(* Specifications: *)
Lemma clos_rt_step_trans : forall (A : Set) (R : A -> A -> Prop) (x y z : A), clos_refl_trans _ R x y -> clos_trans _ R y z -> clos_trans _ R x z.
Lemma step_clos_rt_trans : forall (A : Set) (R : A -> A -> Prop) (x y z : A), clos_trans _ R x y -> clos_refl_trans _ R y z -> clos_trans _ R x z.
Lemma confluent_is_ext : confluent R'.
Lemma strip_confl : forall e : env, commut term (R_rt R e) (transp term (R e)).
Lemma strongly_confluent : confluent (R_rt R).
Lemma confl_church_rosser : church_rosser R.
Lemma closures_are_equal : forall e : env, same_relation term (R_rt R' e) (R_rt R e).
Lemma confl_closure : confluent (R_rt R).
Lemma TML_Church_rosser : church_rosser R.
Lemma clos_refl_trans_ind_right : forall (A : Set) (R : relation A) (M : A) (P : A -> Prop), P M -> (forall P0 N : A, R N P0 -> clos_refl_trans A R P0 M -> P P0 -> P N) -> forall a : A, clos_refl_trans A R a M -> P a.
Theorem beta_sound : rule_sound the_PTS beta.
Theorem delta_sound : rule_sound the_PTS delta.
Theorem is_a_sort : forall t : term, decide (exists s : sort, t = Srt s).