induction as <;> intro a h
α : Type u
r : α → α → Prop
inst✝ : Trans r r r
as : List α
⊢ ∀ {a : α}, Ascending r (a :: as) → forAll (r a) as
case nil
α : Type u
r : α → α → Prop
inst✝ : Trans r r r
a : α
h : Ascending r [a]
⊢ forAll (r a) []

case cons
α : Type u
r : α → α → Prop
inst✝ : Trans r r r
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ {a : α}, Ascending r (a :: tail✝) → forAll (r a) tail✝
a : α
h : Ascending r (a :: head✝ :: tail✝)
⊢ forAll (r a) (head✝ :: tail✝)