(* 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_set_In_fst_elements {A: Type}: forall (T: PTree.t A) i i' a', In i (map fst (PTree.elements T)) -> In i (map fst (PTree.elements (PTree.set i' a' T))).