52dd6cf90b
This commit adds truncated 2-quotients, groupoid quotients, Eilenberg MacLane spaces, chain complexes, the long exact sequence of homotopy groups, the Freudenthal Suspension Theorem, Whitehead's principle, and the computation of homotopy groups of almost all spheres which are known in HoTT.
37 lines
838 B
Text
37 lines
838 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 pointed is_trunc
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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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/- pointed and truncated unit -/
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definition punit [constructor] : Set* :=
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pSet.mk' unit
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notation `unit*` := punit
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end unit
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open unit is_trunc
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