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

comparison src/PFOD.agda @ 1096:55ab5de1ae02

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Fri, 23 Dec 2022 12:54:05 +0900
parents e787d37d27a0
children c2501d308c95
comparison
equal deleted inserted replaced
1095:08b6aa6870d9 1096:55ab5de1ae02
128 128
129 ω→2f≡i1 : (X i : HOD) → (iω : infinite ∋ i) → (lt : ω→2 ∋ X ) → ω→2f X lt (ω→nat i iω) ≡ i1 → X ∋ i 129 ω→2f≡i1 : (X i : HOD) → (iω : infinite ∋ i) → (lt : ω→2 ∋ X ) → ω→2f X lt (ω→nat i iω) ≡ i1 → X ∋ i
130 ω→2f≡i1 X i iω lt eq with ODC.∋-p O X (nat→ω (ω→nat i iω)) 130 ω→2f≡i1 X i iω lt eq with ODC.∋-p O X (nat→ω (ω→nat i iω))
131 ω→2f≡i1 X i iω lt eq | yes p = subst (λ k → X ∋ k ) (nat→ω-iso iω) p 131 ω→2f≡i1 X i iω lt eq | yes p = subst (λ k → X ∋ k ) (nat→ω-iso iω) p
132 132
133 open _⊆_
134
135 -- someday ... 133 -- someday ...
136 -- postulate 134 -- postulate
137 -- ω→2f-iso : (X : HOD) → ( lt : ω→2 ∋ X ) → fω→2 ( ω→2f X lt ) =h= X 135 -- ω→2f-iso : (X : HOD) → ( lt : ω→2 ∋ X ) → fω→2 ( ω→2f X lt ) =h= X
138 -- fω→2-iso : (f : Nat → Two) → ω→2f ( fω→2 f ) (ω2∋f f) ≡ f 136 -- fω→2-iso : (f : Nat → Two) → ω→2f ( fω→2 f ) (ω2∋f f) ≡ f
139 137