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

comparison generic-filter.agda @ 410:6dcea4c7cba1

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Wed, 29 Jul 2020 12:42:05 +0900
parents 48ea49494fd1
children 6eaab908130e
comparison
equal deleted inserted replaced
409:3fba5f805e50 410:6dcea4c7cba1
137 ω2∋f : (f : Nat → Two) → ω→2 ∋ fω→2 f 137 ω2∋f : (f : Nat → Two) → ω→2 ∋ fω→2 f
138 ω2∋f f = power← infinite (fω→2 f) (λ {x} lt → proj1 ((proj2 (selection {fω→2-sel f} {infinite} )) lt)) 138 ω2∋f f = power← infinite (fω→2 f) (λ {x} lt → proj1 ((proj2 (selection {fω→2-sel f} {infinite} )) lt))
139 139
140 ω→2f≡i0 : (X i : HOD) → (iω : infinite ∋ i) → (lt : ω→2 ∋ X ) → ω→2f X lt (ω→nat i iω) ≡ i1 → X ∋ i 140 ω→2f≡i0 : (X i : HOD) → (iω : infinite ∋ i) → (lt : ω→2 ∋ X ) → ω→2f X lt (ω→nat i iω) ≡ i1 → X ∋ i
141 ω→2f≡i0 X i iω lt eq with ODC.∋-p O X (nat→ω (ω→nat i iω)) 141 ω→2f≡i0 X i iω lt eq with ODC.∋-p O X (nat→ω (ω→nat i iω))
142 ω→2f≡i0 X i iω lt eq | yes p = subst (λ k → X ∋ k ) {!!} p 142 ω→2f≡i0 X i iω lt eq | yes p = subst (λ k → X ∋ k ) (nat→ω-iso iω) p
143 143
144 ω→2f-iso : (X : HOD) → ( lt : ω→2 ∋ X ) → fω→2 ( ω→2f X lt ) =h= X 144 ω→2f-iso : (X : HOD) → ( lt : ω→2 ∋ X ) → fω→2 ( ω→2f X lt ) =h= X
145 ω→2f-iso X lt = record { 145 ω→2f-iso X lt = record {
146 eq→ = eq1 146 eq→ = eq1
147 ; eq← = eq2 147 ; eq← = eq2