Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff zf.agda @ 130:3849614bef18
new replacement axiom
| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Tue, 02 Jul 2019 15:59:07 +0900 |
| parents | 0c2cbf37e002 |
| children | 327d49c2478b |
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--- a/zf.agda Tue Jul 02 09:28:26 2019 +0900 +++ b/zf.agda Tue Jul 02 15:59:07 2019 +0900 @@ -77,7 +77,10 @@ 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 ) -- 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 ) + repl-x : {ψ : ZFSet → ZFSet} → { X x : ZFSet } ( lt : x ∈ Replace X ψ ) → ZFSet + repl-x-∈ : {ψ : ZFSet → ZFSet} → { X x : ZFSet } → (lt : x ∈ Replace X ψ ) → repl-x lt ∈ X + 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 ) → x ≈ ψ ( repl-x lt ) -- -- ∀ z [ ∀ x ( x ∈ z → ¬ ( x ≈ ∅ ) ) ∧ ∀ x ∀ y ( x , y ∈ z ∧ ¬ ( x ≈ y ) → x ∩ y ≈ ∅ ) → ∃ u ∀ x ( x ∈ z → ∃ t ( u ∩ x) ≈ ｛ t ｝) ] -- axiom-of-choice : Set (suc n) -- axiom-of-choice = ?