(** * Being inhabited *)

(** The predicate [inhabited] can be used in different contexts. If [A] is
    thought as a type, [inhabited A] states that [A] is inhabited. If [A] is
    thought as a computationally relevant proposition, then
    [inhabited A] weakens [A] so as to hide its computational meaning.
    The so-weakened proof remains computationally relevant but only in
    a propositional context.
*)

Inductive inhabited (A:Type) : Prop := inhabits : A -> inhabited A.(** * Being inhabited *)

(** The predicate [inhabited] can be used in different contexts. If [A] is
    thought as a type, [inhabited A] states that [A] is inhabited. If [A] is
    thought as a computationally relevant proposition, then
    [inhabited A] weakens [A] so as to hide its computational meaning.
    The so-weakened proof remains computationally relevant but only in
    a propositional context.
*)

Inductive inhabited (A:Type) : Prop := inhabits : A -> inhabited A.

Lemma inhabited_covariant (A B : Type) : (A -> B) -> inhabited A -> inhabited B.