next =>
  split at cxy
  next => contradiction
  next =>
    by_contradiction
    | assuming hne =>
      cases Connex.connex (r:=(.<.)) hne 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 : α
inst✝¹ : StableEq α
inst✝ : Connex fun x x_1 => x < x_1
h✝ : ¬x < y
cxy : (if y < x then gt else eq) = eq
⊢ x = y
no goals