2014-07-27 19:17:38 +00:00
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import logic
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2014-09-05 01:41:06 +00:00
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open eq
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2014-09-17 21:39:05 +00:00
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definition subsets (P : Type) := P → Prop.
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2014-07-27 19:17:38 +00:00
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2015-04-22 02:33:21 +00:00
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section
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2014-07-27 19:17:38 +00:00
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hypothesis A : Type.
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hypothesis r : A → subsets A.
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hypothesis i : subsets A → A.
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hypothesis retract {P : subsets A} {a : A} : r (i P) a = P a.
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definition delta (a:A) : Prop := ¬ (r a a).
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2015-04-22 02:33:21 +00:00
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local notation `δ` := delta.
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2014-07-27 19:17:38 +00:00
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theorem delta_aux : ¬ (δ (i delta))
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:= assume H : δ (i delta),
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H (subst (symm retract) H).
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2014-08-08 00:08:59 +00:00
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check delta_aux.
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2014-09-05 01:41:06 +00:00
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end
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