mirror of
https://github.com/luau-lang/luau.git
synced 2024-11-15 22:35:43 +08:00
24 lines
735 B
Agda
24 lines
735 B
Agda
|
module Properties.Equality where
|
||
|
|
|
||
|
|
open import Agda.Builtin.Equality using (_≡_; refl)
|
||
|
|
open import Properties.Contradiction using (¬)
|
||
|
|
|
||
|
|
sym : ∀ {A : Set} {a b : A} → (a ≡ b) → (b ≡ a)
|
||
|
|
sym refl = refl
|
||
|
|
|
||
|
|
trans : ∀ {A : Set} {a b c : A} → (a ≡ b) → (b ≡ c) → (a ≡ c)
|
||
|
|
trans refl refl = refl
|
||
|
|
|
||
|
|
cong : ∀ {A B : Set} {a b : A} (f : A → B) → (a ≡ b) → (f a ≡ f b)
|
||
|
|
cong f refl = refl
|
||
|
|
|
||
|
|
subst₁ : ∀ {A : Set} {a b : A} (F : A → Set) → (a ≡ b) → (F a) → (F b)
|
||
|
|
subst₁ F refl x = x
|
||
|
|
|
||
|
|
subst₂ : ∀ {A B : Set} {a b : A} {c d : B} (F : A → B → Set) → (a ≡ b) → (c ≡ d) → (F a c) → (F b d)
|
||
|
|
subst₂ F refl refl x = x
|
||
|
|
|
||
|
|
_≢_ : ∀ {A : Set} → A → A → Set
|
||
|
|
(a ≢ b) = ¬(a ≡ b)
|
||
|
|
|