conv =>
  rhs
  unfold mergeWith
  unfold mergeWith.loop
  rw [h_ind]
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)
y : Sigma β
ys : List (Sigma β)
h_ind :
  ∀ {xs_r : KVChain (flip r) β} {xs : KVChain r β} {hxs : hingeable xs_r xs}
    {hascend : List.Ascending (Sigma.relOnFst r) ys}
    {hxsys : List.predHead ((fun a => boundLeft a xs_r) ∘ Sigma.fst) ys},
    (mergeWith.loop f xs_r xs hxs ys hascend hxsys).toList =
      List.reverseAux xs_r.toList (mergeWith f xs { toList := ys, ascend := hascend }).toList
xs_r : KVChain (flip r) β
xs✝ : KVChain r β
hascend : List.Ascending (Sigma.relOnFst r) (y :: ys)
hyxs : List.predHead ((fun a => boundLeft a xs_r) ∘ Sigma.fst) (y :: ys)
a : α
b : β a
xs : KVChain r fun a => β a
haxs : boundLeft a xs
a✝ :
  ∀ (hxs : hingeable xs_r xs),
    (mergeWith.loop f xs_r xs hxs (y :: ys) hascend hyxs).toList =
      List.reverseAux xs_r.toList (mergeWith f xs { toList := y :: ys, ascend := hascend }).toList
hxs : hingeable xs_r (KVChain.cons a b xs haxs)
⊢ List.reverseAux
      (insertWithAux f KVChain.nil (KVChain.cons a b xs haxs) True.intro y.fst y.snd True.intro).val.fst.toList
      (mergeWith f (insertWithAux f KVChain.nil (KVChain.cons a b xs haxs) True.intro y.fst y.snd True.intro).val.snd
          { toList := ys, ascend := (_ : List.Ascending (Sigma.relOnFst r) ys) }).toList =
    (mergeWith f (KVChain.cons a b xs haxs) { toList := y :: ys, ascend := hascend }).toList
no goals