Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 54:33fb8228ace9
fix selection axiom
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Mon, 27 May 2019 21:58:17 +0900 |
parents | 83b13f1f4f42 |
children | 164ad5a703d8 |
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--- a/zf.agda Mon May 27 16:14:35 2019 +0900 +++ b/zf.agda Mon May 27 21:58:17 2019 +0900 @@ -76,7 +76,7 @@ -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) infinity∅ : ∅ ∈ infinite infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ Select X ( λ y → x ≈ y )) ∈ infinite - selection : { ψ : ZFSet → Set m } → ∀ ( X y : ZFSet ) → ( y ∈ Select X ψ ) → ψ y + 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 ) → ( ψ x ∈ Replace X ψ )