Global Instance type_Prop : type Prop :=
{ equal := iff
; proper := fun _ => True
}.
Global Instance typeOk_Prop : typeOk type_Prop.

(** Exists **)
Lemma exists_iff : forall T P Q,
(forall x,
P x <-> Q x) ->
((exists x : T, P x) <-> (exists x : T, Q x)).