# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1670717195 -32400
# Node ID fc37082d2a8aca771a61070571c3e7d334924507
# Parent  a09f5e728f92ec0e850c3fb9af1952c5479fd738
another IChain

diff -r a09f5e728f92 -r fc37082d2a8a src/zorn.agda
--- a/src/zorn.agda	Sun Dec 11 08:48:42 2022 +0900
+++ b/src/zorn.agda	Sun Dec 11 09:06:35 2022 +0900
@@ -281,12 +281,14 @@
    = record { od = record { def = λ z → odef A z ∧ UChain {A} {f} {supf} ay x z } ;
        odmax = & A ; <odmax = λ {y} sy → ∈∧P→o< sy }
 
--- Union of all UChain under limit ordinal x
+-- Union of chain lower than x
 
-data IChain  { A : HOD } { f : Ordinal → Ordinal } (supfz : {z : Ordinal } → z o< x → Ordinal)  {y : Ordinal } (ay : odef A y )
-       (x : Ordinal) : (z : Ordinal) → Set n where
-    ic-init : {z : Ordinal } (fc : FClosure A f y z) → IChain supf ay x z
-    ic-is-sup  : (u : Ordinal) {z : Ordinal }  (u<x : u o< x) (supu=u : supf u<x u ≡ u) ( fc : FClosure A f (supf u<x u) z ) → IChain supf ay x z
+record IChain  (A : HOD)  ( f : Ordinal → Ordinal ) {x : Ordinal } (supfz : {z : Ordinal } → z o< x → Ordinal) (z : Ordinal ) : Set n where
+  field
+     i : Ordinal
+     i<x : i o< x
+     s<x : supfz i<x o< x
+     fc : FClosure A f (supfz i<x) z
 
 UnionIC : ( A : HOD ) ( f : Ordinal → Ordinal ) {y : Ordinal } (ay : odef A y ) (supfz : {z : Ordinal } → z o< x → Ordinal) ( x : Ordinal ) → HOD
 UnionIC A f ay supf x