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List all the cases for the other direction

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Danila Fedorin 2023-07-30 19:25:46 -07:00
parent 2c839db924
commit eca6181494
1 changed files with 11 additions and 0 deletions
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Map.agda
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@ -386,3 +386,14 @@ module _ (f : B → B → B) where
... | (_ , (bothᵘ (bothᵘ (single {v₁} v₁∈e₁) (single {v₂} v₂∈e₂)) (single {v₃} v₃∈e₃) , v₁v₂v₃∈m₁₂m₃)) ... | (_ , (bothᵘ (bothᵘ (single {v₁} v₁∈e₁) (single {v₂} v₂∈e₂)) (single {v₃} v₃∈e₃) , v₁v₂v₃∈m₁₂m₃))
rewrite Map-functional {m = union f (union f m₁ m₂) m₃} k,v∈m₁₂m₃ v₁v₂v₃∈m₁₂m₃ = rewrite Map-functional {m = union f (union f m₁ m₂) m₃} k,v∈m₁₂m₃ v₁v₂v₃∈m₁₂m₃ =
(f v₁ (f v₂ v₃) , (f-assoc v₁ v₂ v₃ , ImplInsert.union-combines f u₁ (ImplInsert.union-preserves-Unique f l₂ l₃ u₃) v₁∈e₁ (ImplInsert.union-combines f u₂ u₃ v₂∈e₂ v₃∈e₃))) (f v₁ (f v₂ v₃) , (f-assoc v₁ v₂ v₃ , ImplInsert.union-combines f u₁ (ImplInsert.union-preserves-Unique f l₂ l₃ u₃) v₁∈e₁ (ImplInsert.union-combines f u₂ u₃ v₂∈e₂ v₃∈e₃)))
union-assoc₂ : ∀ (m₁ m₂ m₃ : Map) → subset (_≡_) (union f m₁ (union f m₂ m₃)) (union f (union f m₁ m₂) m₃)
union-assoc₂ m₁@(l₁ , u₁) m₂@(l₂ , u₂) m₃@(l₃ , u₃) k v k,v∈m₁m₂₃
with Expr-Provenance f k ((` m₁) ∪ ((` m₂) ∪ (` m₃))) (∈-cong proj₁ k,v∈m₁m₂₃)
... | (_ , (in₂ k∉ke₁ (in₂ k∉e₂ (single {v₃} v₁∈e₃)) , v₃∈m₁m₂₃)) = {!!}
... | (_ , (in₂ k∉ke₁ (in₁ (single {v₂} v₂∈e₂) k∉e₃) , v₂∈m₁m₂₃)) = {!!}
... | (_ , (in₂ k∉ke₁ (bothᵘ (single {v₂} v₂∈e₂) (single {v₃} v₁∈e₃)) , v₂v₃∈m₁m₂₃)) = {!!}
... | (_ , (in₁ (single {v₁} v₁∈e₁) k∉ke₁₂ , v₁∈m₁m₂₃)) = {!!}
... | (_ , (bothᵘ (single {v₁} v₁∈e₁) (in₂ k∉e₂ (single {v₃} v₁∈e₃)) , v₁v₃∈m₁m₂₃)) = {!!}
... | (_ , (bothᵘ (single {v₁} v₁∈e₁) (in₁ (single {v₂} v₂∈e₂) k∉e₃) , v₁v₂∈m₁m₂₃)) = {!!}
... | (_ , (bothᵘ (single {v₁} v₁∈e₁) (bothᵘ (single {v₂} v₂∈e₂) (single {v₃} v₁∈e₃)) , v₁v₂v₃∈m₁m₂₃)) = {!!}