intuition.
despec.
intuition.
exists x.
intuition.
eapply comp_spec_eq_impl_eq in H; intuition.
rewrite H.
trivial.
Qed.

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.