(** * Composition of bisimulation, expansion, wexpansion relations *)
Section BiComposition.
Variables X Y Z: Type.
Variable TX: reduction_t A X.
Variable TY: reduction_t A Y.
Variable TZ: reduction_t A Z.
Variable R: relation2 X Y.
Variable S: relation2 Y Z.

(* Specifications: *)
Lemma bisimulation_comp: bisimulation TX TY R -> bisimulation TY TZ S -> bisimulation TX TZ (comp R S).
Lemma expansion_comp: expansion TX TY R -> expansion TY TZ S -> expansion TX TZ (comp R S).
Lemma wexpansion_comp: wexpansion TX TY R -> wexpansion TY TZ S -> wexpansion TX TZ (comp R S).
End BiComposition.