lean2/tests/lean/run/set2.lean

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