revert hxs
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
hxs : hingeable xs_r xs
hascend : List.Ascending (Sigma.relOnFst r) (y :: ys)
hyxs : List.predHead ((fun a => boundLeft a xs_r) ∘ Sigma.fst) (y :: ys)
⊢ (match xs.toList with
      | [] =>
        hinge xs_r { toList := y :: ys, ascend := (_ : List.Ascending (Sigma.relOnFst r) (y :: ys)) }
          (_ : hingeable xs_r { toList := y :: ys, ascend := (_ : List.Ascending (Sigma.relOnFst r) (y :: ys)) })
      | head :: tail =>
        match hmatch : insertWithAux f xs_r xs hxs y.fst y.snd hyxs with
        | { val := (xs_r', xs'), property := h } =>
          mergeWith.loop f xs_r' xs' h ys (_ : List.Ascending (Sigma.relOnFst r) ys)
            (_ : List.predHead ((fun a => boundLeft a xs_r') ∘ Sigma.fst) ys)).toList =
    List.reverseAux xs_r.toList (mergeWith f xs { toList := y :: ys, ascend := hascend }).toList
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)
⊢ ∀ {hxs : hingeable xs_r xs},
    (match xs.toList with
        | [] =>
          hinge xs_r { toList := y :: ys, ascend := (_ : List.Ascending (Sigma.relOnFst r) (y :: ys)) }
            (_ : hingeable xs_r { toList := y :: ys, ascend := (_ : List.Ascending (Sigma.relOnFst r) (y :: ys)) })
        | head :: tail =>
          match hmatch : insertWithAux f xs_r xs hxs y.fst y.snd hyxs with
          | { val := (xs_r', xs'), property := h } =>
            mergeWith.loop f xs_r' xs' h ys (_ : List.Ascending (Sigma.relOnFst r) ys)
              (_ : List.predHead ((fun a => boundLeft a xs_r') ∘ Sigma.fst) ys)).toList =
      List.reverseAux xs_r.toList (mergeWith f xs { toList := y :: ys, ascend := hascend }).toList