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

comparison OD.agda @ 235:846e0926bb89

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fix cardinal
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Thu, 15 Aug 2019 04:51:24 +0900
parents e06b76e5b682
children d09437fcfc7c
comparison
equal deleted inserted replaced
234:e06b76e5b682 235:846e0926bb89
488 choice-func' : (X : OD ) → (p∨¬p : ( p : Set (suc n)) → p ∨ ( ¬ p )) → ¬ ( X == od∅ ) → choiced X 488 choice-func' : (X : OD ) → (p∨¬p : ( p : Set (suc n)) → p ∨ ( ¬ p )) → ¬ ( X == od∅ ) → choiced X
489 choice-func' X p∨¬p not = have_to_find where 489 choice-func' X p∨¬p not = have_to_find where
490 ψ : ( ox : Ordinal ) → Set (suc n) 490 ψ : ( ox : Ordinal ) → Set (suc n)
491 ψ ox = (( x : Ordinal ) → x o< ox → ( ¬ def X x )) ∨ choiced X 491 ψ ox = (( x : Ordinal ) → x o< ox → ( ¬ def X x )) ∨ choiced X
492 lemma-ord : ( ox : Ordinal ) → ψ ox 492 lemma-ord : ( ox : Ordinal ) → ψ ox
493 lemma-ord ox = IsOrdinals.TransFinite (Ordinals.isOrdinal O) {ψ} induction ox where 493 lemma-ord ox = TransFinite {ψ} induction ox where
494 ∋-p : (A x : OD ) → Dec ( A ∋ x ) 494 ∋-p : (A x : OD ) → Dec ( A ∋ x )
495 ∋-p A x with p∨¬p (Lift (suc n) ( A ∋ x )) 495 ∋-p A x with p∨¬p (Lift (suc n) ( A ∋ x ))
496 ∋-p A x | case1 (lift t) = yes t 496 ∋-p A x | case1 (lift t) = yes t
497 ∋-p A x | case2 t = no (λ x → t (lift x )) 497 ∋-p A x | case2 t = no (λ x → t (lift x ))
498 ∀-imply-or : {A : Ordinal → Set n } {B : Set (suc n) } 498 ∀-imply-or : {A : Ordinal → Set n } {B : Set (suc n) }
528 Union = ZF.Union OD→ZF 528 Union = ZF.Union OD→ZF
529 Power = ZF.Power OD→ZF 529 Power = ZF.Power OD→ZF
530 Select = ZF.Select OD→ZF 530 Select = ZF.Select OD→ZF
531 Replace = ZF.Replace OD→ZF 531 Replace = ZF.Replace OD→ZF
532 isZF = ZF.isZF OD→ZF 532 isZF = ZF.isZF OD→ZF
533 TransFinite = IsOrdinals.TransFinite (Ordinals.isOrdinal O)