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Rearrange a few functions

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Danila Fedorin 2023-07-30 13:49:38 -07:00
parent eaee73236f
commit af0066eaa7
1 changed files with 26 additions and 26 deletions
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@ -152,22 +152,13 @@ private module ImplInsert (f : B → B → B) where
merge-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ =
insert-preserves-Unique (merge-preserves-Unique xs₁ l₂ u₂)
insert-preserves-∈ : ∀ {k k' : A} {v v' : B} {l : List (A × B)} →
¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l
insert-preserves-∈ {k} {k'} {l = x ∷ xs} k≢k' (here k,v=x)
rewrite sym k,v=x with ≡-dec-A k' k
... | yes k'≡k = absurd (k≢k' (sym k'≡k))
... | no _ = here refl
insert-preserves-∈ {k} {k'} {l = (k'' , _) ∷ xs} k≢k' (there k,v∈xs)
with ≡-dec-A k' k''
... | yes _ = there k,v∈xs
... | no _ = there (insert-preserves-∈ k≢k' k,v∈xs)
insert-preserves-∈k : ∀ {k k' : A} {v' : B} {l : List (A × B)} →
¬ k ≡ k' → k ∈k l → k ∈k insert k' v' l
insert-preserves-∈k k≢k' k∈kl =
let (v , k,v∈l) = locate k∈kl
in ∈-cong proj₁ (insert-preserves-∈ k≢k' k,v∈l)
insert-fresh : ∀ {k : A} {v : B} {l : List (A × B)} →
¬ k ∈k l → (k , v) ∈ insert k v l
insert-fresh {l = []} k∉kl = here refl
insert-fresh {k} {l = (k' , v') ∷ xs} k∉kl
with ≡-dec-A k k'
... | yes k≡k' = absurd (k∉kl (here k≡k'))
... | no _ = there (insert-fresh (λ k∈kxs → k∉kl (there k∈kxs)))
insert-preserves-∉k : ∀ {k k' : A} {v' : B} {l : List (A × B)} →
¬ k ≡ k' → ¬ k ∈k l → ¬ k ∈k insert k' v' l
@ -191,6 +182,23 @@ private module ImplInsert (f : B → B → B) where
... | yes k≡k' = absurd (k∉kl₁ (here k≡k'))
... | no k≢k' = insert-preserves-∉k k≢k' (merge-preserves-∉ (λ k∈kxs₁ → k∉kl₁ (there k∈kxs₁)) k∉kl₂)
insert-preserves-∈ : ∀ {k k' : A} {v v' : B} {l : List (A × B)} →
¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l
insert-preserves-∈ {k} {k'} {l = x ∷ xs} k≢k' (here k,v=x)
rewrite sym k,v=x with ≡-dec-A k' k
... | yes k'≡k = absurd (k≢k' (sym k'≡k))
... | no _ = here refl
insert-preserves-∈ {k} {k'} {l = (k'' , _) ∷ xs} k≢k' (there k,v∈xs)
with ≡-dec-A k' k''
... | yes _ = there k,v∈xs
... | no _ = there (insert-preserves-∈ k≢k' k,v∈xs)
insert-preserves-∈k : ∀ {k k' : A} {v' : B} {l : List (A × B)} →
¬ k ≡ k' → k ∈k l → k ∈k insert k' v' l
insert-preserves-∈k k≢k' k∈kl =
let (v , k,v∈l) = locate k∈kl
in ∈-cong proj₁ (insert-preserves-∈ k≢k' k,v∈l)
merge-preserves-∈₁ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} →
¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ merge l₁ l₂
merge-preserves-∈₁ {l₁ = []} _ k,v∈l₂ = k,v∈l₂
@ -198,14 +206,6 @@ private module ImplInsert (f : B → B → B) where
let recursion = merge-preserves-∈₁ (λ k∈xs₁ → k∉kl₁ (there k∈xs₁)) k,v∈l₂
in insert-preserves-∈ (λ k≡k' → k∉kl₁ (here k≡k')) recursion
insert-fresh : ∀ {k : A} {v : B} {l : List (A × B)} →
¬ k ∈k l → (k , v) ∈ insert k v l
insert-fresh {l = []} k∉kl = here refl
insert-fresh {k} {l = (k' , v') ∷ xs} k∉kl
with ≡-dec-A k k'
... | yes k≡k' = absurd (k∉kl (here k≡k'))
... | no _ = there (insert-fresh (λ k∈kxs → k∉kl (there k∈kxs)))
merge-preserves-∈₂ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} →
Unique (keys l₁) → (k , v) ∈ l₁ → ¬ k ∈k l₂ → (k , v) ∈ merge l₁ l₂
merge-preserves-∈₂ {k} {v} {(k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (there k,v∈xs₁) k∉kl₂ =