# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1662179290 -32400
# Node ID bf1b6c4768d2ecce58830032499b4bf100e03ac2
# Parent  95bbeb622f6eb9d198e0acfd0d84fa5d4874e829
...

diff -r 95bbeb622f6e -r bf1b6c4768d2 src/zorn.agda
--- a/src/zorn.agda	Sat Sep 03 09:43:19 2022 +0900
+++ b/src/zorn.agda	Sat Sep 03 13:28:10 2022 +0900
@@ -973,11 +973,22 @@
                      csupf1 with csupf0
                      ... | ⟪ as , ch-init fc ⟫ = ⟪ as , ch-init fc ⟫ 
                      ... | ⟪ as , ch-is-sup u u≤x record { fcy<sup = fcy<sup ; order = order ; supu=u = supu=u } fc  ⟫ 
-                        =  ⟪ as  , ch-is-sup u u≤x record { fcy<sup = fcy<sup1 ; order = order1 ; supu=u = ? }  ? ⟫  where
+                        =  ⟪ as  , ch-is-sup u u≤x record { fcy<sup = fcy<sup1 ; order = order1 ; supu=u = supu=u1 }  ? ⟫  where
+                         zc13 : supf0 u o< supf0 b
+                         zc13 = ?
+                         zc12 :  odef (UnionCF A f mf ay supf0 b) (supf1 b)
+                         zc12 = subst (λ k → odef (UnionCF A f mf ay supf0 b) k) &iso ( ZChain.csupf-fc zc b≤px zc13 fc  )
                          u≤x1 : u o≤ supf1 b 
                          u≤x1 = u≤x
+                         supu=u0 : supf0 u ≡ u
+                         supu=u0 = supu=u
                          supu=u1 : supf1 u ≡ u
-                         supu=u1 = ?
+                         supu=u1 with trio< u px
+                         ... | tri< a ¬b ¬c = supu=u 
+                         ... | tri≈ ¬a b ¬c = supu=u 
+                         ... | tri> ¬a ¬b c = ? -- supf1 b ≡ sp1 , u o≤ sp1, x o≤ u o≤ supf1 b -- u ≡ x → xsup x → ⊥ 
+                                                                     --    u > x → supf1 u ≡ sp1 → supf1 b o≤ supf1 u
+                          -- px o< u o≤ sp1 , spuf1 u o≤  spuf1 sp1
                          fcy<sup1 : {z : Ordinal} → FClosure A f y z → (z ≡ supf1 u) ∨ (z << supf1 u)
                          fcy<sup1 = ? 
                          order1 : {s z1 : Ordinal} → supf1 s o< supf1 u → FClosure A f (supf1 s) z1