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)).