Section Utilities.
Inductive nf: exp X -> Type :=
nfc k s t T:
(forall t, t ∈ T -> nf t) ->
isAtom s ->
t = Lambda k (AppR s T) ->
nf t.

Lemma AppL_largest (P: exp X -> Prop) (s: exp X):
Dec1 P ->
{ S & { t | (forall s, s ∈ S -> P s) /\
s = AppL S t /\
forall (u v: exp X), t = u v -> ~ P u}}.