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

comparison src/zorn.agda @ 1101:7ce2cc622c92

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Wed, 28 Dec 2022 18:14:29 +0900
parents 40345abc0949
children d122d0c1b094
comparison
equal deleted inserted replaced
1100:c90eec304cfa 1101:7ce2cc622c92
1107 1107
1108 ... | no lim with trio< x o∅ 1108 ... | no lim with trio< x o∅
1109 ... | tri< a ¬b ¬c = ⊥-elim ( ¬x<0 a ) 1109 ... | tri< a ¬b ¬c = ⊥-elim ( ¬x<0 a )
1110 ... | tri≈ ¬a x=0 ¬c = record { supf = λ _ → MinSUP.sup (ysup f mf ay) ; asupf = MinSUP.as (ysup f mf ay) ; supf-mono = λ _ → o≤-refl 1110 ... | tri≈ ¬a x=0 ¬c = record { supf = λ _ → MinSUP.sup (ysup f mf ay) ; asupf = MinSUP.as (ysup f mf ay) ; supf-mono = λ _ → o≤-refl
1111 ; zo≤sz = zo≤sz ; is-minsup = is-minsup ; cfcs = λ a<b b≤0 → ⊥-elim ( ¬x<0 (subst (λ k → _ o< k ) x=0 (ordtrans<-≤ a<b b≤0))) } where 1111 ; zo≤sz = zo≤sz ; is-minsup = is-minsup ; cfcs = λ a<b b≤0 → ⊥-elim ( ¬x<0 (subst (λ k → _ o< k ) x=0 (ordtrans<-≤ a<b b≤0))) } where
1112 -- initial case
1112 1113
1113 mf : ≤-monotonic-f A f 1114 mf : ≤-monotonic-f A f
1114 mf x ax = ⟪ case2 mf00 , proj2 (mf< x ax ) ⟫ where 1115 mf x ax = ⟪ case2 mf00 , proj2 (mf< x ax ) ⟫ where
1115 mf00 : * x < * (f x) 1116 mf00 : * x < * (f x)
1116 mf00 = proj1 ( mf< x ax ) 1117 mf00 = proj1 ( mf< x ax )