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Add another utility proof

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-02-11 12:45:33 -08:00
parent d718338759
commit 2b27e397b6
1 changed files with 6 additions and 2 deletions
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8
Utils.agda
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@ -2,9 +2,9 @@ module Utils where
open import Data.List using (List; []; _∷_; _++_) open import Data.List using (List; []; _∷_; _++_)
open import Data.List.Membership.Propositional using (_∈_) open import Data.List.Membership.Propositional using (_∈_)
open import Data.List.Relation.Unary.All using (All; []; _∷_) 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 using (Any; here; there) -- TODO: re-export these with nicer names from map
open import Relation.Binary.PropositionalEquality using (_≡_; sym) open import Relation.Binary.PropositionalEquality using (_≡_; sym; refl)
open import Relation.Nullary using (¬_) open import Relation.Nullary using (¬_)
data Unique {c} {C : Set c} : List C → Set c where data Unique {c} {C : Set c} : List C → Set c where
@ -30,3 +30,7 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') =
All¬-¬Any : ∀ {p c} {C : Set c} {P : C → Set p} {l : List C} → All (λ x → ¬ P x) l → ¬ Any P l All¬-¬Any : ∀ {p c} {C : Set c} {P : C → Set p} {l : List C} → All (λ x → ¬ P x) l → ¬ Any P l
All¬-¬Any {l = x ∷ xs} (¬Px ∷ _) (here Px) = ¬Px Px All¬-¬Any {l = x ∷ xs} (¬Px ∷ _) (here Px) = ¬Px Px
All¬-¬Any {l = x ∷ xs} (_ ∷ ¬Pxs) (there Pxs) = All¬-¬Any ¬Pxs Pxs All¬-¬Any {l = x ∷ xs} (_ ∷ ¬Pxs) (there Pxs) = All¬-¬Any ¬Pxs Pxs
All-x∈xs : ∀ {a} {A : Set a} (xs : List A) → All (λ x → x ∈ xs) xs
All-x∈xs [] = []
All-x∈xs (x ∷ xs') = here refl ∷ map there (All-x∈xs xs')