--- a/constructible-set.agda	Tue May 14 13:52:19 2019 +0900
+++ b/constructible-set.agda	Thu May 16 10:55:34 2019 +0900
@@ -122,55 +122,37 @@
 
 -- X' = { x ∈ X |  ψ  x } ∪ X , Mα = ( ∪ (β < α) Mβ ) '
 
-data Constructible ( α : Ordinal  )  :  Set (suc n) where
-    fsub : ( ψ : Ordinal  → Set n ) → Constructible  α
-    xself : Ordinal → Constructible  α
-
 record ConstructibleSet  : Set (suc n) where
   field
     α : Ordinal
-    constructible : Constructible α
+    constructible : Ordinal  → Set n 
 
 open ConstructibleSet
 
-data _c∋_  : {α α' : Ordinal  }  →
-        Constructible  α → Constructible   α' → Set n where
-    c> :  {α α' : Ordinal }
-        (ta : Constructible  α ) ( tx : Constructible   α' ) → α' o< α →  ta c∋ tx
-    xself-fsub  :  {α : Ordinal  } 
-         (ta : Ordinal ) ( ψ : Ordinal  → Set n ) → _c∋_  {α} {α} (xself ta ) ( fsub ψ)  
-    fsub-fsub :  {α : Ordinal   } 
-          ( ψ : Ordinal   → Set n ) ( ψ₁ : Ordinal   → Set n ) →
-         ( ∀ ( x :  Ordinal  ) → ψ x →  ψ₁ x ) →  _c∋_  {α} {α} ( fsub ψ ) ( fsub ψ₁) 
-
-_∋_  : (ConstructibleSet ) → (ConstructibleSet  ) → Set n 
-a ∋ x  = constructible a c∋ constructible x
+_∋_  : (ConstructibleSet ) → (ConstructibleSet  ) → Set n
+a ∋ x  =  (α a ≡ α x)  ∨ ( α x o< α a )  
 
 -- transitiveness : (a b c : ConstructibleSet ) → a ∋ b → b ∋ c → a ∋ c
 -- transitiveness  a b c a∋b b∋c with constructible a c∋ constructible b | constructible b c∋ constructible c
 -- ... | t1 | t2 = {!!}
 
-data _c≈_  :  {α α' : Ordinal}  →
-        Constructible  α → Constructible   α' → Set n where
-    crefl :  {α : Ordinal  } → _c≈_  {α} {α} (xself α ) (xself α )
-    feq :  {lv : Nat} {α : Ordinal }
-          → ( ψ : Ordinal  → Set n ) ( ψ₁ : Ordinal → Set n ) 
-          → (∀ ( x :  Ordinal ) → ψ x  ⇔ ψ₁ x ) → _c≈_    {α} {α} ( fsub ψ ) ( fsub ψ₁)
-
-_≈_  : (ConstructibleSet ) → (ConstructibleSet  ) → Set n 
-a ≈ x  = constructible a c≈ constructible x
-
-ConstructibleSet→ZF : ZF {suc n} 
+ConstructibleSet→ZF : ZF {suc n} {suc n}
 ConstructibleSet→ZF   = record { 
     ZFSet = ConstructibleSet 
-    ; _∋_ = _∋_
-    ; _≈_ = _≈_ 
-    ; ∅  = record {  α = record {lv = Zero ; ord = Φ } ; constructible = xself ( record {lv = Zero ; ord = Φ }) }
-    ; _×_ = {!!}
-    ; Union = {!!}
+    ; _∋_ = λ a b → Lift (suc n) ( a ∋ b )
+    ; _≈_ = _≡_ 
+    ; ∅  = record {α = record { lv = Zero ; ord = Φ } ; constructible = λ x → Lift n ⊥ }
+    ; _,_ = _,_
+    ; Union = Union
     ; Power = {!!}
-    ; Select = {!!}
+    ; Select = Select
     ; Replace = {!!}
     ; infinite = {!!}
     ; isZF = {!!}
- }
+ } where
+    Select : (X : ConstructibleSet) → (ConstructibleSet → Set (suc n)) → ConstructibleSet
+    Select = {!!}
+    _,_ : ConstructibleSet → ConstructibleSet → ConstructibleSet
+    a , b  = Select {!!} {!!}
+    Union : ConstructibleSet → ConstructibleSet
+    Union a = {!!}