Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff Ordinals.agda @ 341:27d2933c4bd7
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| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Mon, 13 Jul 2020 13:29:38 +0900 |
| parents | 639fbb6284d8 |
| children | b1ccdbb14c92 |
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--- a/Ordinals.agda Mon Jul 13 09:26:34 2020 +0900 +++ b/Ordinals.agda Mon Jul 13 13:29:38 2020 +0900 @@ -231,6 +231,13 @@ 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 + nexto≡ : {x : Ordinal} → next x ≡ next (osuc x) + nexto≡ {x} with trio< (next x) (next (osuc x) ) + nexto≡ {x} | tri< a ¬b ¬c = {!!} + nexto≡ {x} | tri≈ ¬a b ¬c = b + nexto≡ {x} | tri> ¬a ¬b c = ⊥-elim ((proj2 (proj2 next-limit)) _ (ordtrans <-osuc (proj1 next-limit)) c + (λ z eq → o<¬≡ (sym eq) (proj1 (proj2 next-limit) _ (ordtrans <-osuc (subst (λ k → k o< next (osuc x)) eq {!!} ))))) + record OrdinalSubset (maxordinal : Ordinal) : Set (suc n) where field os→ : (x : Ordinal) → x o< maxordinal → Ordinal