From 4a2e69d92da9d1f82da4cfd6ac74fb42caa9099d Mon Sep 17 00:00:00 2001 From: Jlh18 Date: Sat, 30 Oct 2021 19:02:51 +0100 Subject: [PATCH] added quest 4 and preamble --- 0Trinitarianism/Preambles/P4.agda | 5 +++++ 0Trinitarianism/Quest4.agda | 3 +++ 0Trinitarianism/Quest4Solutions.agda | 21 +++++++++--------- .../agda/0Trinitarianism/Preambles/P4.agdai | Bin 0 -> 20829 bytes .../2.6.2/agda/0Trinitarianism/Quest4.agdai | Bin 0 -> 8355 bytes .../0Trinitarianism/Quest4Solutions.agdai | Bin 152532 -> 139857 bytes 6 files changed, 18 insertions(+), 11 deletions(-) create mode 100644 0Trinitarianism/Preambles/P4.agda create mode 100644 0Trinitarianism/Quest4.agda create mode 100644 _build/2.6.2/agda/0Trinitarianism/Preambles/P4.agdai create mode 100644 _build/2.6.2/agda/0Trinitarianism/Quest4.agdai diff --git a/0Trinitarianism/Preambles/P4.agda b/0Trinitarianism/Preambles/P4.agda new file mode 100644 index 0000000..52a0250 --- /dev/null +++ b/0Trinitarianism/Preambles/P4.agda @@ -0,0 +1,5 @@ +module 0Trinitarianism.Preambles.P4 where + +open import Cubical.Foundations.Prelude using + ( Level ; Type ; _≡_ ; J ; JRefl ; refl ; i1 ; i0 ; I ; cong) public +open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) public diff --git a/0Trinitarianism/Quest4.agda b/0Trinitarianism/Quest4.agda new file mode 100644 index 0000000..36852d0 --- /dev/null +++ b/0Trinitarianism/Quest4.agda @@ -0,0 +1,3 @@ +module 0Trinitarianism.Quest4 where + +open import 0Trinitarianism.Preambles.P4 diff --git a/0Trinitarianism/Quest4Solutions.agda b/0Trinitarianism/Quest4Solutions.agda index af45d3f..7991533 100644 --- a/0Trinitarianism/Quest4Solutions.agda +++ b/0Trinitarianism/Quest4Solutions.agda @@ -1,11 +1,6 @@ module 0Trinitarianism.Quest4Solutions where -open import Cubical.Foundations.Prelude using ( Level ; Type ; _≡_ ; J ; JRefl ; refl ; i1 ; i0 ; I) -open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) - -infixr 30 _∙_ -infix 3 _∎ -infixr 2 _≡⟨_⟩_ +open import 0Trinitarianism.Preambles.P4 private variable @@ -76,11 +71,11 @@ Id→Path rfl = refl Cong : (f : A → B) → Id x y → Id (f x) (f y) Cong f rfl = rfl -cong : (f : A → B) (p : x ≡ y) → f x ≡ f y -cong {x = x} f = J (λ y p → f x ≡ f y) refl - cong' : (f : A → B) (p : x ≡ y) → f x ≡ f y -cong' f p = Id→Path (Cong f (Path→Id p)) +cong' {x = x} f = J (λ y p → f x ≡ f y) refl + +cong'' : (f : A → B) (p : x ≡ y) → f x ≡ f y +cong'' f p = Id→Path (Cong f (Path→Id p)) ------------Path vs Id--------------------- @@ -115,6 +110,10 @@ _ ≡⟨ x≡y ⟩ y≡z = x≡y ∙ y≡z _∎ : (x : A) → x ≡ x _ ∎ = refl +infixr 30 _∙_ +infix 3 _∎ +infixr 2 _≡⟨_⟩_ + TransRefl : {x y : A} → Trans {A} {x} {x} {y} refl ≡ λ q → q TransRefl {x = x} {y = y} = JRefl ((λ y1 p → y1 ≡ y → x ≡ y)) λ q → q @@ -182,7 +181,7 @@ endPtRefl : (B : A → Type) → endPt B (refl {x = x}) ≡ id endPtRefl {x = x} B = JRefl ((λ y p → B x → B y)) id endPt' : (B : A → Type) (p : x ≡ y) → B x → B y -endPt' B p = pathToFun (Cubical.Foundations.Prelude.cong B 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