--- a/OD.agda	Tue Aug 06 15:50:14 2019 +0900
+++ b/OD.agda	Wed Aug 07 09:50:51 2019 +0900
@@ -622,83 +622,3 @@
                      ; eq← = λ {x} lt → ⊥-elim ( ¬x<0 lt )
                    }
 
-         ------------
-         --
-         -- Onto map
-         --          def X x ->  xmap
-         --     X ---------------------------> Y
-         --          ymap   <-  def Y y
-         --
-         record Onto {n : Level } (X Y : OD {n})  : Set (suc n) where
-            field
-                xmap : (x : Ordinal {n}) → def X x → Ordinal {n} 
-                ymap : (y : Ordinal {n}) → def Y y → Ordinal {n} 
-                ymap-on-X  : {y :  Ordinal {n} } → (lty : def Y y ) → def X (ymap y lty)  
-                onto-iso   : {y :  Ordinal {n} } → (lty : def Y y ) → xmap  ( ymap y lty ) (ymap-on-X lty ) ≡ y
-
-         record Cardinal {n : Level } (X  : OD {n}) : Set (suc n) where
-            field
-                cardinal : Ordinal {n}
-                conto : Onto (Ord cardinal) X 
-                cmax : ( y : Ordinal {n} ) → cardinal o< y → ¬ Onto (Ord y) X 
-
-         cardinal : {n : Level } (X  : OD {suc n}) → Cardinal X
-         cardinal {n} X = record {
-                cardinal = sup-o ( λ x → proj1 ( cardinal-p x) )
-              ; conto = onto
-              ; cmax = cmax
-            } where
-             cardinal-p : (x  : Ordinal {suc n}) →  ( Ordinal {suc n} ∧ Dec (Onto (Ord x) X) )
-             cardinal-p x with p∨¬p ( Onto (Ord x) X ) 
-             cardinal-p x | case1 True = record { proj1 = x ; proj2 = yes True }
-             cardinal-p x | case2 False = record { proj1 = o∅ ; proj2 = no False }
-             onto-set : OD {suc n}
-             onto-set = record { def = λ x →  {!!} } -- Onto (Ord (sup-o (λ x → proj1 (cardinal-p x)))) X }
-             onto : Onto (Ord (sup-o (λ x → proj1 (cardinal-p x)))) X
-             onto = record {
-                        xmap = xmap
-                     ;  ymap = ymap
-                     ;  ymap-on-X  = ymap-on-X
-                     ;  onto-iso = onto-iso
-               } where
-                --
-                -- Ord cardinal itself has no onto map, but if we have x o< cardinal, there is one
-                --    od→ord X o< cardinal, so if we have def Y y or def X y, there is an Onto (Ord y) X
-                Y = (Ord (sup-o (λ x → proj1 (cardinal-p x))))
-                lemma1 : (y : Ordinal {suc n}) → def Y y  →  Onto (Ord y) X
-                lemma1 y y<Y with sup-o< {suc n} {λ x → proj1 ( cardinal-p x)} {y} 
-                ... | t = {!!}
-                lemma2 :  def Y (od→ord X)
-                lemma2 = {!!}
-                xmap : (x : Ordinal {suc n}) → def Y x → Ordinal {suc n}
-                xmap = {!!}
-                ymap : (y : Ordinal {suc n}) → def X y → Ordinal {suc n}
-                ymap = {!!}
-                ymap-on-X  : {y :  Ordinal {suc n} } → (lty : def X y ) → def Y (ymap y lty)  
-                ymap-on-X  = {!!}
-                onto-iso   : {y :  Ordinal {suc n} } → (lty : def X y ) → xmap  (ymap y lty) (ymap-on-X lty ) ≡ y
-                onto-iso = {!!}
-             cmax : (y : Ordinal) → sup-o (λ x → proj1 (cardinal-p x)) o< y → ¬ Onto (Ord y) X
-             cmax y lt ontoy = o<> lt (o<-subst {suc n} {_} {_} {y} {sup-o (λ x → proj1 (cardinal-p x))}
-                (sup-o< {suc n} {λ x → proj1 ( cardinal-p x)}{y}  ) lemma refl ) where
-                   lemma : proj1 (cardinal-p y) ≡ y
-                   lemma with  p∨¬p ( Onto (Ord y) X )
-                   lemma | case1 x = refl
-                   lemma | case2 not = ⊥-elim ( not ontoy )
-
-func : {n : Level}  → (f : Ordinal {suc n} → Ordinal {suc n}) → OD {suc n}
-func {n} f = record { def = λ y → (x : Ordinal {suc n}) → y ≡ f x }
-
-Func : {n : Level}  → OD {suc n}
-Func {n} = record { def = λ x →  (f : Ordinal {suc n} → Ordinal {suc n}) → x ≡ od→ord (func f) }
-
-odmap : {n : Level}  → { x : OD {suc n} } → Func ∋ x → Ordinal {suc n} → OD {suc n}
-odmap {n} {f} lt x = record { def = λ y → def f y } 
-
-
-         -----
-         --  All cardinal is ℵ0,  since we are working on Countable Ordinal, 
-         --  Power ω is larger than ℵ0, so it has no cardinal.
-
-
-