### changeset 307:d5c5d87b72df

...
author Shinji KONO Mon, 29 Jun 2020 23:09:14 +0900 b07fc3ef5aab b172ab9f12bc OD.agda 1 files changed, 5 insertions(+), 5 deletions(-) [+]
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```--- a/OD.agda	Mon Jun 29 20:33:19 2020 +0900
+++ b/OD.agda	Mon Jun 29 23:09:14 2020 +0900
@@ -226,7 +226,7 @@
ZFSubset A x =  record { od = record { def = λ y → odef A y ∧  odef x y } ; odmax = {!!} ; <odmax = {!!} }  --   roughly x = A → Set

OPwr :  (A :  HOD ) → HOD
-OPwr  A = Ord ( sup-o {!!} {!!} ) --  ( λ x → od→ord ( ZFSubset A x) ) )
+OPwr  A = Ord ( sup-o A {!!} ) --  ( λ x → od→ord ( ZFSubset A x) ) )

-- _⊆_ :  ( A B : HOD   ) → ∀{ x : HOD  } →  Set n
-- _⊆_ A B {x} = A ∋ x →  B ∋ x
@@ -277,7 +277,7 @@
Select : (X : HOD  ) → ((x : HOD  ) → Set n ) → HOD
Select X ψ = record { od = record { def = λ x →  ( odef X x ∧ ψ ( ord→od x )) } ; odmax = {!!} ; <odmax = {!!} }
Replace : HOD  → (HOD  → HOD  ) → HOD
-    Replace X ψ = record { od = record { def = λ x → (x o< sup-o  {!!} {!!} ) ∧ odef (in-codomain X ψ) x } ; odmax = {!!} ; <odmax = {!!} } -- ( λ x → od→ord (ψ x))
+    Replace X ψ = record { od = record { def = λ x → (x o< sup-o X {!!} ) ∧ odef (in-codomain X ψ) x } ; odmax = {!!} ; <odmax = {!!} } -- ( λ x → od→ord (ψ x))
_∩_ : ( A B : ZFSet  ) → ZFSet
A ∩ B = record { od = record { def = λ x → odef A x ∧ odef B x }  ; odmax = {!!} ; <odmax = {!!} }
Union : HOD  → HOD
@@ -403,7 +403,7 @@
lemma1 :  {a : Ordinal } { t : HOD }
→ (eq : ZFSubset (Ord a) t =h= t)  → od→ord (ZFSubset (Ord a) (ord→od (od→ord t))) ≡ od→ord t
lemma1  {a} {t} eq = subst (λ k → od→ord (ZFSubset (Ord a) k) ≡ od→ord t ) (sym oiso) (cong (λ k → od→ord k ) (==→o≡ eq ))
-              lemma :  od→ord (ZFSubset (Ord a) (ord→od (od→ord t)) ) o< sup-o {!!} {!!} --  (λ x → od→ord (ZFSubset (Ord a) x))
+              lemma :  od→ord (ZFSubset (Ord a) (ord→od (od→ord t)) ) o< sup-o (Ord a) {!!} --  (λ x → od→ord (ZFSubset (Ord a) x))
lemma = {!!} -- sup-o<

--
@@ -441,8 +441,8 @@
≡⟨ sym (==→o≡ ( ∩-≡ t→A )) ⟩
t
∎
-              lemma1 : od→ord t o< sup-o  {!!} {!!} -- (λ x → od→ord (A ∩ x))
-              lemma1 = subst (λ k → od→ord k o< sup-o  {!!} {!!}) --  (λ x → od→ord (A ∩ x)))
+              lemma1 : od→ord t o< sup-o (OPwr (Ord (od→ord A))) {!!} -- (λ x → od→ord (A ∩ x))
+              lemma1 = subst (λ k → od→ord k o< sup-o (OPwr (Ord (od→ord A)))  {!!}) --  (λ x → od→ord (A ∩ x)))
lemma4 {!!} -- (sup-o<  {λ x → od→ord (A ∩ x)}  )
lemma2 :  odef (in-codomain (OPwr (Ord (od→ord A))) (_∩_ A)) (od→ord t)
lemma2 not = ⊥-elim ( not (od→ord t) (record { proj1 = lemma3 ; proj2 = lemma6 }) ) where```