16 lines
608 B
Text
16 lines
608 B
Text
|
definition [inline] bool : Type.{1} := Type.{0}
|
||
|
|
definition and (p q : bool) : bool
|
||
|
|
:= ∀ c : bool, (p → q → c) → c
|
||
|
|
infixl `∧` 25 := and
|
||
|
|
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ q
|
||
|
|
:= λ (c : bool) (H : p → q → c), H H1 H2
|
||
|
|
theorem and_elim_left (p q : bool) (H : p ∧ q) : p
|
||
|
|
:= H p (λ (H1 : p) (H2 : q), H1)
|
||
|
|
theorem and_elim_right (p q : bool) (H : p ∧ q) : q
|
||
|
|
:= H q (λ (H1 : p) (H2 : q), H2)
|
||
|
|
theorem and_comm (p q : bool) (H : p ∧ q) : q ∧ p
|
||
|
|
:= have H1 : p, from and_elim_left p q H,
|
||
|
|
have H2 : q, from and_elim_right p q H,
|
||
|
|
show q ∧ p, from and_intro q p H2 H1
|
||
|
|
|