next =>
  split at cyz
  next => contradiction
  next =>
    cases Comparison.compare hzx y with
    | inl _ => contradiction
    | inr _ => contradiction
case isFalse
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
nxz : ¬x < z
hzx : z < x
h✝¹ : ¬x < y
nyx : ¬y < x
cxy : eq ≠ gt
h✝ : ¬y < z
cyz : (if z < y then gt else eq) ≠ gt
⊢ gt ≠ gt
no goals