Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 23:7293a151d949
Sup
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Sat, 18 May 2019 08:29:08 +0900 |
| parents | 627a79e61116 |
| children | fce60b99dc55 |
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--- a/zf.agda Thu May 16 17:20:45 2019 +0900 +++ b/zf.agda Sat May 18 08:29:08 2019 +0900 @@ -2,6 +2,9 @@ open import Level +data Bool : Set where + true : Bool + false : Bool record _∧_ {n m : Level} (A : Set n) ( B : Set m ) : Set (n ⊔ m) where field @@ -60,8 +63,8 @@ union← : ( X x y : ZFSet ) → Union X ∋ y → X ∋ x → x ∋ y _∈_ : ( A B : ZFSet ) → Set m A ∈ B = B ∋ A - _⊆_ : ( A B : ZFSet ) → ∀{ x : ZFSet } → ∀{ A∋x : Set m } → Set m - _⊆_ A B {x} {A∋x} = B ∋ x + _⊆_ : ( A B : ZFSet ) → ∀{ x : ZFSet } → Set m + _⊆_ A B {x} = A ∋ x → B ∋ x _∩_ : ( A B : ZFSet ) → ZFSet A ∩ B = Select (A , B) ( λ x → ( A ∋ x ) ∧ ( B ∋ x ) ) _∪_ : ( A B : ZFSet ) → ZFSet @@ -72,8 +75,8 @@ field empty : ∀( x : ZFSet ) → ¬ ( ∅ ∋ x ) -- power : ∀ X ∃ A ∀ t ( t ∈ A ↔ t ⊆ X ) ) - power→ : ∀( A t : ZFSet ) → Power A ∋ t → ∀ {x} {y} → _⊆_ t A {x} {y} - power← : ∀( A t : ZFSet ) → ∀ {x} {y} → _⊆_ t A {x} {y} → Power A ∋ t + power→ : ∀( A t : ZFSet ) → Power A ∋ t → ∀ {x} → _⊆_ t A {x} + power← : ∀( A t : ZFSet ) → ∀ {x} → _⊆_ t A {x} → Power A ∋ t -- extentionality : ∀ z ( z ∈ x ⇔ z ∈ y ) ⇒ ∀ w ( x ∈ w ⇔ y ∈ w ) extentionality : ( A B z : ZFSet ) → (( A ∋ z ) ⇔ (B ∋ z) ) → A ≈ B -- regularity : ∀ x ( x ≠ ∅ → ∃ y ∈ x ( y ∩ x = ∅ ) )