# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1591529352 -32400
# Node ID 5de8905a5a2b83d3a4a364fca1d881e450135cec
# Parent  4ae48eed654a51d7bfac5c168c4731e302657a94
...

diff -r 4ae48eed654a -r 5de8905a5a2b LEMC.agda
--- a/LEMC.agda	Sun May 10 09:25:18 2020 +0900
+++ b/LEMC.agda	Sun Jun 07 20:29:12 2020 +0900
@@ -32,12 +32,6 @@
 
 open choiced
 
-double-neg-eilm : {A : Set (suc n)} → ¬ ¬ A → A      -- we don't have this in intutionistic logic
-double-neg-eilm  {A} notnot with p∨¬p A                         -- assuming axiom of choice
-... | case1 p = p
-... | case2 ¬p = ⊥-elim ( notnot ¬p )
-
-
 OD→ZFC : ZFC
 OD→ZFC   = record { 
     ZFSet = OD 
diff -r 4ae48eed654a -r 5de8905a5a2b OD.agda
--- a/OD.agda	Sun May 10 09:25:18 2020 +0900
+++ b/OD.agda	Sun Jun 07 20:29:12 2020 +0900
@@ -246,7 +246,7 @@
     ; infinite = infinite
     ; isZF = isZF 
  } where
-    ZFSet = OD 
+    ZFSet = OD             -- is less than Ords because of maxod
     Select : (X : OD  ) → ((x : OD  ) → Set n ) → OD 
     Select X ψ = record { def = λ x →  ( def X x ∧ ψ ( ord→od x )) }
     Replace : OD  → (OD  → OD  ) → OD 
@@ -260,7 +260,7 @@
     Power : OD  → OD 
     Power A = Replace (Def (Ord (od→ord A))) ( λ x → A ∩ x )
     -- ｛_｝ : ZFSet → ZFSet
-    -- ｛ x ｝ = ( x ,  x )
+    -- ｛ x ｝ = ( x ,  x )     -- it works but we don't use 
 
     data infinite-d  : ( x : Ordinal  ) → Set n where
         iφ :  infinite-d o∅
diff -r 4ae48eed654a -r 5de8905a5a2b filter.agda
--- a/filter.agda	Sun May 10 09:25:18 2020 +0900
+++ b/filter.agda	Sun Jun 07 20:29:12 2020 +0900
@@ -43,8 +43,11 @@
 
 open Filter
 
+L⊆L : (L : OD) → L ⊆ L
+L⊆L L = record { incl = λ {x} lt → lt }
+
 L-filter : {L : OD} → (P : Filter L ) → {p : OD} → filter P ∋ p → filter P ∋ L
-L-filter {L} P {p} lt = filter1 P {p} {L} {!!} lt {!!}
+L-filter {L} P {p} lt = filter1 P {p} {L} (L⊆L L) lt {!!}
 
 prime-filter : {L : OD} → Filter L → ∀ {p q : OD } → Set n
 prime-filter {L} P {p} {q} =  filter P ∋ ( p ∪ q) → ( filter P ∋ p ) ∨ ( filter P ∋ q )
@@ -83,7 +86,7 @@
    import ordinal
 
    -- open  ordinal.C-Ordinal-with-choice 
-
+   -- both Power and infinite is too ZF, it is better to use simpler one
    Hω2 : Filter (Power (Power infinite))
    Hω2 = {!!}