Mercurial > hg > Members > kono > Proof > ZF-in-agda
comparison LEMC.agda @ 287:5de8905a5a2b
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Sun, 07 Jun 2020 20:29:12 +0900 |
parents | 313140ae5e3d |
children | 0faa7120e4b5 |
comparison
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286:4ae48eed654a | 287:5de8905a5a2b |
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29 field | 29 field |
30 a-choice : OD | 30 a-choice : OD |
31 is-in : X ∋ a-choice | 31 is-in : X ∋ a-choice |
32 | 32 |
33 open choiced | 33 open choiced |
34 | |
35 double-neg-eilm : {A : Set (suc n)} → ¬ ¬ A → A -- we don't have this in intutionistic logic | |
36 double-neg-eilm {A} notnot with p∨¬p A -- assuming axiom of choice | |
37 ... | case1 p = p | |
38 ... | case2 ¬p = ⊥-elim ( notnot ¬p ) | |
39 | |
40 | 34 |
41 OD→ZFC : ZFC | 35 OD→ZFC : ZFC |
42 OD→ZFC = record { | 36 OD→ZFC = record { |
43 ZFSet = OD | 37 ZFSet = OD |
44 ; _∋_ = _∋_ | 38 ; _∋_ = _∋_ |