Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 76:8e8f54e7a030
extensionality done
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Sun, 02 Jun 2019 11:56:43 +0900 |
| parents | dd430a95610f |
| children | 75ba8cf64707 |
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--- a/zf.agda Sun Jun 02 10:53:52 2019 +0900 +++ b/zf.agda Sun Jun 02 11:56:43 2019 +0900 @@ -70,7 +70,7 @@ power→ : ∀( A t : ZFSet ) → Power A ∋ t → ∀ {x} → _⊆_ t A {x} 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 z : ZFSet } → (( A ∋ z ) ⇔ (B ∋ z) ) → A ≈ B + extensionality : { A B : ZFSet } → ( (z : ZFSet) → ( A ∋ z ) ⇔ (B ∋ z) ) → A ≈ B -- regularity : ∀ x ( x ≠ ∅ → ∃ y ∈ x ( y ∩ x = ∅ ) ) minimul : (x : ZFSet ) → ¬ (x ≈ ∅) → ZFSet regularity : ∀( x : ZFSet ) → (not : ¬ (x ≈ ∅)) → ( minimul x not ∈ x ∧ ( minimul x not ∩ x ≈ ∅ ) )