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

changeset 1066:86f6cc26e315

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Tue, 13 Dec 2022 00:14:03 +0900
parents e053ad9c1afb
children 074b6a506b1b
files src/zorn.agda
diffstat 1 files changed, 7 insertions(+), 3 deletions(-) [+]
line wrap: on
line diff
--- a/src/zorn.agda	Mon Dec 12 23:14:22 2022 +0900
+++ b/src/zorn.agda	Tue Dec 13 00:14:03 2022 +0900
@@ -1340,9 +1340,13 @@
               uz01 : Tri (a < b) (a ≡ b) (b < a )
               uz01 with pchainx⊆chain ia
               ... | ⟪ ai , ch-init fc ⟫ = ZChain.f-total (pzc (pic<x (proj2 ib)))  ⟪ ai , ch-init fc ⟫  (pchainx⊆chain ib) 
-              ... | ⟪ ai , ch-is-sup u u<x su=u fc ⟫ = ZChain.f-total (pzc (pic<x (proj2 ib))) ⟪ ai , ch-is-sup u ? ? ? ⟫ (pchainx⊆chain ib) 
-                 uz02 : u o< osuc (IChain-i (proj2 ia))
-                 uz02 = ?
+              ... | ⟪ ai , ch-is-sup u u<x su=u fc ⟫ = ZChain.f-total (pzc (pic<x (proj2 ib))) ⟪ ai , ch-is-sup u uz02 uz03 uz04 ⟫ (pchainx⊆chain ib) where
+                 uz02 : u o< osuc (IChain-i (proj2 ib))
+                 uz02 with osuc-≡< (ZChain.supf-mono (pzc (pic<x (proj2 ia))) (o<→≤ u<x))
+                 ... | case1 eq = ⊥-elim ( o<¬≡ (trans (sym su=u) eq) (subst (λ k → u o< k) ? u<x) )
+                 ... | case2 lt = ZChain.supf-inject (pzc (pic<x (proj2 ia))) ?
+                 uz03 :  ZChain.supf (pzc (pic<x (proj2 ib))) u ≡ u
+                 uz03 =  trans (zeq _ _ ? ?) su=u
                  uz04 :  FClosure A f (ZChain.supf (pzc (pic<x (proj2 ib))) u) (& a)
                  uz04 = subst (λ k → FClosure A f k (& a)) ? fc
           ... | tri> ¬a ¬b ib<ia = uz01 where