Ltac despec := 
  match goal with
    | [H : comp_spec _ _ _  |- _] => destruct H
  end.

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.