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✝¹ : ¬x < y
h✝ : ¬y < x
cxy : eq = eq
⊢ x = y
no goals