intro
| AA.TwoOfThree.oneAndTwo (_ : n < m) (_ : n ≃ m) =>
  show False
  have ⟨_, (_ : n ≄ m)⟩ := lt_defn.mp ‹n < m›
  exact absurd ‹n ≃ m› ‹n ≄ m›
| AA.TwoOfThree.oneAndThree (_ : n < m) (_ : n > m) =>
  show False
  have ⟨(_ : n ≤ m), (_ : n ≄ m)⟩ := lt_defn.mp ‹n < m›
  have ⟨(_ : m ≤ n), _⟩ := lt_defn.mp ‹n > m›
  have : n ≃ m := le_antisymm ‹n ≤ m› ‹m ≤ n›
  exact absurd ‹n ≃ m› ‹n ≄ m›
| AA.TwoOfThree.twoAndThree (_ : n ≃ m) (_ : n > m) =>
  show False
  have ⟨_, (_ : m ≄ n)⟩ := lt_defn.mp ‹n > m›
  exact absurd ‹n ≃ m› (Rel.symm ‹m ≄ n›)
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
⊢ ¬AA.TwoOfThree (n < m) (n ≃ m) (n > m)
no goals