Notation Fst_3 := (fst_3 _ _ _) (only parsing).Notation Snd_3 := (snd_3 _ _ _) (only parsing).Notation Thd_3 := (thd_3 _ _ _) (only parsing).Notation Triplet := (triplet _ _ _) (only parsing).

Lemma triplet_fst_snd_thd : forall (A B C : Set) (c : prod_3 A B C), triplet _ _ _ (fst_3 _ _ _ c) (snd_3 _ _ _ c) (thd_3 _ _ _ c) = c.