lean2/library/logic/classes/nonempty.lean

-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Leonardo de Moura, Jeremy Avigad

import logic.connectives.basic .inhabited

using inhabited

namespace nonempty

inductive nonempty (A : Type) : Prop :=
nonempty_intro : A → nonempty A

definition nonempty_elim {A : Type} {B : Type} (H1 : nonempty A) (H2 : A → B) : B :=
nonempty_rec H2 H1

theorem inhabited_imp_nonempty [instance] {A : Type} (H : inhabited A) : nonempty A :=
nonempty_intro (default A)

end nonempty