Definition function_inverse {X Y:Type} (f:X->Y)
(i:invertible f) : { g:Y->X | (forall x:X, g (f x) = x) /\
(forall y:Y, f (g y) = y) }
:=
(constructive_definite_description _
(unique_inverse f i)).

Lemma bijective_impl_invertible: forall {X Y:Type} (f:X->Y),
bijective f -> invertible f.