lean2/tests/lean/tst11.lean

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definition xor (x y : Bool) : Bool := (not x) = y
infixr 50 ⊕ : xor
print xor true false
eval xor true true
eval xor true false
variable a : Bool
print a ⊕ a ⊕ a
check @subst
theorem EM2 (a : Bool) : a \/ (not a) :=
case (fun x : Bool, x \/ (not x)) trivial trivial a
check EM2
check EM2 a