(* elimination rules for equivalence *)
Parameter detachR     : forall (p q:Prop), (p ≡≡ q) -> q -> p.
(* substitution rules for equivalence -> use rewrite *)

(* introduction of equivalence  *)
Lemma intro_eqP : forall (P Q:Prop), P -> Q -> (P ≡≡ Q).
Add Parametric Relation  : Prop (eqP)
reflexivity proved by (ProtoReflex)
symmetry proved by (ProtoSymm)
transitivity proved by (ProtoTrans)
as eq_Prop.