intro
α : Type u_1
inst : LT α
inst✝² : DecidableRel fun x x_1 => x < x_1
x y z : α
inst✝¹ : Transitive fun x x_1 => x < x_1
inst✝ : Comparison fun x x_1 => x < x_1
cxy : (if x < y then lt else if y < x then gt else eq) ≠ gt
cyz : (if y < z then lt else if z < y then gt else eq) ≠ gt
h✝ : x < z
⊢ lt ≠ gt
α : Type u_1
inst : LT α
inst✝² : DecidableRel fun x x_1 => x < x_1
x y z : α
inst✝¹ : Transitive fun x x_1 => x < x_1
inst✝ : Comparison fun x x_1 => x < x_1
cxy : (if x < y then lt else if y < x then gt else eq) ≠ gt
cyz : (if y < z then lt else if z < y then gt else eq) ≠ gt
h✝ : x < z
a✝ : lt = gt
⊢ False