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Prove walk splitting

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2025-11-29 21:34:39 -08:00
parent d1700f23fa
commit a277c8f969
2 changed files with 87 additions and 10 deletions
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9
Utils.agda
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@@ -9,6 +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.All.Properties using (++⁻ˡ)
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)
@@ -36,6 +37,14 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') =
help {[]} _ = x'≢x ∷ []
help {e ∷ es} (x'≢e ∷ x'≢es) = x'≢e ∷ help x'≢es
Unique-++⁻ˡ : ∀ {c} {C : Set c} (xs : List C) {ys : List C} → Unique (xs ++ ys) → Unique xs
Unique-++⁻ˡ [] Unique-ys = empty
Unique-++⁻ˡ (x ∷ xs) {ys} (push x≢xs++ys Unique-xs++ys) = push (++⁻ˡ xs {ys = ys} x≢xs++ys) (Unique-++⁻ˡ xs Unique-xs++ys)
Unique-++⁻ʳ : ∀ {c} {C : Set c} (xs : List C) {ys : List C} → Unique (xs ++ ys) → Unique ys
Unique-++⁻ʳ [] Unique-ys = Unique-ys
Unique-++⁻ʳ (x ∷ xs) {ys} (push x≢xs++ys Unique-xs++ys) = Unique-++⁻ʳ xs Unique-xs++ys
All-≢-map : ∀ {c d} {C : Set c} {D : Set d} (x : C) {xs : List C} (f : C → D) →
Injective (_≡_ {_} {C}) (_≡_ {_} {D}) f →
All (λ x' → ¬ x ≡ x') xs → All (λ y' → ¬ (f x) ≡ y') (mapˡ f xs)