Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff OD.agda @ 330:0faa7120e4b5
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Sun, 05 Jul 2020 15:49:00 +0900 |
parents | 72f3e3b44c27 |
children | daafa2213dd2 |
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--- a/OD.agda Sun Jul 05 12:32:09 2020 +0900 +++ b/OD.agda Sun Jul 05 15:49:00 2020 +0900 @@ -260,6 +260,15 @@ ε-induction-ord : (ox : Ordinal) { oy : Ordinal } → oy o< ox → ψ (ord→od oy) ε-induction-ord ox {oy} lt = TransFinite {λ oy → ψ (ord→od oy)} induction oy +ε-induction1 : { ψ : HOD → Set (suc n)} + → ( {x : HOD } → ({ y : HOD } → x ∋ y → ψ y ) → ψ x ) + → (x : HOD ) → ψ x +ε-induction1 {ψ} ind x = subst (λ k → ψ k ) oiso (ε-induction-ord (osuc (od→ord x)) <-osuc ) where + induction : (ox : Ordinal) → ((oy : Ordinal) → oy o< ox → ψ (ord→od oy)) → ψ (ord→od ox) + induction ox prev = ind ( λ {y} lt → subst (λ k → ψ k ) oiso (prev (od→ord y) (o<-subst (c<→o< lt) refl diso ))) + ε-induction-ord : (ox : Ordinal) { oy : Ordinal } → oy o< ox → ψ (ord→od oy) + ε-induction-ord ox {oy} lt = TransFinite1 {λ oy → ψ (ord→od oy)} induction oy + HOD→ZF : ZF HOD→ZF = record { ZFSet = HOD