diff zf.agda @ 14:e11e95d5ddee

separete constructible set
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Tue, 14 May 2019 03:38:26 +0900
parents 2df90eb0896c
children 627a79e61116
line wrap: on
line diff
--- a/zf.agda	Mon May 13 20:51:45 2019 +0900
+++ b/zf.agda	Tue May 14 03:38:26 2019 +0900
@@ -121,88 +121,3 @@
 --  russel with Select ( λ x →  x ∋ x  ) 
 --  ... | s = {!!}
 
-module constructible-set  where
-
-  open import Data.Nat renaming ( zero to Zero ; suc to Suc ;  ℕ to Nat ) 
-  
-  open import  Relation.Binary.PropositionalEquality
-  
-  data Ordinal {n : Level }  :  Set n where
-     Φ : {lv : Nat} → Ordinal {n} lv
-     T-suc : {lv : Nat} → Ordinal {n} lv → Ordinal lv
-     ℵ_ :  (lv : Nat) → Ordinal (Suc lv)
-
-  data _o<_ {n : Level } :  Ordinal {n}  →  Ordinal {n}  → Set n where
-     l< : {lx ly : Nat }  → {x : Ordinal {n} lx } →  {y : Ordinal {n} ly } → lx < ly → x o< y
-     Φ<  : {lx : Nat} → {x : Ordinal {n} lx}  →  Φ {n} {lx} o< T-suc {n} {lx} x
-     s<  : {lx : Nat} → {x : Ordinal {n} lx}  →  x o< T-suc {n} {lx} x
-     ℵΦ< : {lx : Nat} → {x : Ordinal {n} lx } →  Φ {n} {lx} o< (ℵ lx) 
-     ℵ<  : {lx : Nat} → {x : Ordinal {n} lx } →  T-suc {n} {lx} x o< (ℵ lx) 
-
-  _o≈_ : {n : Level } {lv : Nat } → Rel ( Ordinal {n} lv ) n
-  _o≈_  = {!!}
-
-  triO : {n : Level } → {lx ly : Nat}   → Trichotomous  _o≈_ ( _o<_ {n} {lx} {ly} )
-  triO {n} {lv} Φ y = {!!}
-  triO {n} {lv} (T-suc x) y = {!!}
-  triO {n} {.(Suc lv)} (ℵ lv) y = {!!}
-
-
-  max = Data.Nat._⊔_
-  
-  maxα : {n : Level } → { lx ly : Nat } → Ordinal {n} lx  →  Ordinal {n} ly  → Ordinal {n} (max lx ly)
-  maxα x y with x o< y
-  ... | t = {!!}
-
-  -- X' = { x ∈ X |  ψ  x } ∪ X , Mα = ( ∪ (β < α) Mβ ) '
-
-  data Constructible {n : Level } {lv : Nat} ( α : Ordinal {n} lv )  :  Set (suc n) where
-     fsub : ( ψ : Ordinal {n} lv → Set n ) → Constructible  α
-     xself : Ordinal {n} lv → Constructible  α
-  
-  record ConstructibleSet {n : Level } : Set (suc n) where
-   field
-      level : Nat
-      α : Ordinal {n} level 
-      constructible : Constructible α
-  
-  open ConstructibleSet
-  
-  data _c∋_ {n : Level } : {lv lv' : Nat} {α : Ordinal {n} lv } {α' : Ordinal {n} lv' } →
-        Constructible {n} {lv} α → Constructible {n} {lv'} α' → Set n where
-     c> : {lv lv' : Nat} {α : Ordinal {n} lv } {α' : Ordinal {n} lv' }
-        (ta : Constructible {n} {lv} α ) ( tx : Constructible {n} {lv'} α' ) → α' o< α →  ta c∋ tx
-     xself-fsub  : {lv : Nat} {α : Ordinal {n} lv } 
-         (ta : Ordinal {n} lv ) ( ψ : Ordinal {n} lv → Set n ) → _c∋_ {n} {_} {_} {α} {α} (xself ta ) ( fsub ψ)  
-     fsub-fsub : {lv lv' : Nat} {α : Ordinal {n} lv } 
-          ( ψ : Ordinal {n} lv → Set n ) ( ψ₁ : Ordinal {n} lv → Set n ) →
-         ( ∀ ( x :  Ordinal {n} lv ) → ψ x →  ψ₁ x ) →  _c∋_ {n} {_} {_} {α} {α} ( fsub ψ ) ( fsub ψ₁) 
-
-  _∋_  : {n : Level} → (ConstructibleSet {n}) → (ConstructibleSet {n} ) → Set n 
-  a ∋ x  = constructible a c∋ constructible x
-
-  data _c≈_ {n : Level } : {lv lv' : Nat} {α : Ordinal {n} lv } {α' : Ordinal {n} lv' } →
-        Constructible {n} {lv} α → Constructible {n} {lv'} α' → Set n where
-      crefl :  {lv : Nat} {α : Ordinal {n} lv } → _c≈_ {n} {_} {_} {α} {α} (xself α ) (xself α )
-      feq :  {lv : Nat} {α : Ordinal {n} lv }
-          → ( ψ : Ordinal {n} lv → Set n ) ( ψ₁ : Ordinal {n} lv → Set n ) 
-          → (∀ ( x :  Ordinal {n} lv ) → ψ x  ⇔ ψ₁ x ) → _c≈_ {n} {_} {_} {α} {α} ( fsub ψ ) ( fsub ψ₁)
-
-  _≈_  : {n : Level} → (ConstructibleSet {n}) → (ConstructibleSet {n} ) → Set n 
-  a ≈ x  = constructible a c≈ constructible x
-      
-  
-  ConstructibleSet→ZF : {n : Level } → ZF {suc n} {n}
-  ConstructibleSet→ZF {n}  = record {
-       ZFSet = ConstructibleSet 
-     ; _∋_ = _∋_
-     ; _≈_ = _≈_ 
-     ; ∅  = record { level = Zero ; α = Φ ; constructible = xself Φ }
-     ; _×_ = {!!}
-     ; Union = {!!}
-     ; Power = {!!}
-     ; Select = {!!}
-     ; Replace = {!!}
-     ; infinite = {!!}
-     ; isZF = {!!}
-    } where