let and_intro : ∀ (p q : Bool),
                  p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q :=
      λ (p q : Bool) (H1 : p) (H2 : q) (c : Bool) (H : p → q → c),
        H H1 H2,
    and_elim_left : ∀ (p q : Bool),
                      (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → p :=
      λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
        H p (λ (H1 : p) (H2 : q), H1),
    and_elim_right : ∀ (p q : Bool),
                       (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → q :=
      λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
        H q (λ (H1 : p) (H2 : q), H2)
in and_intro :
  ∀ (p q : Bool),
    p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q
let1.lean:17:20: error: type mismatch at application
  (λ (and_intro : ∀ (p q : Bool), p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) q p),
     let and_elim_left : ∀ (p q : Bool),
                           (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → p :=
           λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
             H p (λ (H1 : p) (H2 : q), H1),
         and_elim_right : ∀ (p q : Bool),
                            (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → q :=
           λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
             H q (λ (H1 : p) (H2 : q), H2)
     in and_intro)
    (λ (p q : Bool) (H1 : p) (H2 : q) (c : Bool) (H : p → q → c), H H1 H2)
expected type:
  ∀ (p q : Bool),
    p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) q p
given type:
  ∀ (p q : Bool),
    p → q → (∀ (c : Bool), (p → q → c) → c)