Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff OD.agda @ 341:27d2933c4bd7
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Mon, 13 Jul 2020 13:29:38 +0900 |
parents | 639fbb6284d8 |
children | b1ccdbb14c92 |
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--- a/OD.agda Mon Jul 13 09:26:34 2020 +0900 +++ b/OD.agda Mon Jul 13 13:29:38 2020 +0900 @@ -393,16 +393,22 @@ lemma6 = <odmax (ord→od y , (ord→od y , ord→od y)) (subst ( λ k → def (od (ord→od y , (ord→od y , ord→od y))) k ) diso (case1 refl)) lemma8 : od→ord (ord→od y , ord→od y) o< next (odmax (ord→od y , ord→od y)) lemma8 = ho< + lemmab : {x : HOD} → od→ord (x , x) o< next (od→ord x) + lemmab {x} = subst (λ k → od→ord (x , x) o< k ) lemmab0 lemmab1 where + lemmab0 : next (odmax (x , x)) ≡ next (od→ord x) + lemmab0 = {!!} + lemmab1 : od→ord (x , x) o< next ( odmax (x , x)) + lemmab1 = ho< + lemmac : {x y : HOD} → od→ord x o< od→ord y → od→ord (x , y) o< od→ord (y , y) + lemmac = {!!} + lemmaa : {x y : HOD} → od→ord x o< od→ord y → od→ord (x , y) o< next (od→ord y) + lemmaa x<y = ordtrans (lemmac x<y) lemmab lemma81 : od→ord (ord→od y , ord→od y) o< next (od→ord (ord→od y)) lemma81 = nexto=n (subst (λ k → od→ord (ord→od y , ord→od y) o< k ) (cong (λ k → next k) (omxx _)) lemma8) - lemma7 : od→ord (ord→od y , (ord→od y , ord→od y)) o< next (odmax (ord→od y , (ord→od y , ord→od y))) lemma91 : od→ord (ord→od y) o< od→ord (ord→od y , ord→od y) lemma91 = c<→o< (case1 refl) - lemma92 : od→ord (ord→od y , (ord→od y , ord→od y)) o< next y - lemma92 = {!!} lemma9 : od→ord (ord→od y , (ord→od y , ord→od y)) o< next (od→ord (ord→od y , ord→od y)) - lemma9 = next< {!!} lemma92 - lemma7 = ho< + lemma9 = lemmaa {!!} lemma71 : od→ord (ord→od y , (ord→od y , ord→od y)) o< next (od→ord (ord→od y)) lemma71 = next< lemma81 lemma9 lemma1 : od→ord (u y) o< next (osuc (od→ord (ord→od y , (ord→od y , ord→od y))))