Mercurial > hg > Members > kono > Proof > ZF-in-agda

changeset 1061:fc37082d2a8a

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another IChain
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 11 Dec 2022 09:06:35 +0900
parents a09f5e728f92
children 88731edfa691
files src/zorn.agda
diffstat 1 files changed, 7 insertions(+), 5 deletions(-) [+]
line wrap: on
line diff
--- 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