(** When the crelation on the domain is symmetric, a predicate is compatible with [iff] as soon as it is compatible with [impl]. Same with a binary crelation. *)

(* Specifications: *)
Lemma proper_sym_impl_iff : forall `(Symmetric A R)`(Proper _ (R==>impl) f),
Proper (R==>iff) f.
Lemma proper_sym_arrow_iffT : forall `(Symmetric A R)`(Proper _ (R==>arrow) f),
Proper (R==>iffT) f.
Lemma proper_sym_impl_iff_2 :
forall `(Symmetric A R)`(Symmetric B R')`(Proper _ (R==>R'==>impl) f),
Proper (R==>R'==>iff) f.
Lemma proper_sym_arrow_iffT_2 :
forall `(Symmetric A R)`(Symmetric B R')`(Proper _ (R==>R'==>arrow) f),
Proper (R==>R'==>iffT) f.