25 lines
457 B
Text
25 lines
457 B
Text
|
open nat
|
||
|
|
open eq.ops
|
||
|
|
|
||
|
|
inductive even : nat → Type :=
|
||
|
|
even_zero : even zero,
|
||
|
|
even_succ_of_odd : ∀ {a}, odd a → even (succ a)
|
||
|
|
with odd : nat → Type :=
|
||
|
|
odd_succ_of_even : ∀ {a}, even a → odd (succ a)
|
||
|
|
|
||
|
|
example : even 1 → empty :=
|
||
|
|
begin
|
||
|
|
intro He1,
|
||
|
|
cases He1 with (a, Ho0),
|
||
|
|
cases Ho0
|
||
|
|
end
|
||
|
|
|
||
|
|
example : even 3 → empty :=
|
||
|
|
begin
|
||
|
|
intro He3,
|
||
|
|
cases He3 with (a, Ho2),
|
||
|
|
cases Ho2 with (a, He1),
|
||
|
|
cases He1 with (a, Ho0),
|
||
|
|
cases Ho0
|
||
|
|
end
|