lean2/library/logic/inhabited.lean

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-- 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
inductive inhabited [class] (A : Type) : Type :=
mk : A → inhabited A
namespace inhabited
protected definition destruct {A : Type} {B : Type} (H1 : inhabited A) (H2 : A → B) : B :=
inhabited.rec H2 H1
definition Prop_inhabited [instance] : inhabited Prop :=
mk true
definition fun_inhabited [instance] (A : Type) {B : Type} (H : inhabited B) : inhabited (A → B) :=
destruct H (λb, mk (λa, b))
definition dfun_inhabited [instance] (A : Type) {B : A → Type} (H : Πx, inhabited (B x)) :
inhabited (Πx, B x) :=
mk (λa, destruct (H a) (λb, b))
definition default (A : Type) [H : inhabited A] : A := destruct H (take a, a)
end inhabited