# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1665042189 -32400
# Node ID aa496c2326044f43b11fbcf06705949f274d0d30
# Parent  b09e39629d86f35b42c2a2c82a4e9fdc533c9be1
sp1 = supf (& A)

diff -r b09e39629d86 -r aa496c232604 src/zorn.agda
--- a/src/zorn.agda	Thu Oct 06 15:57:08 2022 +0900
+++ b/src/zorn.agda	Thu Oct 06 16:43:09 2022 +0900
@@ -707,6 +707,7 @@
      fixpoint f mf zc = z14 where
            chain = ZChain.chain zc
            supf = ZChain.supf zc
+           sp1 : SUP A chain
            sp1 = sp0 f mf as0 zc 
            z10 :  {a b : Ordinal } → (ca : odef chain a ) → supf b o< supf (& A) → (ab : odef A b ) 
               →  HasPrev A chain b f ∨  IsSup A chain {b} ab 
@@ -715,7 +716,11 @@
            z21 : supf (& (SUP.sup sp1)) o< supf (& A)
            z21 with osuc-≡< ( ZChain.supf-mono zc (o<→≤ (c<→o< ( SUP.as sp1))) )
            ... | case2 lt = lt
-           ... | case1 eq = ?
+           ... | case1 eq = ? where
+               z24 : supf (& (SUP.sup sp1)) ≡ & (SUP.sup sp1) 
+               z24 = ZChain.sup=u zc ? ? ?
+               z25 : supf (& A) ≡ MinSUP.sup ( ZChain.minsup zc o≤-refl )
+               z25 = ZChain.supf-is-minsup zc o≤-refl 
            z12 : odef chain (& (SUP.sup sp1))
            z12 with o≡? (& s) (& (SUP.sup sp1))
            ... | yes eq = subst (λ k → odef chain k) eq ( ZChain.chain∋init zc )