Added side quests and preambles for side quests
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1FundamentalGroup/Preambles/PEmpty.agda
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6
1FundamentalGroup/Preambles/PEmpty.agda
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module 1FundamentalGroup.Preambles.PEmpty where
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open import Cubical.Foundations.Prelude public
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open import Cubical.Data.Empty renaming (rec to ⊥Rec) public
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open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) public
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1FundamentalGroup/Preambles/PTrueNotFalse.agda
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1FundamentalGroup/Preambles/PTrueNotFalse.agda
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module 1FundamentalGroup.Preambles.PTrueNotFalse where
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open import Cubical.Data.Empty public
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open import Cubical.Data.Unit renaming ( Unit to ⊤ ) public
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open import Cubical.Data.Bool using (Bool ; true ; false) public
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open import Cubical.Foundations.Prelude public
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-- ignore this
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module 1FundamentalGroup.Quest0 where
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-- ignore this
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open import 1FundamentalGroup.Preambles.P0
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Refl : base ≡ base
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@ -1,13 +1,10 @@
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module 1FundamentalGroup.Quest0SideQuests.Empty where
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open import Cubical.Foundations.Prelude
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open import Cubical.Data.Empty renaming (rec to ⊥Rec)
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open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_)
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open import 1FundamentalGroup.Preambles.PEmpty
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toEmpty : (A : Type) → Type
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toEmpty A = {!!}
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-- why Type₁
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pathEmpty : (A : Type) → Type₁
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pathEmpty A = {!!}
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@ -15,10 +12,10 @@ isoEmpty : (A : Type) → Type
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isoEmpty A = {!!}
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toEmpty→isoEmpty : (A : Type) → toEmpty A → isoEmpty A
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toEmpty→isoEmpty A f = {!!}
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toEmpty→isoEmpty A = {!!}
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isoEmpty→pathEmpty : (A : Type) → isoEmpty A → pathEmpty A
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isoEmpty→pathEmpty A = {!!}
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pathEmpty→toEmpty : (A : Type) → pathEmpty A → toEmpty A
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pathEmpty→toEmpty A p = {!!}
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pathEmpty→toEmpty A = {!!}
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@ -1,13 +1,10 @@
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module 1FundamentalGroup.Quest0SideQuests.EmptySolutions where
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open import Cubical.Foundations.Prelude
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open import Cubical.Data.Empty renaming (rec to ⊥Rec)
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open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_)
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open import 1FundamentalGroup.Preambles.PEmpty
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toEmpty : (A : Type) → Type
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toEmpty A = A → ⊥
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-- why Type₁
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pathEmpty : (A : Type) → Type₁
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pathEmpty A = A ≡ ⊥
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@ -27,4 +24,4 @@ isoEmpty→pathEmpty : (A : Type) → isoEmpty A → pathEmpty A
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isoEmpty→pathEmpty A = isoToPath
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pathEmpty→toEmpty : (A : Type) → pathEmpty A → toEmpty A
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pathEmpty→toEmpty A p = J (λ B q → toEmpty B) (λ x → x) (sym p)
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pathEmpty→toEmpty A p x = transport p x
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@ -1,9 +1,6 @@
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module 1FundamentalGroup.Quest0SideQuests.TrueNotFalse where
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open import Cubical.Data.Empty
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open import Cubical.Data.Unit renaming ( Unit to ⊤ )
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open import Cubical.Data.Bool using (Bool ; true ; false)
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open import Cubical.Foundations.Prelude
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open import 1FundamentalGroup.Preambles.PTrueNotFalse
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true≢false : true ≡ false → ⊥
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true≢false = {!!}
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module 1FundamentalGroup.Quest0SideQuests.TrueNotFalseSolutions where
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open import Cubical.Data.Empty
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open import Cubical.Data.Unit renaming ( Unit to ⊤ )
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open import Cubical.Data.Bool using (Bool ; true ; false)
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open import Cubical.Foundations.Prelude
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open import 1FundamentalGroup.Preambles.PTrueNotFalse
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true≢false : true ≡ false → ⊥
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true≢false h = transport ⊤≡⊥ tt where
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-- ignore
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module 1FundamentalGroup.Quest1 where
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-- ignore
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open import 1FundamentalGroup.Preambles.P1
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Ω : (A : Type) (a : A) → Type
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_build/2.6.2/agda/1FundamentalGroup/Preambles/PEmpty.agdai
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