25 lines
499 B
Text
25 lines
499 B
Text
import logic
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abbreviation subsets (P : Type) := P → Prop.
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section
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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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notation `δ` := delta.
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-- Crashes unifier!
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theorem false_aux : ¬ (δ (i delta))
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:= assume H : δ (i delta),
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have H' : r (i delta) (i delta),
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from eq.rec H (symm retract),
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H H'.
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end
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