(* TODO: This is obviously true. Ask Xavior to remove the definition list_norepet.*)
Axiom list_norepet_NoDup: forall {A: Type} (l: list A), list_norepet l <-> NoDup l.

Lemma PTree_In_fst_elements {A: Type}: forall (T: PTree.t A) i, In i (map fst (PTree.elements T)) <-> exists a, PTree.get i T = Some a.