Mercurial > hg > Members > kono > Proof > ZF-in-agda
comparison 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 |
comparison
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53:d13a10a1723e | 54:33fb8228ace9 |
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74 minimul : (x : ZFSet ) → ¬ (x ≈ ∅) → ZFSet | 74 minimul : (x : ZFSet ) → ¬ (x ≈ ∅) → ZFSet |
75 regularity : ∀( x : ZFSet ) → (not : ¬ (x ≈ ∅)) → ( minimul x not ∈ x ∧ ( minimul x not ∩ x ≈ ∅ ) ) | 75 regularity : ∀( x : ZFSet ) → (not : ¬ (x ≈ ∅)) → ( minimul x not ∈ x ∧ ( minimul x not ∩ x ≈ ∅ ) ) |
76 -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) | 76 -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) |
77 infinity∅ : ∅ ∈ infinite | 77 infinity∅ : ∅ ∈ infinite |
78 infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ Select X ( λ y → x ≈ y )) ∈ infinite | 78 infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ Select X ( λ y → x ≈ y )) ∈ infinite |
79 selection : { ψ : ZFSet → Set m } → ∀ ( X y : ZFSet ) → ( y ∈ Select X ψ ) → ψ y | 79 selection : { ψ : ZFSet → Set m } → ∀ { X y : ZFSet } → ( ( y ∈ X ) ∧ ψ y ) ⇔ (y ∈ Select X ψ ) |
80 -- replacement : ∀ x ∀ y ∀ z ( ( ψ ( x , y ) ∧ ψ ( x , z ) ) → y = z ) → ∀ X ∃ A ∀ y ( y ∈ A ↔ ∃ x ∈ X ψ ( x , y ) ) | 80 -- replacement : ∀ x ∀ y ∀ z ( ( ψ ( x , y ) ∧ ψ ( x , z ) ) → y = z ) → ∀ X ∃ A ∀ y ( y ∈ A ↔ ∃ x ∈ X ψ ( x , y ) ) |
81 replacement : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → ( ψ x ∈ Replace X ψ ) | 81 replacement : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → ( ψ x ∈ Replace X ψ ) |
82 | 82 |
83 record ZF {n m : Level } : Set (suc (n ⊔ m)) where | 83 record ZF {n m : Level } : Set (suc (n ⊔ m)) where |
84 infixr 210 _,_ | 84 infixr 210 _,_ |