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

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