Mercurial > hg > Members > kono > Proof > ZF-in-agda
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Fri, 26 Jul 2019 21:08:06 +0900 |
parents | |
children | 9eb6a8691f02 |
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open import Level module filter where open import zf open import ordinal open import OD open import Relation.Nullary open import Relation.Binary open import Data.Empty open import Relation.Binary open import Relation.Binary.Core open import Relation.Binary.PropositionalEquality record Filter {n : Level} ( P max : OD {suc n} ) : Set (suc (suc n)) where field _⊇_ : OD {suc n} → OD {suc n} → Set (suc n) G : OD {suc n} G∋1 : G ∋ max Gmax : { p : OD {suc n} } → P ∋ p → p ⊇ max Gless : { p q : OD {suc n} } → G ∋ p → P ∋ q → p ⊇ q → G ∋ q Gcompat : { p q : OD {suc n} } → G ∋ p → G ∋ q → ¬ ( ( r : OD {suc n}) → (( p ⊇ r ) ∧ ( p ⊇ r ))) dense : {n : Level} → Set (suc (suc n)) dense {n} = { D P p : OD {suc n} } → ({x : OD {suc n}} → P ∋ p → ¬ ( ( q : OD {suc n}) → D ∋ q → od→ord p o< od→ord q )) open OD.OD -- H(ω,2) = Power ( Power ω ) = Def ( Def ω)) Pred : {n : Level} ( Dom : OD {suc n} ) → OD {suc n} Pred {n} dom = record { def = λ x → def dom x → Set n } Hω2 : {n : Level} → OD {suc n} Hω2 {n} = record { def = λ x → {dom : Ordinal {suc n}} → x ≡ od→ord ( Pred ( ord→od dom )) } _⊆_ : {n : Level} → ( A B : OD {suc n} ) → ∀{ x : OD {suc n} } → Set (suc n) _⊆_ A B {x} = A ∋ x → B ∋ x Hω2Filter : {n : Level} → Filter {n} Hω2 od∅ Hω2Filter {n} = record { _⊇_ = {!!} ; G = {!!} ; G∋1 = {!!} ; Gmax = {!!} ; Gless = {!!} ; Gcompat = {!!} } where P = Hω2 _⊇_ : OD {suc n} → OD {suc n} → Set (suc n) _⊇_ = {!!} G : OD {suc n} G = {!!} G∋1 : G ∋ od∅ G∋1 = {!!} Gmax : { p : OD {suc n} } → P ∋ p → p ⊇ od∅ Gmax = {!!} Gless : { p q : OD {suc n} } → G ∋ p → P ∋ q → p ⊇ q → G ∋ q Gless = {!!} Gcompat : { p q : OD {suc n} } → G ∋ p → G ∋ q → ¬ ( ( r : OD {suc n}) → (( p ⊇ r ) ∧ ( p ⊇ r ))) Gcompat = {!!}