apply trichot_cases (r:=LT.lt) (motive:=λ a b => ¬ a < b → a=b ∨ a > b)
α : Type u_1
inst✝ : LinearLT α
a b : α
⊢ ¬a < b → a = b ∨ a > b
case of_rfl
α : Type u_1
inst✝ : LinearLT α
a b : α
⊢ ∀ (a : α), ¬a < a → a = a ∨ a > a

case of_rel
α : Type u_1
inst✝ : LinearLT α
a b : α
⊢ ∀ (a b : α), a < b → ¬a < b → a = b ∨ a > b

case of_opp
α : Type u_1
inst✝ : LinearLT α
a b : α
⊢ ∀ (a b : α), b < a → ¬a < b → a = b ∨ a > b