Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff LEMC.agda @ 331:12071f79f3cf
HOD done
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Sun, 05 Jul 2020 16:56:21 +0900 |
parents | 0faa7120e4b5 |
children | 2a8a51375e49 |
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--- a/LEMC.agda Sun Jul 05 15:49:00 2020 +0900 +++ b/LEMC.agda Sun Jul 05 16:56:21 2020 +0900 @@ -112,7 +112,7 @@ lemma : {y : Ordinal} → OD.def (od x) y ∧ OD.def (od u) y → y o< omin (odmax x) (odmax u) lemma {y} lt = min1 (<odmax x (proj1 lt)) (<odmax u (proj2 lt)) np : ¬ (p =h= od∅) - np p∅ = NP (λ y p∋y → ∅< p∋y p∅ ) + np p∅ = NP (λ y p∋y → ∅< {p} {_} p∋y p∅ ) y1choice : choiced p y1choice = choice-func p np y1 : HOD @@ -126,9 +126,9 @@ cx : {x : HOD} → ¬ (x =h= od∅ ) → choiced x cx {x} nx = choice-func x nx minimal : (x : HOD ) → ¬ (x =h= od∅ ) → HOD - minimal x not = min (Min2 (a-choice (cx not) ) x (is-in (cx not))) + minimal x ne = min (Min2 (a-choice (cx {x} ne) ) x (is-in (cx ne))) x∋minimal : (x : HOD ) → ( ne : ¬ (x =h= od∅ ) ) → odef x ( od→ord ( minimal x ne ) ) - x∋minimal x ne = x∋min (Min2 (a-choice (cx ne) ) x (is-in (cx ne))) + x∋minimal x ne = x∋min (Min2 (a-choice (cx {x} ne) ) x (is-in (cx ne))) minimal-1 : (x : HOD ) → ( ne : ¬ (x =h= od∅ ) ) → (y : HOD ) → ¬ ( odef (minimal x ne) (od→ord y)) ∧ (odef x (od→ord y) ) minimal-1 x ne y = min-empty (Min2 (a-choice (cx ne) ) x (is-in (cx ne))) y