Remark var_names_app:
  forall vars1 vars2, var_names (vars1 ++ vars2) = var_names vars1 ++ var_names vars2.Remark filter_app:
  forall (A: Type) (f: A -> bool) l1 l2,
  List.filter f (l1 ++ l2) = List.filter f l1 ++ List.filter f l2.Remark filter_charact:
  forall (A: Type) (f: A -> bool) x l,
  In x (List.filter f l) <-> In x l /\ f x = true.Remark filter_norepet:
  forall (A: Type) (f: A -> bool) l,
  list_norepet l -> list_norepet (List.filter f l).Remark filter_map:
  forall (A B: Type) (f: A -> B) (pa: A -> bool) (pb: B -> bool),
  (forall a, pb (f a) = pa a) ->
  forall l, List.map f (List.filter pa l) = List.filter pb (List.map f l).

Lemma vars_and_temps_properties: forall cenv params vars temps, list_norepet (var_names params ++ var_names vars) -> list_disjoint (var_names params) (var_names temps) -> list_norepet (var_names params) /\ list_norepet (var_names (remove_lifted cenv (params ++ vars))) /\ list_disjoint (var_names params) (var_names (add_lifted cenv vars temps)).