Added side quests and preambles for side quests

This commit is contained in:
Jlh18 2021-09-27 16:00:26 +01:00
parent 166142b14c
commit 72be8e3e42
14 changed files with 23 additions and 21 deletions

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@ -0,0 +1,6 @@
module 1FundamentalGroup.Preambles.PEmpty where
open import Cubical.Foundations.Prelude public
open import Cubical.Data.Empty renaming (rec to ⊥Rec) public
open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) public

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module 1FundamentalGroup.Preambles.PTrueNotFalse where
open import Cubical.Data.Empty public
open import Cubical.Data.Unit renaming ( Unit to ) public
open import Cubical.Data.Bool using (Bool ; true ; false) public
open import Cubical.Foundations.Prelude public

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-- ignore this
module 1FundamentalGroup.Quest0 where
-- ignore this
open import 1FundamentalGroup.Preambles.P0
Refl : base base

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module 1FundamentalGroup.Quest0SideQuests.Empty where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Empty renaming (rec to ⊥Rec)
open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_)
open import 1FundamentalGroup.Preambles.PEmpty
toEmpty : (A : Type) Type
toEmpty A = {!!}
-- why Type₁
pathEmpty : (A : Type) Type₁
pathEmpty A = {!!}
@ -15,10 +12,10 @@ isoEmpty : (A : Type) → Type
isoEmpty A = {!!}
toEmpty→isoEmpty : (A : Type) toEmpty A isoEmpty A
toEmpty→isoEmpty A f = {!!}
toEmpty→isoEmpty A = {!!}
isoEmpty→pathEmpty : (A : Type) isoEmpty A pathEmpty A
isoEmpty→pathEmpty A = {!!}
pathEmpty→toEmpty : (A : Type) pathEmpty A toEmpty A
pathEmpty→toEmpty A p = {!!}
pathEmpty→toEmpty A = {!!}

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module 1FundamentalGroup.Quest0SideQuests.EmptySolutions where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Empty renaming (rec to ⊥Rec)
open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_)
open import 1FundamentalGroup.Preambles.PEmpty
toEmpty : (A : Type) Type
toEmpty A = A
-- why Type₁
pathEmpty : (A : Type) Type₁
pathEmpty A = A
@ -27,4 +24,4 @@ isoEmpty→pathEmpty : (A : Type) → isoEmpty A → pathEmpty A
isoEmpty→pathEmpty A = isoToPath
pathEmpty→toEmpty : (A : Type) pathEmpty A toEmpty A
pathEmpty→toEmpty A p = J (λ B q toEmpty B) (λ x x) (sym p)
pathEmpty→toEmpty A p x = transport p x

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module 1FundamentalGroup.Quest0SideQuests.TrueNotFalse where
open import Cubical.Data.Empty
open import Cubical.Data.Unit renaming ( Unit to )
open import Cubical.Data.Bool using (Bool ; true ; false)
open import Cubical.Foundations.Prelude
open import 1FundamentalGroup.Preambles.PTrueNotFalse
true≢false : true false
true≢false = {!!}

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module 1FundamentalGroup.Quest0SideQuests.TrueNotFalseSolutions where
open import Cubical.Data.Empty
open import Cubical.Data.Unit renaming ( Unit to )
open import Cubical.Data.Bool using (Bool ; true ; false)
open import Cubical.Foundations.Prelude
open import 1FundamentalGroup.Preambles.PTrueNotFalse
true≢false : true false
true≢false h = transport ⊤≡⊥ tt where

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-- ignore
module 1FundamentalGroup.Quest1 where
-- ignore
open import 1FundamentalGroup.Preambles.P1
Ω : (A : Type) (a : A) Type