Mercurial > hg > Members > kono > Proof > ZF-in-agda
changeset 8:cb014a103467
fix
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Sun, 12 May 2019 11:08:17 +0900 |
| parents | 813f1b3b000b |
| children | 5ed16e2d8eb7 |
| files | zf.agda |
| diffstat | 1 files changed, 10 insertions(+), 9 deletions(-) [+] |
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--- a/zf.agda Sat May 11 19:14:16 2019 +0900 +++ b/zf.agda Sun May 12 11:08:17 2019 +0900 @@ -62,21 +62,21 @@ 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} {y} → _⊆_ t A {x} {y} + power← : ∀( A t : ZFSet ) → ∀ {x} {y} → _⊆_ t A {x} {y} → 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 = ∅ ) ) smaller : ZFSet → ZFSet - regularity : ( x : ZFSet ) → ¬ (x ≈ ∅) → smaller x ∩ x ≈ ∅ + regularity : ∀( x : ZFSet ) → ¬ (x ≈ ∅) → ( smaller x ∈ x ∧ ( smaller x ∩ x ≈ ∅ ) ) -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) infinity∅ : ∅ ∈ infinite - infinity : ( x : ZFSet ) → x ∈ infinite → ( x ∪ Restrict ( λ y → x ≈ y )) ∈ infinite + infinity : ∀( x : ZFSet ) → x ∈ infinite → ( x ∪ Restrict ( λ y → x ≈ y )) ∈ infinite -- replacement : ∀ x ∀ y ∀ z ( ( ψ ( x , y ) ∧ ψ ( x , z ) ) → y = z ) → ∀ X ∃ A ∀ y ( y ∈ A ↔ ∃ x ∈ X ψ ( x , y ) ) - replacement : ( ψ : ZFSet → Set m ) → ( y : ZFSet ) → y ∈ Restrict ψ → ψ y + -- this form looks like specification + replacement : ( ψ : ZFSet → Set m ) → ( x : ZFSet ) → x ∈ Restrict ψ → ψ x record ZF {n m : Level } : Set (suc (n ⊔ m)) where - coinductive infixr 210 _×_ infixl 200 _∋_ infixr 220 _≈_ @@ -126,9 +126,10 @@ open import Relation.Binary.PropositionalEquality --- data Transtive {n : Level } ( lv : Nat) : Set n where --- Φ : lv ≡ Zero → Transtive lv --- pair : (s : Transtive (prev lv) ) → (t : Transtive (prev lv) ) → Transtive lv +data Transtive {n : Level } : ( lv : Nat) → Set n where + Φ : {lv : Nat} → lv ≡ Zero → Transtive lv + T-suc : {lv : Nat} → lv ≡ Zero → Transtive {n} lv → Transtive lv + ℵ : {lv : Nat} → Transtive {n} lv → Transtive (Suc lv)