2014-12-17 21:36:41 +00:00
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-- Copyright (c) 2014 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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2015-02-21 00:30:32 +00:00
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open is_trunc
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2014-12-17 21:36:41 +00:00
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-- Axiomatize the truncation operator as long as we do not have
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-- Higher inductive types
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axiom truncate (A : Type) (n : trunc_index) : Type
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axiom truncate.mk {A : Type} (n : trunc_index) (a : A) : truncate A n
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axiom truncate.is_trunc (A : Type) (n : trunc_index) : is_trunc n (truncate A n)
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axiom truncate.rec_on {A : Type} {n : trunc_index} {C : truncate A n → Type}
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(ta : truncate A n)
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[H : Π (ta : truncate A n), is_trunc n (C ta)]
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(CC : Π (a : A), C (truncate.mk n a)) : C ta
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