Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 65:164ad5a703d8
¬∅=→∅∈ : {n : Level} → { x : OD {suc n} } → ¬ ( x == od∅ {suc n} ) → x ∋ od∅ {suc n}
¬∅=→∅∈ {n} {x} ne = def-subst (lemma (od→ord x) (subst (λ k → ¬ (k == od∅ {suc n} )) (sym oiso) ne )) oiso refl where
lemma : (ox : Ordinal {suc n}) → ¬ (ord→od ox == od∅ {suc n} ) → ord→od ox ∋ od∅ {suc n}
lemma ox = TransFinite {suc n} {λ ox → ¬ (ord→od ox == od∅ {suc n} ) → ord→od ox ∋ od∅ {suc n} } { }0 { }1 { }2 ox
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Thu, 30 May 2019 01:02:47 +0900 |
| parents | 33fb8228ace9 |
| children | 93abc0133b8a |
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--- a/zf.agda Wed May 29 18:50:57 2019 +0900 +++ b/zf.agda Thu May 30 01:02:47 2019 +0900 @@ -68,8 +68,8 @@ -- 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 - -- extentionality : ∀ z ( z ∈ x ⇔ z ∈ y ) ⇒ ∀ w ( x ∈ w ⇔ y ∈ w ) - extentionality : ( A B z : ZFSet ) → (( A ∋ z ) ⇔ (B ∋ z) ) → A ≈ B + -- extensionality : ∀ z ( z ∈ x ⇔ z ∈ y ) ⇒ ∀ w ( x ∈ w ⇔ y ∈ w ) + extensionality : ( A B 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 ≈ ∅ ) )