DanilaFe/agda-spa
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Add some helpers

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2025-11-29 13:24:27 -08:00
parent eb2d64f3b5
commit d1700f23fa
2 changed files with 31 additions and 2 deletions
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5
Utils.agda
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@@ -9,7 +9,7 @@ open import Data.List using (List; cartesianProduct; []; _∷_; _++_; foldr; fil
open import Data.List.Membership.Propositional using (_∈_)
open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
open import Data.List.Relation.Unary.All using (All; []; _∷_; map)
open import Data.List.Relation.Unary.Any using (Any; here; there) -- TODO: re-export these with nicer names from map
open import Data.List.Relation.Unary.Any as Any using (Any; here; there) -- TODO: re-export these with nicer names from map
open import Data.Sum using (_⊎_)
open import Function.Definitions using (Injective)
open import Relation.Binary.PropositionalEquality using (_≡_; sym; refl; cong)
@@ -52,6 +52,9 @@ All¬-¬Any : ∀ {p c} {C : Set c} {P : C → Set p} {l : List C} → All (λ x
All¬-¬Any {l = x ∷ xs} (¬Px ∷ _) (here Px) = ¬Px Px
All¬-¬Any {l = x ∷ xs} (_ ∷ ¬Pxs) (there Pxs) = All¬-¬Any ¬Pxs Pxs
¬Any-map : ∀ {p₁ p₂ c} {C : Set c} {P₁ : C → Set p₁} {P₂ : C → Set p₂} {l : List C} → (∀ {x} → P₁ x → P₂ x) → ¬ Any P₂ l → ¬ Any P₁ l
¬Any-map f ¬Any-P₂ Any-P₁ = ¬Any-P₂ (Any.map f Any-P₁)
All-single : ∀ {p c} {C : Set c} {P : C → Set p} {c : C} {l : List C} → All P l → c ∈ l → P c
All-single {c = c} {l = x ∷ xs} (p ∷ ps) (here refl) = p
All-single {c = c} {l = x ∷ xs} (p ∷ ps) (there c∈xs) = All-single ps c∈xs