cases ys using Vector.inductionOn
case h.e'_2
α : Type u_1
r : α → α → Prop
n : ℕ
IH :
  ∀ (x z : α) (ys : Vector α n.succ),
    (x = ys.head ∧ z = ys.last ∧ ∀ (i : Fin n), r (ys.get i.castSucc) (ys.get i.succ)) → Relation.ReflTransGen r x z
x z : α
ys : Vector α (n + 1).succ
x_is_head : x = ys.head
z_is_last : z = ys.last
y : α := ys.tail.head
steprel : r x (ys.get 1)
⊢ y = ys.get 1
case h.e'_2.h_cons
α : Type u_1
r : α → α → Prop
n : ℕ
IH :
  ∀ (x z : α) (ys : Vector α n.succ),
    (x = ys.head ∧ z = ys.last ∧ ∀ (i : Fin n), r (ys.get i.castSucc) (ys.get i.succ)) → Relation.ReflTransGen r x z
x z x✝ : α
w✝ : Vector α (n + 1)
x_is_head : x = (x✝ ::ᵥ w✝).head
z_is_last : z = (x✝ ::ᵥ w✝).last
y : α := (x✝ ::ᵥ w✝).tail.head
steprel : r x ((x✝ ::ᵥ w✝).get 1)
a✝ : (n + 1).succ = n + 1 → HEq (x✝ ::ᵥ w✝) w✝ → y = (x✝ ::ᵥ w✝).get 1
⊢ y = (x✝ ::ᵥ w✝).get 1