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

changeset 991:c190f708862a

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f (supf x) = supf x
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Thu, 17 Nov 2022 00:22:58 +0900
parents 9672214d4e13
children 4aaecae58da5
files src/zorn.agda
diffstat 1 files changed, 10 insertions(+), 0 deletions(-) [+]
line wrap: on
line diff
--- a/src/zorn.agda	Thu Nov 17 00:04:52 2022 +0900
+++ b/src/zorn.agda	Thu Nov 17 00:22:58 2022 +0900
@@ -829,6 +829,16 @@
            ax : odef A x
            is-sup : IsMinSUP A B f ax
 
+     supf-fc : ( f : Ordinal → Ordinal ) → (mf : ≤-monotonic-f A f ) {y : Ordinal} (ay : odef A y) → Ordinal  → Ordinal
+     supf-fc f mf {y} ay x = TransFinite0 ind x where
+            ind : (x : Ordinal) → ((z : Ordinal) → z o< x → Ordinal ) → Ordinal
+            ind x prev  with trio< x o∅ 
+            ... | tri< a ¬b ¬c = ?
+            ... | tri≈ ¬a b ¬c = MinSUP.sup (ysup f mf ay)
+            ... | tri> ¬a ¬b 0<x with Oprev-p x
+            ... | yes op = ?
+            ... | no lim = ?
+
      --
      -- create all ZChains under o< x
      --