2016-02-02 18:44:01 +00:00
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/-
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Copyright (c) Jakob von Raumer. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Jakob von Raumer
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Logic lemmas we don't want/need in the prelude.
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-/
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import types.pi
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open eq is_trunc decidable
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2016-02-15 20:18:07 +00:00
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theorem dif_pos {c : Type} [H : decidable c] [P : is_prop c] (Hc : c)
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2016-02-02 18:44:01 +00:00
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{A : Type} {t : c → A} {e : ¬ c → A} : dite c t e = t Hc :=
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2016-02-15 20:18:07 +00:00
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by induction H with Hc Hnc; apply ap t; apply is_prop.elim; apply absurd Hc Hnc
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2016-02-02 18:44:01 +00:00
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theorem dif_neg {c : Type} [H : decidable c] (Hnc : ¬c)
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{A : Type} {t : c → A} {e : ¬ c → A} : dite c t e = e Hnc :=
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2016-02-15 20:18:07 +00:00
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by induction H with Hc Hnc; apply absurd Hc Hnc; apply ap e; apply is_prop.elim
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