38 lines
1.9 KiB
Text
38 lines
1.9 KiB
Text
let and_intro : ∀ (p q : Prop),
|
|
p → q → (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q :=
|
|
λ (p q : Prop) (H1 : p) (H2 : q) (c : Prop) (H : p → q → c),
|
|
H H1 H2,
|
|
and_elim_left : ∀ (p q : Prop),
|
|
(λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q → p :=
|
|
λ (p q : Prop) (H : (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q),
|
|
H p (λ (H1 : p) (H2 : q), H1),
|
|
and_elim_right : ∀ (p q : Prop),
|
|
(λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q → q :=
|
|
λ (p q : Prop) (H : (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q),
|
|
H q (λ (H1 : p) (H2 : q), H2)
|
|
in and_intro :
|
|
∀ (p q : Prop),
|
|
p → q → (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q
|
|
let1.lean:16:10: error: type mismatch at application
|
|
let and_intro : ∀ (p q : Prop),
|
|
p → q → (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) q p :=
|
|
λ (p q : Prop) (H1 : p) (H2 : q) (c : Prop) (H : p → q → c),
|
|
H H1 H2,
|
|
and_elim_left : ∀ (p q : Prop),
|
|
(λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q → p :=
|
|
λ (p q : Prop) (H : (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q),
|
|
H p (λ (H1 : p) (H2 : q), H1),
|
|
and_elim_right : ∀ (p q : Prop),
|
|
(λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q → q :=
|
|
λ (p q : Prop) (H : (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) p q),
|
|
H q (λ (H1 : p) (H2 : q), H2)
|
|
in and_intro
|
|
term
|
|
λ (p q : Prop) (H1 : p) (H2 : q) (c : Prop) (H : p → q → c),
|
|
H H1 H2
|
|
has type
|
|
∀ (p q : Prop),
|
|
p → q → (∀ (c : Prop), (p → q → c) → c)
|
|
but is expected to have type
|
|
∀ (p q : Prop),
|
|
p → q → (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) q p
|