18 lines
357 B
Text
18 lines
357 B
Text
|
open nat
|
||
|
|
open eq.ops
|
||
|
|
|
||
|
|
inductive even : nat → Prop :=
|
||
|
|
even_zero : even zero,
|
||
|
|
even_succ_of_odd : ∀ {a}, odd a → even (succ a)
|
||
|
|
with odd : nat → Prop :=
|
||
|
|
odd_succ_of_even : ∀ {a}, even a → odd (succ a)
|
||
|
|
|
||
|
|
example : even 1 → false :=
|
||
|
|
begin
|
||
|
|
intro H,
|
||
|
|
cases H with (a, ho),
|
||
|
|
assert (Hz : odd zero),
|
||
|
|
apply (a_eq ▸ ho),
|
||
|
|
inversion Hz
|
||
|
|
end
|