cases as
α : Type u
r : α → α → Prop
a : α
as : List α
p : α → Prop
hup : ∀ (a b : α), p a → r a b → p b
hchain : Ascending r (a :: as)
hpa : predHead p (a :: as)
⊢ predHead p as
case nil
α : Type u
r : α → α → Prop
a : α
p : α → Prop
hup : ∀ (a b : α), p a → r a b → p b
hchain : Ascending r [a]
hpa : predHead p [a]
⊢ predHead p []

case cons
α : Type u
r : α → α → Prop
a : α
p : α → Prop
hup : ∀ (a b : α), p a → r a b → p b
head✝ : α
tail✝ : List α
hchain : Ascending r (a :: head✝ :: tail✝)
hpa : predHead p (a :: head✝ :: tail✝)
⊢ predHead p (head✝ :: tail✝)