Section programming_3.
Variable A B C : Set.
simple induction 1; try trivial.
Defined.
simple induction 1; try trivial.
Defined.
simple induction 1; try trivial.
Defined.
End programming_3.
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.