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Prove that variables in a program all come from the program's code

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2024-03-10 16:41:21 -07:00
parent 51accb6438
commit 0705df708e
3 changed files with 134 additions and 15 deletions
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7
Lattice/Map.agda
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@@ -553,11 +553,18 @@ open ImplInsert _⊔₂_ using
; union-preserves-∈₂
; union-preserves-∉
; union-preserves-∈k₁
; union-preserves-∈k₂
)
⊔-combines : ∀ {k : A} {v₁ v₂ : B} {m₁ m₂ : Map} → (k , v₁) ∈ m₁ → (k , v₂) ∈ m₂ → (k , v₁ ⊔₂ v₂) ∈ (m₁ ⊔ m₂)
⊔-combines {k} {v₁} {v₂} {kvs₁ , u₁} {kvs₂ , u₂} k,v₁∈m₁ k,v₂∈m₂ = union-combines u₁ u₂ k,v₁∈m₁ k,v₂∈m₂
⊔-preserves-∈k₁ : ∀ {k : A} → {m₁ m₂ : Map} → k ∈k m₁ → k ∈k (m₁ ⊔ m₂)
⊔-preserves-∈k₁ {k} {(l₁ , _)} {(l₂ , _)} k∈km₁ = union-preserves-∈k₁ {l₁ = l₁} {l₂ = l₂} k∈km₁
⊔-preserves-∈k₂ : ∀ {k : A} → {m₁ m₂ : Map} → k ∈k m₂ → k ∈k (m₁ ⊔ m₂)
⊔-preserves-∈k₂ {k} {(l₁ , _)} {(l₂ , _)} k∈km₁ = union-preserves-∈k₂ {l₁ = l₁} {l₂ = l₂} k∈km₁
open ImplInsert _⊓₂_ using
( restrict-needs-both
; updates