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Prove that EPOCH not depends on expired dreps #941
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251fd8a
Proof that EPOCH not depends on expired dreps
carlostome 9405c28
trigger hydra
carlostome f0f68e5
Fix broken computational EPOCH module
carlostome 4425f04
Fix GovDepsMatch
carlostome d9265a3
Remove postulates; import module from Epoch.Properties
carlostome 7f56f45
Add temporary overlay to overwrite agda-sets
carlostome 45cb060
use opaque to improve tc time
carlostome cb6e546
Fix tc error
carlostome 9b55dfe
Implement agda-sets properties locally
carlostome 3c20f8f
Fix typechecking
carlostome 5c7ef72
Merge branch 'master' into bisimulation-expired-dreps
carlostome 77500fc
Incorporate William's suggestions
carlostome 0b21e85
Fill leftover goal
carlostome 128558d
Make literate agda file; add explanation
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48 changes: 48 additions & 0 deletions
48
src-lib-exts/abstract-set-theory/Axiom/Set/Properties.agda
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,48 @@ | ||
| {-# OPTIONS --safe --no-import-sorts #-} | ||
| open import Axiom.Set using (Theory) | ||
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| module abstract-set-theory.Axiom.Set.Properties {ℓ} (th : Theory {ℓ}) where | ||
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| open import abstract-set-theory.Prelude hiding (isEquivalence; trans; map; map₂) | ||
| open Theory th | ||
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| open Equivalence | ||
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| private variable | ||
| A B C : Type ℓ | ||
| X Y Z : Set A | ||
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| module _ {P Q : A → Type} {sp-P : specProperty P} {sp-Q : specProperty Q} where | ||
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| open import Relation.Unary using (_⇒_; Universal) | ||
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| filter-⇒ : (P⇒Q : Universal (P ⇒ Q)) → filter sp-P (filter sp-Q X) ≡ᵉ filter sp-P X | ||
| filter-⇒ P⇒Q = filter-⇒-⊆ , filter-⇒-⊇ | ||
| where | ||
| filter-⇒-⊆ : filter sp-P (filter sp-Q X) ⊆ filter sp-P X | ||
| filter-⇒-⊆ p with from ∈-filter p | ||
| ... | (q , p) with from ∈-filter p | ||
| ... | (_ , p) = to ∈-filter (q , p) | ||
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| filter-⇒-⊇ : filter sp-P X ⊆ filter sp-P (filter sp-Q X) | ||
| filter-⇒-⊇ p with from ∈-filter p | ||
| ... | (q , p) = to ∈-filter (q , (to ∈-filter (P⇒Q _ q , p))) | ||
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| module _ {P : A → Type} {sp-P : specProperty P} {Q : B → Type} {sp-Q : specProperty Q} where | ||
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| open import Relation.Unary using (_⇒_; Universal) | ||
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| filter-map : ∀ {f : A → B} (Qf⇒P : Universal ((Q ∘ f) ⇒ P)) | ||
| → filter sp-Q (map f X) ≡ᵉ filter sp-Q (map f (filter sp-P X)) | ||
| filter-map {f = f} Qf⇒P = filter-map-⊆ , filter-map-⊇ | ||
| where | ||
| filter-map-⊆ : filter sp-Q (map f X) ⊆ filter sp-Q (map f (filter sp-P X)) | ||
| filter-map-⊆ p with from ∈-filter p | ||
| ... | Qa , p with from ∈-map p | ||
| ... | (a , refl , p) = to ∈-filter (Qa , (to ∈-map (_ , (refl , (to ∈-filter (Qf⇒P a Qa , p)))))) | ||
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| filter-map-⊇ : filter sp-Q (map f (filter sp-P X)) ⊆ filter sp-Q (map f X) | ||
| filter-map-⊇ p with from ∈-filter p | ||
| ... | Qfa , p with from ∈-map p | ||
| ... | (a , refl , p) with from ∈-filter p | ||
| ... | (Pa , p) = to ∈-filter (Qfa , (to ∈-map (a , (refl , p)))) |
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I just happened to see this PR, we actually have a lemma for this already:
computational⇒rightUniqueinInterface.ComputationalRelation.