2014-08-22 03:26:30 +00:00
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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Jeremy Avigad
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import data.unit data.bool data.nat
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import data.prod data.sum data.sigma
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using unit bool nat prod sum sigma
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inductive fibrant (T : Type) : Type :=
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2014-08-22 22:46:10 +00:00
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fibrant_mk : fibrant T
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2014-08-22 03:26:30 +00:00
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namespace fibrant
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axiom unit_fibrant : fibrant unit
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axiom nat_fibrant : fibrant nat
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axiom bool_fibrant : fibrant bool
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2014-08-22 23:36:47 +00:00
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axiom sum_fibrant {A B : Type} (C1 : fibrant A) (C2 : fibrant B) : fibrant (A ⊎ B)
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2014-08-22 03:26:30 +00:00
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axiom prod_fibrant {A B : Type} (C1 : fibrant A) (C2 : fibrant B) : fibrant (A × B)
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axiom sigma_fibrant {A : Type} {B : A → Type} (C1 : fibrant A) (C2 : Πx : A, fibrant (B x)) :
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fibrant (Σx : A, B x)
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axiom pi_fibrant {A : Type} {B : A → Type} (C1 : fibrant A) (C2 : Πx : A, fibrant (B x)) :
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fibrant (Πx : A, B x)
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instance unit_fibrant
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instance nat_fibrant
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instance bool_fibrant
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instance sum_fibrant
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instance prod_fibrant
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instance sigma_fibrant
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instance pi_fibrant
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2014-08-22 23:36:47 +00:00
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theorem test_fibrant : fibrant (nat × (nat ⊎ nat)) := _
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2014-08-22 03:26:30 +00:00
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end fibrant
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