Defined: xor
⊤ ⊕ ⊥
⊥
⊤
  Assumed: a
a ⊕ a ⊕ a
Π (A : Type u) (a b : A) (P : A → Bool) (H1 : P a) (H2 : a = b), P b
  Proved: EM2
Π a : Bool, a ∨ ¬ a
a ∨ ¬ a