(** Interpretation of booleans as propositions *)

Inductive eq_true : bool -> Prop := is_eq_true : eq_true true.(** Interpretation of booleans as propositions *)

Inductive eq_true : bool -> Prop := is_eq_true : eq_true true.(** Another way of interpreting booleans as propositions *)

Definition is_true b := b = true.

(* Specifications: *)
Lemma eq_true_ind_r : forall (P : bool -> Prop) (b : bool), P b -> eq_true b -> P true.
Lemma eq_true_rec_r : forall (P : bool -> Set) (b : bool), P b -> eq_true b -> P true.
Lemma eq_true_rect_r : forall (P : bool -> Type) (b : bool), P b -> eq_true b -> P true.