Qed.

Lemma resource_at_remake_rmap: forall f g lev H Hg, resource_at (proj1_sig (remake_rmap f g lev H Hg)) = f.
refine (fun f g lev H Hg => match proj2_sig (remake_rmap f g lev H Hg) with
| conj _ (conj RESOURCE_AT _) => RESOURCE_AT
end).