DanilaFe/agda-spa
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Add a helpful utility function

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-03-01 19:08:11 -08:00
parent 52e7a7a208
commit 3a537f54ba
1 changed files with 4 additions and 0 deletions
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Utils.agda
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@ -32,6 +32,10 @@ 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} (¬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-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
All-x∈xs : ∀ {a} {A : Set a} (xs : List A) → All (λ x → x ∈ xs) xs All-x∈xs : ∀ {a} {A : Set a} (xs : List A) → All (λ x → x ∈ xs) xs
All-x∈xs [] = [] All-x∈xs [] = []
All-x∈xs (x ∷ xs') = here refl ∷ map there (All-x∈xs xs') All-x∈xs (x ∷ xs') = here refl ∷ map there (All-x∈xs xs')