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

comparison zf.agda @ 140:312e27aa3cb5

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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
comparison
equal deleted inserted replaced
139:53077af367e9 140:312e27aa3cb5
73 minimul : (x : ZFSet ) → ¬ (x ≈ ∅) → ZFSet 73 minimul : (x : ZFSet ) → ¬ (x ≈ ∅) → ZFSet
74 regularity : ∀( x : ZFSet ) → (not : ¬ (x ≈ ∅)) → ( minimul x not ∈ x ∧ ( minimul x not ∩ x ≈ ∅ ) ) 74 regularity : ∀( x : ZFSet ) → (not : ¬ (x ≈ ∅)) → ( minimul x not ∈ x ∧ ( minimul x not ∩ x ≈ ∅ ) )
75 -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) ) 75 -- infinity : ∃ A ( ∅ ∈ A ∧ ∀ x ∈ A ( x ∪ { x } ∈ A ) )
76 infinity∅ : ∅ ∈ infinite 76 infinity∅ : ∅ ∈ infinite
77 infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ ｛ x ｝) ∈ infinite 77 infinity : ∀( X x : ZFSet ) → x ∈ infinite → ( x ∪ ｛ x ｝) ∈ infinite
78 selection : ∀ { X : ZFSet } → { ψ : (x : ZFSet ) → Set m } → ∀ { y : ZFSet } → (((y : ZFSet) → y ∈ X → ψ y ) ∧ ( y ∈ X ) ) ⇔ (y ∈ Select X ψ ) 78 selection : { ψ : ZFSet → Set m } → ∀ { X y : ZFSet } → ( ( y ∈ X ) ∧ ψ y ) ⇔ (y ∈ Select X ψ )
79 -- replacement : ∀ x ∀ y ∀ z ( ( ψ ( x , y ) ∧ ψ ( x , z ) ) → y = z ) → ∀ X ∃ A ∀ y ( y ∈ A ↔ ∃ x ∈ X ψ ( x , y ) ) 79 -- replacement : ∀ x ∀ y ∀ z ( ( ψ ( x , y ) ∧ ψ ( x , z ) ) → y = z ) → ∀ X ∃ A ∀ y ( y ∈ A ↔ ∃ x ∈ X ψ ( x , y ) )
80 replacement← : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → x ∈ X → ψ x ∈ Replace X ψ 80 replacement← : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → x ∈ X → ψ x ∈ Replace X ψ
81 replacement→ : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → ( lt : x ∈ Replace X ψ ) → ¬ ( ∀ (y : ZFSet) → ¬ ( x ≈ ψ y ) ) 81 replacement→ : {ψ : ZFSet → ZFSet} → ∀ ( X x : ZFSet ) → ( lt : x ∈ Replace X ψ ) → ¬ ( ∀ (y : ZFSet) → ¬ ( x ≈ ψ y ) )
82 -- -- ∀ z [ ∀ x ( x ∈ z → ¬ ( x ≈ ∅ ) ) ∧ ∀ x ∀ y ( x , y ∈ z ∧ ¬ ( x ≈ y ) → x ∩ y ≈ ∅ ) → ∃ u ∀ x ( x ∈ z → ∃ t ( u ∩ x) ≈ ｛ t ｝) ] 82 -- -- ∀ z [ ∀ x ( x ∈ z → ¬ ( x ≈ ∅ ) ) ∧ ∀ x ∀ y ( x , y ∈ z ∧ ¬ ( x ≈ y ) → x ∩ y ≈ ∅ ) → ∃ u ∀ x ( x ∈ z → ∃ t ( u ∩ x) ≈ ｛ t ｝) ]
83 -- axiom-of-choice : Set (suc n) 83 -- axiom-of-choice : Set (suc n)