20 lines
366 B
Text
20 lines
366 B
Text
import logic
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open bool
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namespace set
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definition set (T : Type) := T → bool
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definition mem {T : Type} (a : T) (s : set T) := s a = tt
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infix `∈`:50 := mem
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section
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variable {T : Type}
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definition empty : set T := λx, ff
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notation `∅` := empty
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theorem mem_empty (x : T) : ¬ (x ∈ ∅)
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:= not_intro (λH : x ∈ ∅, absurd H ff_ne_tt)
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end
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end set
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