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

Theorem comp_spec_consequence : forall (A B : Set){eqda1 eqda2 : EqDec A}{eqdb1 eqdb2 : EqDec B}(p1 p2 : A -> B -> Prop) c1 c2, (@comp_spec _ _ eqda1 eqdb1 p1 c1 c2) -> (forall a b, p1 a b -> p2 a b) -> (@comp_spec _ _ eqda2 eqdb2 p2 c1 c2).