--- a/BAlgbra.agda	Mon Jul 20 16:22:44 2020 +0900
+++ b/BAlgbra.agda	Mon Jul 20 16:28:12 2020 +0900
@@ -1,4 +1,3 @@
-{-# OPTIONS --allow-unsolved-metas #-}
 open import Level
 open import Ordinals
 module BAlgbra {n : Level } (O : Ordinals {n})   where
@@ -56,13 +55,13 @@
     lemma2 {x} (case2 B∋x) = subst (λ k → odef (Union (A , B)) k) diso ( IsZF.union→ isZF (A , B) (ord→od x) B
        (record { proj1 = case2 refl ; proj2 = subst (λ k → odef B k) (sym diso) B∋x}))
 
-∩-Select : { A B : HOD } →  Select A (  λ x _ → ( A ∋ x ) ∧ ( B ∋ x )  ) ≡ ( A ∩ B )
+∩-Select : { A B : HOD } →  Select A (  λ x → ( A ∋ x ) ∧ ( B ∋ x )  ) ≡ ( A ∩ B )
 ∩-Select {A} {B} = ==→o≡ ( record { eq→ =  lemma1 ; eq← = lemma2 } ) where
-    lemma1 : {x : Ordinal} → odef (Select A (λ x₁ _ → (A ∋ x₁) ∧ (B ∋ x₁))) x → odef (A ∩ B) x
-    lemma1 {x} lt = record { proj1 = proj1 {!!} ; proj2 = subst (λ k → odef B k ) diso (proj2 (proj2 {!!} )) }
-    lemma2 : {x : Ordinal} → odef (A ∩ B) x → odef (Select A (λ x₁ _ → (A ∋ x₁) ∧ (B ∋ x₁))) x
-    lemma2 {x} lt = {!!} -- record { proj1 = proj1 lt ; proj2 =
-        -- record { proj1 = subst (λ k → odef A k) (sym diso) (proj1 lt) ; proj2 = subst (λ k → odef B k ) (sym diso) (proj2 lt) } }
+    lemma1 : {x : Ordinal} → odef (Select A (λ x₁ → (A ∋ x₁) ∧ (B ∋ x₁))) x → odef (A ∩ B) x
+    lemma1 {x} lt = record { proj1 = proj1 lt ; proj2 = subst (λ k → odef B k ) diso (proj2 (proj2 lt)) }
+    lemma2 : {x : Ordinal} → odef (A ∩ B) x → odef (Select A (λ x₁ → (A ∋ x₁) ∧ (B ∋ x₁))) x
+    lemma2 {x} lt = record { proj1 = proj1 lt ; proj2 =
+        record { proj1 = subst (λ k → odef A k) (sym diso) (proj1 lt) ; proj2 = subst (λ k → odef B k ) (sym diso) (proj2 lt) } }
 
 dist-ord : {p q r : HOD } → p ∩ ( q ∪ r ) ≡   ( p ∩ q ) ∪ ( p ∩ r )
 dist-ord {p} {q} {r} = ==→o≡ ( record { eq→ = lemma1 ; eq← = lemma2 } ) where