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Use the new provenance function to clean up some proofs

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2024-03-07 19:59:14 -08:00
parent 48983c55b1
commit 34203840c8
2 changed files with 67 additions and 97 deletions
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10
Lattice/FiniteValueMap.agda
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@@ -36,6 +36,7 @@ open import Lattice.Map A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A lB
; _∈_
; Map-functional
; Expr-Provenance
; Expr-Provenance-≡
; _∩_; _∪_; `_
; in₁; in₂; bothᵘ; single
; ⊔-combines
@@ -212,17 +213,16 @@ module IterProdIsomorphism where
Provenance-union : ∀ {ks : List A} (fm₁ fm₂ : FiniteMap ks) {k : A} {v : B} →
(k , v) ∈ᵐ (fm₁ ⊔ᵐ fm₂) → FromBothMaps k v fm₁ fm₂
Provenance-union fm₁@(m₁ , ks₁≡ks) fm₂@(m₂ , ks₂≡ks) {k} {v} k,v∈fm₁fm₂
with Expr-Provenance k ((` m₁) ∪ (` m₂)) (forget {m = proj₁ (fm₁ ⊔ᵐ fm₂)} k,v∈fm₁fm₂)
... | (_ , (in₁ (single k,v∈m₁) k∉km₂ , _))
with Expr-Provenance-≡ ((` m₁) ∪ (` m₂)) k,v∈fm₁fm₂
... | in₁ (single k,v∈m₁) k∉km₂
with k∈km₁ ← (forget {m = m₁} k,v∈m₁)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₂ k∈km₁)
... | (_ , (in₂ k∉km₁ (single k,v∈m₂) , _))
... | in₂ k∉km₁ (single k,v∈m₂)
with k∈km₂ ← (forget {m = m₂} k,v∈m₂)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₁ k∈km₂)
... | (v₁⊔v₂ , (bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) , k,v₁⊔v₂∈m₁m₂))
rewrite Map-functional {m = proj₁ (fm₁ ⊔ᵐ fm₂)} k,v∈fm₁fm₂ k,v₁⊔v₂∈m₁m₂ =
... | bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) =
((v₁ , v₂) , (refl , (k,v₁∈m₁ , k,v₂∈m₂)))
pop-⊔-distr : ∀ {k : A} {ks : List A} (fm₁ fm₂ : FiniteMap (k ∷ ks)) →