From 8afbf9d4c266d4b2d46de2cfb954c1aff6725317 Mon Sep 17 00:00:00 2001 From: Jlh18 Date: Fri, 5 Nov 2021 23:31:43 +0000 Subject: [PATCH] edits to trinitarianism/quest 5 --- 0Trinitarianism/Quest5Solutions.agda | 32 ++++++------------ .../0Trinitarianism/Quest5Solutions.agdai | Bin 64064 -> 67287 bytes 2 files changed, 11 insertions(+), 21 deletions(-) diff --git a/0Trinitarianism/Quest5Solutions.agda b/0Trinitarianism/Quest5Solutions.agda index 682d74d..6af97f0 100644 --- a/0Trinitarianism/Quest5Solutions.agda +++ b/0Trinitarianism/Quest5Solutions.agda @@ -3,7 +3,7 @@ module 0Trinitarianism.Quest5Solutions where open import Cubical.Foundations.Prelude renaming (subst to endPt ; transport to pathToFun) open import Cubical.HITs.S1 using ( S¹ ; base ; loop ) open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) -open import Cubical.Foundations.Path +open import Cubical.Foundations.Path renaming (PathPIsoPath to PathPIsoPathD) open import 1FundamentalGroup.Quest0Solutions open import Cubical.Data.Bool @@ -17,33 +17,23 @@ outOfS¹P B b p base = b outOfS¹P B b p (loop i) = p i outOfS¹D : (B : S¹ → Type) → (b : B base) → b ≡ b along (λ i → B (loop i)) → (x : S¹) → B x -outOfS¹D B b p x = outOfS¹P B b (_≅_.inv (PathPIsoPath (λ i → B (loop i)) b b) p) x - --- example : (x : S¹) → doubleCover x → Bool --- example = outOfS¹D (λ x → doubleCover x → Bool) (λ x → true) --- (pathToFun (λ i → (doubleCover (loop i)) → Bool) (λ x → true) --- ≡⟨ refl ⟩ --- pathToFun (λ i → flipPath i → Bool) (λ x → true) --- ≡⟨ refl ⟩ --- (λ x → true) --- ∎) +outOfS¹D B b p x = outOfS¹P B b (_≅_.inv (PathPIsoPathD (λ i → B (loop i)) b b) p) x example : (x : S¹) → doubleCover x → doubleCover x example base = Flip example (loop i) = p i where - p : PathP (λ i → doubleCover (loop i) → doubleCover (loop i)) Flip Flip - p = {!!} + lem : (x : Bool) → pathToFun (λ i → flipPath i → flipPath i) Flip x ≡ Flip x + lem false = refl + lem true = refl + + p : PathP (λ i → flipPath i → flipPath i) Flip Flip + p = _≅_.inv (PathPIsoPathD (λ i → flipPath i → flipPath i) Flip Flip) (funExt lem) + +-- repeating the example but using our API example' : (x : S¹) → doubleCover x → doubleCover x -example' = outOfS¹D (λ x → doubleCover x → doubleCover x) Flip - ( - pathToFun (λ i → doubleCover (loop i) → doubleCover (loop i)) Flip - ≡⟨ refl ⟩ - pathToFun (λ i → flipPath i → flipPath i) Flip - ≡⟨ funExt lem ⟩ - Flip - ∎) where +example' = outOfS¹D (λ x → doubleCover x → doubleCover x) Flip (funExt lem) where lem : (x : Bool) → pathToFun (λ i → flipPath i → flipPath i) Flip x ≡ Flip x lem false = refl diff --git a/_build/2.6.2/agda/0Trinitarianism/Quest5Solutions.agdai b/_build/2.6.2/agda/0Trinitarianism/Quest5Solutions.agdai index 345b18712d436124b8706b644a712035ed5e5a60..2c0297b79c3474bf73c9dc5c4edb36be3db9128f 100644 GIT binary patch delta 51685 zcmXuLd0dR^|37}+bI(>y)3on(m#BzJ5ox(wXb?@DL)KCvjw2Fjy>Cg1)T9nsn+oOU z5Ke~^sSu`)CCtYmOO}a5Vn`+}-`738e~$*qdH~hanY|%TL 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