Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 77:75ba8cf64707
Power Set on going ...
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Sun, 02 Jun 2019 15:12:26 +0900 |
parents | 8e8f54e7a030 |
children | 9a7a64b2388c |
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--- a/zf.agda Sun Jun 02 11:56:43 2019 +0900 +++ b/zf.agda Sun Jun 02 15:12:26 2019 +0900 @@ -11,23 +11,15 @@ proj1 : A proj2 : B -open _∧_ - - data _∨_ {n m : Level} (A : Set n) ( B : Set m ) : Set (n ⊔ m) where case1 : A → A ∨ B case2 : B → A ∨ B --- open import Relation.Binary.PropositionalEquality - _⇔_ : {n : Level } → ( A B : Set n ) → Set n -_⇔_ A B = ( A → B ) ∧ ( B → A ) +_⇔_ A B = ( A → B ) ∧ ( B → A ) -open import Data.Empty open import Relation.Nullary - open import Relation.Binary -open import Relation.Binary.Core infixr 130 _∧_ infixr 140 _∨_ @@ -68,7 +60,7 @@ empty : ∀( x : ZFSet ) → ¬ ( ∅ ∋ x ) -- power : ∀ X ∃ A ∀ t ( t ∈ A ↔ t ⊆ X ) ) power→ : ∀( A t : ZFSet ) → Power A ∋ t → ∀ {x} → _⊆_ t A {x} - power← : ∀( A t : ZFSet ) → ∀ {x} → _⊆_ t A {x} → Power A ∋ t + power← : ∀( A t : ZFSet ) → ( ∀ {x} → _⊆_ t A {x}) → Power A ∋ t -- extensionality : ∀ z ( z ∈ x ⇔ z ∈ y ) ⇒ ∀ w ( x ∈ w ⇔ y ∈ w ) extensionality : { A B : ZFSet } → ( (z : ZFSet) → ( A ∋ z ) ⇔ (B ∋ z) ) → A ≈ B -- regularity : ∀ x ( x ≠ ∅ → ∃ y ∈ x ( y ∩ x = ∅ ) ) @@ -99,20 +91,3 @@ infinite : ZFSet isZF : IsZF ZFSet _∋_ _≈_ ∅ _,_ Union Power Select Replace infinite -module zf-exapmle {n m : Level } ( zf : ZF {m} {n} ) where - - _≈_ = ZF._≈_ zf - ZFSet = ZF.ZFSet zf - Select = ZF.Select zf - ∅ = ZF.∅ zf - _∩_ = ( IsZF._∩_ ) (ZF.isZF zf) - _∋_ = ZF._∋_ zf - replacement = IsZF.replacement ( ZF.isZF zf ) - selection = IsZF.selection ( ZF.isZF zf ) - minimul = IsZF.minimul ( ZF.isZF zf ) - regularity = IsZF.regularity ( ZF.isZF zf ) - --- russel : Select ( λ x → x ∋ x ) ≈ ∅ --- russel with Select ( λ x → x ∋ x ) --- ... | s = {!!} -