Source code on Github
{-# OPTIONS --cubical-compatible --safe #-}
module Data.Maybe.Relation.Unary.All.Properties where
open import Data.Maybe.Base
open import Data.Maybe.Relation.Unary.All as All
using (All; nothing; just)
open import Data.Maybe.Relation.Binary.Connected
open import Data.Product using (_×_; _,_)
open import Function
open import Level
open import Relation.Unary
open import Relation.Binary.Core
private
variable
a b p q ℓ : Level
A : Set a
B : Set b
P : Pred A p
Q : Pred B q
All⇒Connectedˡ : ∀ {R : Rel A ℓ} {x y} →
All (R x) y → Connected R (just x) y
All⇒Connectedˡ (just x) = just x
All⇒Connectedˡ nothing = just-nothing
All⇒Connectedʳ : ∀ {R : Rel A ℓ} {x y} →
All (λ v → R v y) x → Connected R x (just y)
All⇒Connectedʳ (just x) = just x
All⇒Connectedʳ nothing = nothing-just
map⁺ : ∀ {f : A → B} {mx} → All (P ∘ f) mx → All P (map f mx)
map⁺ (just p) = just p
map⁺ nothing = nothing
map⁻ : ∀ {f : A → B} {mx} → All P (map f mx) → All (P ∘ f) mx
map⁻ {mx = just x} (just px) = just px
map⁻ {mx = nothing} nothing = nothing
gmap : ∀ {f : A → B} → P ⊆ Q ∘ f → All P ⊆ All Q ∘ map f
gmap g = map⁺ ∘ All.map g
<∣>⁺ : ∀ {mx my} → All P mx → All P my → All P (mx <∣> my)
<∣>⁺ (just px) pmy = just px
<∣>⁺ nothing pmy = pmy
<∣>⁻ : ∀ mx {my} → All P (mx <∣> my) → All P mx
<∣>⁻ (just x) pmxy = pmxy
<∣>⁻ nothing pmxy = nothing