theorem ex1 : ∀ {n : Nat} (a b : Nat) (as : Vec Nat n), foo (Vec.cons a as) (Vec.cons b as) id 0 = a + b :=
fun {n} a b as =>
  of_eq_true
    (Eq.trans
      (Eq.trans
        (congrFun'
          (congrArg Eq
            (Eq.trans
              (congrArg (fun x => x (Vec.cons a as) (Vec.cons b as) (fun v w => 0) fun a n a_1 b a_2 v w => a + b)
                (congr (congrArg (foo.match_1 (fun n x x_1 v w => Nat) (n + 1)) (map_id (Vec.cons a as)))
                  (map_id (Vec.cons b as))))
              (foo.match_1.eq_2 (fun n x x_1 v w => Nat) a n as b as (Vec.cons a as) (Vec.cons b as) (fun v w => 0)
                fun a n a_1 b a_2 v w => a + b)))
          (a + b))
        Nat.add_left_cancel_iff._simp_1)
      (eq_self b))
theorem ex2 : ∀ {b : Bool}, b = false → bla b (fun x => x + 1) id 10 = 10 :=
fun {b} h =>
  of_eq_true
    (Eq.trans
      (congrFun'
        (congrArg Eq
          (congrArg
            (fun x =>
              (match (motive := Bool → Nat → Nat) x with
                | true => fun x => x + 1
                | false => id)
                10)
            h))
        10)
      (eq_self 10))