have notTwo : ¬ AA.TwoOfThree (lt n m) (n ≃ m) (lt m n) :=
  (trichotomy (order_inst := order) n m).atMostOne
n m : Nat
x✝ : lt m n
⊢ compare n m = Ordering.gt
n m : Nat
x✝ : lt m n
notTwo : ¬AA.TwoOfThree (lt n m) (n ≃ m) (lt m n)
⊢ compare n m = Ordering.gt