cases this
case e.e
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)
s : (a : α) → β a → β a → Prop
f : (a : α) → β a → β a → β a
xs✝¹ ys✝¹ zs✝ : KVChain r β
hsf_right : ∀ (a : α) (b₁ b : β a), s a b₁ (f a b b₁)
hsf_stab : ∀ (a : α) (b₁ b₂ b : β a), s a b₁ b₂ → s a (f a b₁ b) (f a b₂ b)
z₁ : α
z₂ : β z₁
zs : KVChain r fun a => β a
hzs : boundLeft z₁ zs
h_ind_zs :
  (fun zs =>
      ∀ (xs ys : KVChain r fun a => β a),
        KVChain.rklex s xs ys →
          KVChain.rklex s (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) xs zs)
            (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) ys zs))
    zs
xs✝ ys✝ : KVChain r fun a => β a
h : KVChain.rklex s xs✝ ys✝
a₁ a₂ : α
b₁ : β a₁
b₂ : β a₂
xs ys : KVChain r fun a => β a
haxs : boundLeft a₁ xs
hays : boundLeft a₂ ys
ha₂a₁ : r a₂ a₁
hz₁a₂ : ¬r z₁ a₂
ha₂z₁ : ¬r a₂ z₁
this : z₁ = a₂
⊢ KVChain.rklex s (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) (KVChain.cons a₁ b₁ xs haxs) (KVChain.cons z₁ z₂ zs hzs))
    (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) (KVChain.cons a₂ b₂ ys hays) (KVChain.cons z₁ z₂ zs hzs))
case e.e.refl
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)
s : (a : α) → β a → β a → Prop
f : (a : α) → β a → β a → β a
xs✝¹ ys✝¹ zs✝ : KVChain r β
hsf_right : ∀ (a : α) (b₁ b : β a), s a b₁ (f a b b₁)
hsf_stab : ∀ (a : α) (b₁ b₂ b : β a), s a b₁ b₂ → s a (f a b₁ b) (f a b₂ b)
z₁ : α
z₂ : β z₁
zs : KVChain r fun a => β a
hzs : boundLeft z₁ zs
h_ind_zs :
  (fun zs =>
      ∀ (xs ys : KVChain r fun a => β a),
        KVChain.rklex s xs ys →
          KVChain.rklex s (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) xs zs)
            (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) ys zs))
    zs
xs✝ ys✝ : KVChain r fun a => β a
h : KVChain.rklex s xs✝ ys✝
a₁ : α
b₁ : β a₁
xs ys : KVChain r fun a => β a
haxs : boundLeft a₁ xs
b₂ : β z₁
hays : boundLeft z₁ ys
ha₂a₁ : r z₁ a₁
hz₁a₂ ha₂z₁ : ¬r z₁ z₁
⊢ KVChain.rklex s (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) (KVChain.cons a₁ b₁ xs haxs) (KVChain.cons z₁ z₂ zs hzs))
    (mergeWith (fun a b₁ b₂ => some (f a b₁ b₂)) (KVChain.cons z₁ b₂ ys hays) (KVChain.cons z₁ z₂ zs hzs))