intuition.
eapply comp_spec_eq_trans_l;
eauto.
Qed.

Theorem comp_spec_eq_trans_r :
forall (A B : Set){eqd : EqDec A}{eqd : EqDec B}(c1 : Comp A)(c2 c3 : Comp B) P,
comp_spec P c1 c2 ->
comp_spec eq c2 c3 ->
comp_spec P c1 c3.