intros
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)
ys : KVChain r β
a : α
b : β a
⊢ ∀ (xs : KVChain (flip r) fun a => β a) (hxsys : hingeable xs KVChain.nil) (haxs : boundLeft a xs),
    (insertWithAux f xs KVChain.nil hxsys a b haxs).val.snd =
      (insertWithAux f KVChain.nil KVChain.nil True.intro a b True.intro).val.snd
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)
ys : KVChain r β
a : α
b : β a
xs✝ : KVChain (flip r) fun a => β a
hxsys✝ : hingeable xs✝ KVChain.nil
haxs✝ : boundLeft a xs✝
⊢ (insertWithAux f xs✝ KVChain.nil hxsys✝ a b haxs✝).val.snd =
    (insertWithAux f KVChain.nil KVChain.nil True.intro a b True.intro).val.snd