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

comparison src/zorn.agda @ 1061:fc37082d2a8a

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another IChain
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 11 Dec 2022 09:06:35 +0900
parents a09f5e728f92
children 88731edfa691
comparison
equal deleted inserted replaced
1060:a09f5e728f92 1061:fc37082d2a8a
279 UnionCF : ( A : HOD ) ( f : Ordinal → Ordinal ) {y : Ordinal } (ay : odef A y ) ( supf : Ordinal → Ordinal ) ( x : Ordinal ) → HOD 279 UnionCF : ( A : HOD ) ( f : Ordinal → Ordinal ) {y : Ordinal } (ay : odef A y ) ( supf : Ordinal → Ordinal ) ( x : Ordinal ) → HOD
280 UnionCF A f ay supf x 280 UnionCF A f ay supf x
281 = record { od = record { def = λ z → odef A z ∧ UChain {A} {f} {supf} ay x z } ; 281 = record { od = record { def = λ z → odef A z ∧ UChain {A} {f} {supf} ay x z } ;
282 odmax = & A ; <odmax = λ {y} sy → ∈∧P→o< sy } 282 odmax = & A ; <odmax = λ {y} sy → ∈∧P→o< sy }
283 283
284 -- Union of all UChain under limit ordinal x 284 -- Union of chain lower than x
285 285
286 data IChain { A : HOD } { f : Ordinal → Ordinal } (supfz : {z : Ordinal } → z o< x → Ordinal) {y : Ordinal } (ay : odef A y ) 286 record IChain (A : HOD) ( f : Ordinal → Ordinal ) {x : Ordinal } (supfz : {z : Ordinal } → z o< x → Ordinal) (z : Ordinal ) : Set n where
287 (x : Ordinal) : (z : Ordinal) → Set n where 287 field
288 ic-init : {z : Ordinal } (fc : FClosure A f y z) → IChain supf ay x z 288 i : Ordinal
289 ic-is-sup : (u : Ordinal) {z : Ordinal } (u<x : u o< x) (supu=u : supf u<x u ≡ u) ( fc : FClosure A f (supf u<x u) z ) → IChain supf ay x z 289 i<x : i o< x
290 s<x : supfz i<x o< x
291 fc : FClosure A f (supfz i<x) z
290 292
291 UnionIC : ( A : HOD ) ( f : Ordinal → Ordinal ) {y : Ordinal } (ay : odef A y ) (supfz : {z : Ordinal } → z o< x → Ordinal) ( x : Ordinal ) → HOD 293 UnionIC : ( A : HOD ) ( f : Ordinal → Ordinal ) {y : Ordinal } (ay : odef A y ) (supfz : {z : Ordinal } → z o< x → Ordinal) ( x : Ordinal ) → HOD
292 UnionIC A f ay supf x 294 UnionIC A f ay supf x
293 = record { od = record { def = λ z → odef A z ∧ IChain {A} {f} supf ay x z } ; 295 = record { od = record { def = λ z → odef A z ∧ IChain {A} {f} supf ay x z } ;
294 odmax = & A ; <odmax = λ {y} sy → ∈∧P→o< sy } 296 odmax = & A ; <odmax = λ {y} sy → ∈∧P→o< sy }