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>
date Sun, 07 Jun 2020 20:29:12 +0900
parents 313140ae5e3d
children 0faa7120e4b5
comparison
equal deleted inserted replaced
286:4ae48eed654a 287:5de8905a5a2b
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 ; _∋_ = _∋_