Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 140:312e27aa3cb5
remove otrans again. start over
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Sun, 07 Jul 2019 23:02:47 +0900 |
| parents | 567084f2278f |
| children | 3675bd617ac8 |
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--- a/zf.agda Sun Jul 07 22:23:02 2019 +0900 +++ b/zf.agda Sun Jul 07 23:02:47 2019 +0900 @@ -75,7 +75,7 @@ -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) infinity∅ : ∅ ∈ infinite infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ ｛ x ｝) ∈ infinite - selection : ∀ { X : ZFSet } → { ψ : (x : ZFSet ) → Set m } → ∀ { y : ZFSet } → (((y : ZFSet) → y ∈ X → ψ y ) ∧ ( y ∈ X ) ) ⇔ (y ∈ Select X ψ ) + selection : { ψ : ZFSet → Set m } → ∀ { X y : ZFSet } → ( ( y ∈ X ) ∧ ψ y ) ⇔ (y ∈ Select X ψ ) -- 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 → ZFSet} → ∀ ( X x : ZFSet ) → x ∈ X → ψ x ∈ Replace X ψ replacement→ : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → ( lt : x ∈ Replace X ψ ) → ¬ ( ∀ (y : ZFSet) → ¬ ( x ≈ ψ y ) )