import logic data.num
open tactic inhabited

namespace foo
inductive sum (A : Type) (B : Type) : Type :=
| inl  : A → sum A B
| inr  : B → sum A B

theorem inl_inhabited {A : Type} (B : Type) (H : inhabited A) : inhabited (sum A B)
:= inhabited.destruct H (λ a, inhabited.mk (sum.inl B a))

theorem inr_inhabited (A : Type) {B : Type} (H : inhabited B) : inhabited (sum A B)
:= inhabited.destruct H (λ b, inhabited.mk (sum.inr A b))

theorem T : inhabited (sum false num) :=
inhabited.mk (sum.inr false 0)

end foo