Hint Resolve trans_incl.
Hint Resolve comp_incl.
Hint Resolve union_incl.
Hint Resolve star_incl.
Hint Resolve plus_incl.
Hint Resolve trans_eeq.
Hint Resolve comp_eeq.
Hint Resolve union_eeq.
Hint Resolve star_eeq.
Hint Resolve plus_eeq.
Section InclEeq.
Variables X Y: Type.
Variables S R T: relation2 X Y.

Lemma star_trans: forall x y z, star R x y -> star R y z -> star R x z.