Mercurial > hg > Members > kono > Proof > ZF-in-agda

comparison zf.agda @ 54:33fb8228ace9

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fix selection axiom
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 27 May 2019 21:58:17 +0900
parents 83b13f1f4f42
children 164ad5a703d8
comparison
equal deleted inserted replaced
53:d13a10a1723e 54:33fb8228ace9
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 _,_