Section Eeq2.
Variables I X Y Z: Type.
Variables R R': relation2 X Y.
Variable  S: relation2 Y Z.
Variable  T: relation X.
Variable  F: I -> relation2 X Y.

(* Specifications: *)
Lemma inv_inv: eeq (trans (trans T)) T.
Lemma inv_comp: eeq (trans (comp R S)) (comp (trans S) (trans R)).
Lemma inv_union: eeq (trans (union F)) (union (fun i => trans (F i))).
Lemma inv_star: eeq (trans (star T)) (star (trans T)).
Lemma inv_plus: eeq (trans (plus T)) (plus (trans T)).
Lemma inv_union2: eeq (trans (union2 R R')) (union2 (trans R) (trans R')).
Lemma comp_assoc: forall W: Type, forall U: relation2 Z W,
eeq (comp (comp R S) U) (comp R (comp S U)).
Lemma comp_star_star: eeq (comp (star T) (star T)) (star T).
Lemma comp_plus_star: eeq (comp (plus T) (star T)) (plus T).
Lemma comp_star_plus: eeq (comp (star T) (plus T)) (plus T).
End Eeq2.