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

diff Ordinals.agda @ 340:639fbb6284d8

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 13 Jul 2020 09:26:34 +0900
parents feb0fcc430a9
children 27d2933c4bd7
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line diff
--- a/Ordinals.agda	Sun Jul 12 19:55:37 2020 +0900
+++ b/Ordinals.agda	Mon Jul 13 09:26:34 2020 +0900
@@ -228,6 +228,9 @@
         next< {x} {y} {z} x<nz y<nx | tri> ¬a ¬b c = ⊥-elim (proj2 (proj2 next-limit) (next z) x<nz (ordtrans c y<nx )
            (λ w nz=ow → o<¬≡ (sym nz=ow) (proj1 (proj2 next-limit) _ (subst (λ k → w o< k ) (sym nz=ow) <-osuc ))))
 
+        nexto=n : {x y : Ordinal} → x o< next (osuc y)  → x o< next y 
+        nexto=n {x} {y} x<noy = next< (proj1 (proj2 next-limit) _ (proj1 next-limit)) x<noy
+
         record OrdinalSubset (maxordinal : Ordinal) : Set (suc n) where
           field
             os→ : (x : Ordinal) → x o< maxordinal → Ordinal