30 lines
696 B
Text
30 lines
696 B
Text
/-
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Copyright (c) 2015 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Theorems about the unit type
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-/
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open equiv option eq
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namespace unit
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protected definition eta : Π(u : unit), ⋆ = u
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| eta ⋆ := idp
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definition unit_equiv_option_empty [constructor] : unit ≃ option empty :=
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begin
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fapply equiv.MK,
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{ intro u, exact none},
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{ intro e, exact star},
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{ intro e, cases e, reflexivity, contradiction},
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{ intro u, cases u, reflexivity},
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end
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-- equivalences involving unit and other type constructors are in the file
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-- of the other constructor
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end unit
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open unit is_trunc
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