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

comparison src/Tychonoff.agda @ 1202:d6781ad8149e

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author kono
date Thu, 02 Mar 2023 12:42:22 +0800
parents 03684784bc5f
children 2f09ce1dd2a1
comparison
equal deleted inserted replaced
1201:03684784bc5f 1202:d6781ad8149e
91 N : {X : Ordinal} → (CSX : * X ⊆ CS TP) → fip CSX → HOD 91 N : {X : Ordinal} → (CSX : * X ⊆ CS TP) → fip CSX → HOD
92 N {X} CSX fp = record { od = record { def = λ u → FBase P X u } ; odmax = osuc (& P) 92 N {X} CSX fp = record { od = record { def = λ u → FBase P X u } ; odmax = osuc (& P)
93 ; <odmax = λ {x} lt → subst₂ (λ j k → j o< osuc k) &iso refl (⊆→o≤ (FBase.u⊆P lt)) } 93 ; <odmax = λ {x} lt → subst₂ (λ j k → j o< osuc k) &iso refl (⊆→o≤ (FBase.u⊆P lt)) }
94 N⊆PP : {X : Ordinal } → (CSX : * X ⊆ CS TP) → (fp : fip CSX) → N CSX fp ⊆ Power P 94 N⊆PP : {X : Ordinal } → (CSX : * X ⊆ CS TP) → (fp : fip CSX) → N CSX fp ⊆ Power P
95 N⊆PP CSX fp nx b xb = FBase.u⊆P nx xb 95 N⊆PP CSX fp nx b xb = FBase.u⊆P nx xb
96 -- filter base is not empty
96 nc : {X : Ordinal} → (CSX : * X ⊆ CS TP) → (fip : fip CSX) → HOD 97 nc : {X : Ordinal} → (CSX : * X ⊆ CS TP) → (fip : fip CSX) → HOD
97 nc {X} CSX fip with trio< o∅ X 98 nc {X} CSX fip with trio< o∅ X
98 ... | tri< 0<X ¬b ¬c = ODC.minimal O (* (& e)) (0<P→ne (subst (λ k → o∅ o< k) (sym &iso) (fip (gi Xe))) ) where 99 ... | tri< 0<X ¬b ¬c = ODC.minimal O (* (& e)) (0<P→ne (subst (λ k → o∅ o< k) (sym &iso) (fip (gi Xe))) ) where
99 e : HOD -- we have an element of X 100 e : HOD -- we have an element of X
100 e = ODC.minimal O (* X) (0<P→ne (subst (λ k → o∅ o< k) (sym &iso) 0<X) ) 101 e = ODC.minimal O (* X) (0<P→ne (subst (λ k → o∅ o< k) (sym &iso) 0<X) )