Inductive reflect : Prop -> bool -> Prop :=
| ReflectT : forall (P:Prop), P -> reflect P true
| ReflectF : forall (P:Prop), ~ P -> reflect P false.Inductive reflect : Prop -> bool -> Prop :=
| ReflectT : forall (P:Prop), P -> reflect P true
| ReflectF : forall (P:Prop), ~ P -> reflect P false.Inductive reflect : Prop -> bool -> Prop :=
| ReflectT : forall (P:Prop), P -> reflect P true
| ReflectF : forall (P:Prop), ~ P -> reflect P false.Inductive reflect (P : Prop) : bool -> Prop :=
| ReflectT : P -> reflect P true
| ReflectF : ~ P -> reflect P false.Inductive reflect (P : Prop) : bool -> Prop :=
| ReflectT : P -> reflect P true
| ReflectF : ~ P -> reflect P false.Inductive reflect (P : Prop) : bool -> Prop :=
| ReflectT : P -> reflect P true
| ReflectF : ~ P -> reflect P false.

Theorem reflect_iff : forall P b, reflect P b -> (P <-> b = true).