intro xs_r xs hxs hascend hyxs
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)}
    {hxsys : List.predHead ((fun a => boundLeft a xs_r) ∘ Sigma.fst) (y :: ys)},
    (mergeWith.loop f xs_r xs hxs (y :: ys) hascend hxsys).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
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)
⊢ (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