(** ** Boolean propositions and decisions *)
Coercion bool2Prop (b : bool) := if b then True else False.

(* Specifications: *)
Lemma bool_Prop_true b :
b = true -> b.
Lemma bool_Prop_false b :
b = false -> ~ b.
Lemma bool_Prop_true b :
b = true -> b.
Lemma bool_Prop_false b :
b = false -> ~ b.