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

comparison src/zorn.agda @ 942:d396af76c559

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sat, 29 Oct 2022 17:26:17 +0900
parents 6f342473f298
children df68bb333cd0
comparison
equal deleted inserted replaced
941:6f342473f298 942:d396af76c559
1473 z22 {a} ⟪ aa , ch-is-sup u u<x is-sup fc ⟫ = ? 1473 z22 {a} ⟪ aa , ch-is-sup u u<x is-sup fc ⟫ = ?
1474 -- u<x : ZChain.supf zc u o< ZChain.supf zc d 1474 -- u<x : ZChain.supf zc u o< ZChain.supf zc d
1475 -- supf u o< spuf c → order 1475 -- supf u o< spuf c → order
1476 1476
1477 not-hasprev : ¬ HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) d) d (cf nmx) 1477 not-hasprev : ¬ HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) d) d (cf nmx)
1478 not-hasprev hp = ⊥-elim (z29 spd ? hp) where 1478 not-hasprev hp = ⊥-elim (z29 {mc} {asc} spd hp) where
1479 -- z31 : odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx d)
1480 -- z31 = ?
1481 z29 : {mc : Ordinal } {asc : odef A (supf mc)} (spd : MinSUP A (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc )) 1479 z29 : {mc : Ordinal } {asc : odef A (supf mc)} (spd : MinSUP A (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc ))
1482 → odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx (MinSUP.sup spd))
1483 → HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) (MinSUP.sup spd)) (MinSUP.sup spd) (cf nmx) 1480 → HasPrev A (UnionCF A (cf nmx) (cf-is-≤-monotonic nmx) as0 (ZChain.supf zc) (MinSUP.sup spd)) (MinSUP.sup spd) (cf nmx)
1484 → ⊥ 1481 → ⊥
1485 z29 {mc} {asc} spd ufd hp = <-irr ? z30 where 1482 z29 {mc} {asc} spd hp = <-irr z26 z30 where
1486 y : Ordinal 1483 y : Ordinal
1487 y = HasPrev.y hp 1484 y = HasPrev.y hp
1488 d1 : Ordinal 1485 d1 : Ordinal
1489 d1 = MinSUP.sup spd -- supf d1 ≡ d 1486 d1 = MinSUP.sup spd -- supf d1 ≡ d
1490 z30 : * d1 < * (cf nmx d1) 1487 z30 : * d1 < * (cf nmx d1)
1491 z30 = ? 1488 z30 = proj1 (cf-is-<-monotonic nmx d1 (MinSUP.asm spd))
1489 z31 : odef (uchain (cf nmx) (cf-is-≤-monotonic nmx) asc) (cf nmx d1)
1490 z31 = ?
1492 z24 : y << d1 1491 z24 : y << d1
1493 z24 = subst (λ k → y << k) (sym (HasPrev.x=fy hp)) ( proj1 (cf-is-<-monotonic nmx y (proj1 (HasPrev.ay hp) ) )) 1492 z24 = subst (λ k → y << k) (sym (HasPrev.x=fy hp)) ( proj1 (cf-is-<-monotonic nmx y (proj1 (HasPrev.ay hp) ) ))
1494 -- z26 : (* (cf nmx (MinSUP.sup spd)) ≡ * (MinSUP.sup spd)) ∨ (* (cf nmx (MinSUP.sup spd)) < * (MinSUP.sup spd)) 1493 z26 : (* (cf nmx d1) ≡ * d1) ∨ (* (cf nmx d1) < * d1)
1495 -- z26 with MinSUP.x<sup spd ? 1494 z26 with MinSUP.x<sup spd z31
1496 -- ... | case1 eq = ? 1495 ... | case1 eq = case1 (cong (*) eq)
1497 -- ... | case2 lt = ? 1496 ... | case2 lt = case2 lt
1498 z25 : odef (ZChain.chain zc) (cf nmx d) 1497 z25 : odef (ZChain.chain zc) (cf nmx d)
1499 z25 = ZChain.f-next zc (subst (λ k → odef (ZChain.chain zc) k) (sym (HasPrev.x=fy hp)) 1498 z25 = ZChain.f-next zc (subst (λ k → odef (ZChain.chain zc) k) (sym (HasPrev.x=fy hp))
1500 (ZChain.f-next zc 1499 (ZChain.f-next zc
1501 (chain-mono (cf nmx) (cf-is-≤-monotonic nmx) as0 supf (ZChain.supf-mono zc) (o<→≤ d<A) ( HasPrev.ay hp )))) 1500 (chain-mono (cf nmx) (cf-is-≤-monotonic nmx) as0 supf (ZChain.supf-mono zc) (o<→≤ d<A) ( HasPrev.ay hp ))))
1502 1501