# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1667031977 -32400
# Node ID d396af76c5592ba036a4a86f829d034503b06838
# Parent  6f342473f298926645c7fea4ac03e421f2aa0408
...

diff -r 6f342473f298 -r d396af76c559 src/zorn.agda
--- a/src/zorn.agda	Sat Oct 29 14:17:04 2022 +0900
+++ b/src/zorn.agda	Sat Oct 29 17:26:17 2022 +0900
@@ -1475,26 +1475,25 @@
                     --     supf u o< spuf c → order
 
           not-hasprev : ¬ HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) d) d (cf nmx)
-          not-hasprev hp = ⊥-elim (z29 spd ? hp)  where
-               -- z31 : odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx d)
-               -- z31 = ?
+          not-hasprev hp = ⊥-elim (z29 {mc} {asc} spd hp)  where
                z29 : {mc : Ordinal } {asc : odef A (supf mc)} (spd : MinSUP A (uchain (cf nmx)  (cf-is-≤-monotonic nmx) asc )) 
-                  →  odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx (MinSUP.sup spd))
                   →  HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) (MinSUP.sup spd)) (MinSUP.sup spd) (cf nmx)
                   →  ⊥
-               z29 {mc} {asc} spd ufd hp = <-irr ? z30 where
+               z29 {mc} {asc} spd hp = <-irr z26 z30 where
                    y : Ordinal
                    y = HasPrev.y hp
                    d1 :  Ordinal
                    d1 = MinSUP.sup spd -- supf d1 ≡ d
                    z30 : * d1 < * (cf nmx d1)
-                   z30 = ?
+                   z30 = proj1 (cf-is-<-monotonic nmx d1 (MinSUP.asm spd))
+                   z31 : odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx d1)
+                   z31 = ?
                    z24 : y << d1
                    z24 = subst (λ k → y <<  k) (sym (HasPrev.x=fy hp)) ( proj1 (cf-is-<-monotonic nmx y (proj1 (HasPrev.ay hp) ) ))
-                   -- z26 : (* (cf nmx (MinSUP.sup spd)) ≡ * (MinSUP.sup spd)) ∨ (* (cf nmx (MinSUP.sup spd)) < * (MinSUP.sup spd))
-                   -- z26 with  MinSUP.x<sup spd ?
-                   -- ... | case1 eq = ?
-                   -- ... | case2 lt = ?
+                   z26 : (* (cf nmx d1) ≡ * d1) ∨ (* (cf nmx d1) < * d1)
+                   z26 with  MinSUP.x<sup spd z31
+                   ... | case1 eq = case1 (cong (*) eq)
+                   ... | case2 lt = case2 lt
                z25 : odef (ZChain.chain zc) (cf nmx d)
                z25 = ZChain.f-next zc (subst (λ k → odef (ZChain.chain zc) k) (sym (HasPrev.x=fy hp))
                    (ZChain.f-next zc