case a.cons =>
  intro a₁ b₁ xs ha₁xs _ haa₁
  dsimp [boundLeft, List.predHead] at haa₁
  rw [insertWithAux_cons_flip haa₁]
α : Type u
r : α → α → Prop
inst✝¹ : StrictLinearOrder r
inst✝ : DecidableRel r
β : α → Type v
f : (a : α) → β a → β a → Option (β a)
xs : KVChain r β
a : α
b : β a
ys : KVChain r β
hays : boundLeft a ys
⊢ ∀ (a_1 : α) (b_1 : β a_1) (xs : KVChain r fun a => β a) (haxs : boundLeft a_1 xs),
    (fun xs =>
          boundLeft a xs →
            (insertWithAux f KVChain.nil xs True.intro a b True.intro).val =
              ({ toList := [{ fst := a, snd := b }],
                  ascend := (_ : List.Ascending (Sigma.relOnFst (flip r)) [{ fst := a, snd := b }]) },
                xs))
        xs →
      (fun xs =>
          boundLeft a xs →
            (insertWithAux f KVChain.nil xs True.intro a b True.intro).val =
              ({ toList := [{ fst := a, snd := b }],
                  ascend := (_ : List.Ascending (Sigma.relOnFst (flip r)) [{ fst := a, snd := b }]) },
                xs))
        (KVChain.cons a_1 b_1 xs haxs)
no goals