Section EquivalenceInversions.

Lemma equiv_AppL_elim S1 S2 t1 t2:
AppL S1 t1 ≡ AppL S2 t2 ->
(forall s, s ∈ S1 -> isAtom (head s)) ->
(forall s, s ∈ S2 -> isAtom (head s)) ->
length S1 = length S2 ->
S1 ≡₊ S2 /\ t1 ≡ t2.