Notation Formula := (Formula L) (only parsing).Notation Formulas := (Formulas L) (only parsing).Notation System := (System L) (only parsing).Notation Term := (Term L) (only parsing).Notation Terms := (Terms L) (only parsing).Definition cTriple (a b c : nat) : nat := cPair a (cPair b c).Definition cTriplePi1 (n : nat) : nat := cPairPi1 n.Definition cTriplePi2 (n : nat) : nat := cPairPi1 (cPairPi2 n).Definition cTriplePi3 (n : nat) : nat := cPairPi2 (cPairPi2 n).

Lemma cTripleProj : forall a : nat, cTriple (cTriplePi1 a) (cTriplePi2 a) (cTriplePi3 a) = a.