24 lines
449 B
Text
24 lines
449 B
Text
import data.nat
|
|
open nat
|
|
|
|
inductive lift .{l} (A : Type.{l}) : Type.{l+1} :=
|
|
up : A → lift A
|
|
|
|
namespace lift
|
|
definition down {A : Type} (a : lift A) : A :=
|
|
lift.rec (λ a, a) a
|
|
|
|
theorem down_up {A : Type} (a : A) : down (up a) = a :=
|
|
rfl
|
|
|
|
|
|
theorem up_down {A : Type} (a' : lift A) : up (down a') = a' :=
|
|
lift.induction_on a' (λ a, rfl)
|
|
|
|
end lift
|
|
|
|
set_option pp.universes true
|
|
check nat
|
|
check lift nat
|
|
open lift
|
|
definition one1 : lift nat := up 1
|