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 p ) +endPt' B p = pathToFun (cong B p ) --------------funExt--------------------- diff --git a/_build/2.6.2/agda/0Trinitarianism/Preambles/P4.agdai b/_build/2.6.2/agda/0Trinitarianism/Preambles/P4.agdai new file mode 100644 index 0000000..1b6a314 Binary files /dev/null and b/_build/2.6.2/agda/0Trinitarianism/Preambles/P4.agdai differ diff --git a/_build/2.6.2/agda/0Trinitarianism/Quest4.agdai b/_build/2.6.2/agda/0Trinitarianism/Quest4.agdai new file mode 100644 index 0000000..e0d8f59 Binary files /dev/null and b/_build/2.6.2/agda/0Trinitarianism/Quest4.agdai differ diff --git a/_build/2.6.2/agda/0Trinitarianism/Quest4Solutions.agdai b/_build/2.6.2/agda/0Trinitarianism/Quest4Solutions.agdai index 83dfe40..8b0208a 100644 Binary files a/_build/2.6.2/agda/0Trinitarianism/Quest4Solutions.agdai and b/_build/2.6.2/agda/0Trinitarianism/Quest4Solutions.agdai differ