Section Completeness.
Fixpoint size (s: exp X) :=
match s with
| var x => 0
| const x => 0
| lambda s => S (size s)
| app s1 s2 => S(size s1 + size s2)
end.

Lemma eqs_size_induction P:
(forall E, (forall E' x, Vars' E' ⊆ Vars' E -> x ∈ Vars' E -> ~ x ∈ Vars' E' -> P E') -> P E) ->
forall E, P E.