(** * 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.
#[global]
Hint Resolve inhabits: core.

Lemma exists_inhabited : forall (A:Type) (P:A->Prop),
(exists x, P x) -> inhabited A.