lean2/library/data/empty.lean
2014-10-05 10:50:13 -07:00

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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jeremy Avigad, Floris van Doorn
-- Empty type
-- ----------
import logic.cast
inductive empty : Type
namespace empty
protected theorem elim (A : Type) (H : empty) : A :=
rec (λe, A) H
end empty
namespace false
theorem to_empty (H : false) : empty :=
cast (false_elim H) true
theorem rec_type (A : Type) (H : false) : A :=
empty.rec (λx,A) (to_empty H)
end false