Section Update.
Context {X: Const}.
Definition update x v (sigma: fin -> exp X) :=
fun y => if x == y then v else sigma y.

Lemma singlepoint_subst_Vars'_variable x s E:
x ∈ Vars' (update x s var •₊₊ E) -> x ∈ vars s /\ x ∈ Vars' E.