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 decomp_irrefl s t E:
decomp s t = Some E -> forall u v, (u,v) ∈ E -> u <> v.