides d a -> divides d b -> divides d c) ->
      is_gcd a b c.(**********************************************************************)
 
Inductive is_gcd (a b c : nat) : Prop :=
    is_gcd_intro :
      divides c a ->
      divides c b ->
      (forall d : nat, divides d a -> divides d b -> divides d c) ->
      is_gcd a b c.

Lemma is_gcd_ref : forall x : nat, is_gcd x x x.