From ccb193a8814e480ec899ec6a11bd4628826e0a4e Mon Sep 17 00:00:00 2001 From: Jlh18 Date: Sat, 2 Oct 2021 16:41:34 +0100 Subject: [PATCH] changed transport to pathToFun --- 1FundamentalGroup/Preambles/P0.agda | 5 +- 1FundamentalGroup/Preambles/P1.agda | 5 +- 1FundamentalGroup/Preambles/P2.agda | 5 +- 1FundamentalGroup/Quest0Solutions.agda | 4 +- 1FundamentalGroup/Quest2Solutions.agda | 58 +++++++++--------- .../agda/1FundamentalGroup/Preambles/P0.agdai | Bin 49411 -> 49605 bytes .../agda/1FundamentalGroup/Preambles/P1.agdai | Bin 53253 -> 53398 bytes .../agda/1FundamentalGroup/Preambles/P2.agdai | Bin 51270 -> 52059 bytes .../1FundamentalGroup/Quest0Solutions.agdai | Bin 65772 -> 65772 bytes .../1FundamentalGroup/Quest1Solutions.agdai | Bin 45686 -> 45641 bytes .../1FundamentalGroup/Quest2Solutions.agdai | Bin 50301 -> 38075 bytes 11 files changed, 43 insertions(+), 34 deletions(-) diff --git a/1FundamentalGroup/Preambles/P0.agda b/1FundamentalGroup/Preambles/P0.agda index 4dc19c6..13e74e3 100644 --- a/1FundamentalGroup/Preambles/P0.agda +++ b/1FundamentalGroup/Preambles/P0.agda @@ -3,7 +3,10 @@ module 1FundamentalGroup.Preambles.P0 where open import Cubical.Data.Empty using (⊥) public open import Cubical.Data.Unit renaming ( Unit to ⊤ ) public open import Cubical.Data.Bool public -open import Cubical.Foundations.Prelude renaming ( subst to endPt ) public +open import Cubical.Foundations.Prelude + renaming ( subst to endPt + ; transport to pathToFun + ) public open import Cubical.Foundations.Isomorphism renaming ( Iso to _≅_ ) public open import Cubical.Foundations.Path public open import Cubical.HITs.S1 public diff --git a/1FundamentalGroup/Preambles/P1.agda b/1FundamentalGroup/Preambles/P1.agda index 23c3d31..0c9c2a7 100644 --- a/1FundamentalGroup/Preambles/P1.agda +++ b/1FundamentalGroup/Preambles/P1.agda @@ -4,6 +4,9 @@ open import Cubical.HITs.S1 using (S¹ ; base ; loop) public open import Cubical.Data.Nat using (ℕ ; suc ; zero) public open import Cubical.Data.Int using (ℤ ; pos ; negsuc ; -_) public open import Cubical.Data.Empty public -open import Cubical.Foundations.Prelude renaming (subst to endPt) public +open import Cubical.Foundations.Prelude + renaming ( subst to endPt + ; transport to pathToFun + ) public open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) public open import 1FundamentalGroup.Quest0Solutions using ( Refl ; Refl≢loop ) public diff --git a/1FundamentalGroup/Preambles/P2.agda b/1FundamentalGroup/Preambles/P2.agda index 6f027da..83a8993 100644 --- a/1FundamentalGroup/Preambles/P2.agda +++ b/1FundamentalGroup/Preambles/P2.agda @@ -3,6 +3,9 @@ module 1FundamentalGroup.Preambles.P2 where open import Cubical.Data.Nat public open import Cubical.Data.Int using (ℤ ; pos ; negsuc ; -_) public open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) public -open import Cubical.Foundations.Prelude renaming (subst to endPt) public +open import Cubical.Foundations.Prelude + renaming ( subst to endPt + ; transport to pathToFun + ) public open import Cubical.HITs.S1 using (S¹ ; base ; loop) public open import 1FundamentalGroup.Quest1Solutions public diff --git a/1FundamentalGroup/Quest0Solutions.agda b/1FundamentalGroup/Quest0Solutions.agda index de9b7ea..2002e49 100644 --- a/1FundamentalGroup/Quest0Solutions.agda +++ b/1FundamentalGroup/Quest0Solutions.agda @@ -61,12 +61,12 @@ isoEmpty→pathEmpty : (A : Type) → isoEmpty A → pathEmpty A isoEmpty→pathEmpty A = isoToPath pathEmpty→toEmpty : (A : Type) → pathEmpty A → toEmpty A -pathEmpty→toEmpty A p x = transport p x +pathEmpty→toEmpty A p x = pathToFun p x ------------------- Side Quests - true≢false -------------------- true≢false' : true ≡ false → ⊥ -true≢false' h = transport ⊤≡⊥ tt where +true≢false' h = pathToFun ⊤≡⊥ tt where propify : Bool → Type propify false = ⊥ diff --git a/1FundamentalGroup/Quest2Solutions.agda b/1FundamentalGroup/Quest2Solutions.agda index 1a828fb..45df76b 100644 --- a/1FundamentalGroup/Quest2Solutions.agda +++ b/1FundamentalGroup/Quest2Solutions.agda @@ -2,40 +2,40 @@ module 1FundamentalGroup.Quest2Solutions where open import 1FundamentalGroup.Preambles.P2 -sucℤ : ℤ → ℤ -sucℤ (pos n) = pos (suc n) -sucℤ (negsuc zero) = pos zero -sucℤ (negsuc (suc n)) = negsuc n +-- sucℤ : ℤ → ℤ +-- sucℤ (pos n) = pos (suc n) +-- sucℤ (negsuc zero) = pos zero +-- sucℤ (negsuc (suc n)) = negsuc n -predℤ : ℤ → ℤ -predℤ (pos zero) = negsuc zero -predℤ (pos (suc n)) = pos n -predℤ (negsuc n) = negsuc (suc n) +-- predℤ : ℤ → ℤ +-- predℤ (pos zero) = negsuc zero +-- predℤ (pos (suc n)) = pos n +-- predℤ (negsuc n) = negsuc (suc n) -sucℤIso : ℤ ≅ ℤ -sucℤIso = iso sucℤ predℤ s r where +-- sucℤIso : ℤ ≅ ℤ +-- sucℤIso = iso sucℤ predℤ s r where - s : section sucℤ predℤ - s (pos zero) = refl - s (pos (suc n)) = refl - s (negsuc zero) = refl - s (negsuc (suc n)) = refl +-- s : section sucℤ predℤ +-- s (pos zero) = refl +-- s (pos (suc n)) = refl +-- s (negsuc zero) = refl +-- s (negsuc (suc n)) = refl - r : retract sucℤ predℤ - r (pos zero) = refl - r (pos (suc n)) = refl - r (negsuc zero) = refl - r (negsuc (suc n)) = refl +-- r : retract sucℤ predℤ +-- r (pos zero) = refl +-- r (pos (suc n)) = refl +-- r (negsuc zero) = refl +-- r (negsuc (suc n)) = refl -sucℤPath : ℤ ≡ ℤ -sucℤPath = isoToPath sucℤIso +-- sucℤPath : ℤ ≡ ℤ +-- sucℤPath = isoToPath sucℤIso -helix : S¹ → Type -helix base = ℤ -helix (loop i) = sucℤPath i +-- helix : S¹ → Type +-- helix base = ℤ +-- helix (loop i) = sucℤPath i -windingNumberBase : base ≡ base → ℤ -windingNumberBase p = endPt helix p (pos zero) +-- windingNumberBase : base ≡ base → ℤ +-- windingNumberBase p = endPt helix p (pos zero) -windingNumber : (x : S¹) → base ≡ x → helix x -windingNumber x p = endPt helix p (pos zero) +-- windingNumber : (x : S¹) → base ≡ x → helix x +-- windingNumber x p = endPt helix p (pos zero) diff --git a/_build/2.6.2/agda/1FundamentalGroup/Preambles/P0.agdai 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