Variant unlift_spec n h i : option 'I_n.-1 -> Type :=
| UnliftSome j of i = lift h j : unlift_spec h i (Some j)
| UnliftNone   of i = h        : unlift_spec h i None.

Lemma unliftP n (h i : 'I_n) : unlift_spec h i (unlift h i).